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2/24/2015 Energy, heat, and work in Chemistry

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Chem1 General Chemistry Virtual Textbook → Chemical Energetics → Energy, heat and work

Energy, heat and workAn introduction to chemical energetics and thermodynamics - 1

All chemical changes are accompanied by the absorption or release of heat. The intimate connection between matter andenergy has been a source of wonder and speculation from the most primitive times; it is no accident that fire was consideredone of the four basic elements (along with earth, air, and water) as early as the fifth century BCE. In this unit we will reviewsome of the fundamental concepts of energy and heat and the relation between them. We will begin the study ofthermodynamics, which treats the energetic aspects of change in general, and we will finally apply this specifically tochemical change. Our purpose will be to provide you with the tools to predict the energy changes associated with chemicalprocesses. This will build the groundwork for a more ambitious goal: to predict the direction and extent of change itself.

1 What is Energy?Energy is one of the most fundamental and universal concepts of physical science, but one that is remarkably difficult todefine in way that is meaningful to most people. This perhaps reflects the fact that energy is not a “thing” that exists byitself, but is rather an attribute of matter (and also of electromagnetic radiation) that can manifest itself in different ways. Itcan be observed and measured only indirectly through its effects on matter that acquires, loses, or possesses it.

The concept that we call energy was very slow to develop; it took more than a hundred years just to get people to agree onthe definitions of many of the terms we use to describe energy and the interconversion between its various forms. But evennow, most people have some difficulty in explaining what it is; somehow, the definition we all learned in elementaryscience ("the capacity to do work") seems less than adequate to convey its meaning.

Although the term "energy" was not used in science prior to 1802, it had long beensuggested that certain properties related to the motions of objects exhibit anendurance which is incorporated into the modern concept of "conservation of energy".René Descartes (1596-1650) stated it explicitly:

When God created the world, He "caused some of its parts to push others and totransfer their motions to others..." and thus "He conserves motion".*

In the 17th Century, the great mathematician Gottfried Leibniz (1646-1716)suggested the distinction between vis viva ("live force") and vis mortua ("deadforce"), which later became known as kinetic energy (1829) and potential energy(1853).

Kinetic energy and potential energy

Whatever energy may be, there are basically two kinds.

Kinetic energy is associated with the motion of an object, and its direct consequences are part of everyone's dailyexperience; the faster the ball you catch in your hand, and the heavier it is, the more you feel it. Quantitatively, a body witha mass m and moving at a velocity v possesses the kinetic energy mv2/2.

Problem Example 1A rifle shoots a 4.25 g bullet at a velocity of 965 m s–1. What is its kinetic energy?

Solution: The only additional information you need here is that 1 J = 1 kg m2 s–2:

KE = ½ × (.00425 kg) (965 m s–1)2 = 1980 J

http://plato.stanford.edu/entries/descartes-physics/#4

http://en.wikipedia.org/wiki/Descartes

http://scienceworld.wolfram.com/biography/Leibniz.html



Potential energy is energy a body has by virtue of its location. But there is more: the body must be subject to a"restoring force" of some kind that tends to move it to a location of lower potential energy. Think of an arrow that issubjected to the force from a stretched bowstring; the more tightly the arrow is pulled back against the string, the more potential energy it has.

More generally, the restoring force comes from what we call a force field— a gravitational, electrostaticl, or magnetic field.We observe the consequences of gravitational potential energy all the time, such as when we walk, but seldom give it anythought.

If an object of mass m is raised off the floor to a height h, its potential energy increases by mgh, where g is a proportionalityconstant known as the acceleration of gravity; its value at the earth's surface is 9.8 m s–2.

Problem Example 2Find the change in potential energy of a 2.6 kg textbook that falls from the 66-cm height of a table top onto the floor.

Solution: PE = m g h = (2.6 kg)(9.8 m s–2)(0.66 m) = 16.8 kg m2 s–2 = 16.8 J

Similarly, the potential energy of a particle having an electric charge q depends on its location in an electrostatic field.

"Chemical energy"

Electrostatic potential energy plays a major role in chemistry; the potential energies of electrons in the force field created byatomic nuclei lie at the heart of the chemical behavior of atoms and molecules.

"Chemical energy" usually refers to the energy that is stored in the chemical bonds of molecules. These bonds form whenelectrons are able to respond to the force fields created by two or more atomic nuclei, so they can be regarded asmanifestations of electrostatic potential energy.

In an exothermic chemical reaction, the electrons and nuclei within the reactants undergo rearrangment into productspossessing lower energies, and the difference is released to the environment in the form of heat.



Transitions between potential and kineticenergy are such an intimate part of our dailylives that we hardly give them a thought. Ithappens in walking as the body moves upand down.

Our bodies utilize the chemical energy inglucose to keep us warm and to move ourmuscles. In fact, life itself depends on theconversion of chemical energy to otherforms.

Interconversion of potential and kinetic energy

Energy is conserved: it can neither becreated nor destroyed. So when yougo uphill, your kinetic energy istransformed into potential energy,which gets changed back into kineticenergy as you coast down the otherside. And where did the kineticenergy you expended in peddlinguphill come from? By conversion ofsome of the chemical potential energy in your breakfast cereal.

When drop a book, its potential energy is transformed into kinetic energy. When itstrikes the floor, this transformation is complete. What happens to the energy then? Thekinetic energy that at the moment of impact was formerly situated exclusively in themoving book, now becomes shared between the book and the floor, and in the form ofrandomized thermal motions of the molecular units of which they are made; we canobserve this effect as a rise in temperature.

← Much of the potential energy of falling water can be captured by a water wheel orother device that transforms the kinetic energy of the exit water into kinetic energy. Theoutput of a hydroelectric power is directly proportional to its height above the level ofthe generator turbines in the valley below. At this point, the kinetic energy of the exitwater is transferred to that of the turbine, most of which (up to 90 percent in the largestinstallations) is then converted into electrical energy.

Will the temperature of the water at the bottom of a water fall be greater than that at thetop? James Joule himself predicted that it would be. It has been calculated that at Niagrafalls, that complete conversion of the potential energy of 1 kg of water at the top intokinetic energy when it hits the plunge pool 58 meters below will result in a temperatureincrease of about 0.14 C°. (But there are lots of complications. For example, some of the

water breaks up into tiny droplets as it falls, and water evaporates from droplets quite rapidly, producing a cooling effect.)

Chemical energy can also be converted, at least partially, into electrical energy: this is whathappens in a battery. If a highly exothermic reaction also produces gaseous products, thelatter may expand so rapidly that the result is an explosion — a net conversion of chemicalenergy into kinetic energy (including sound).

Thermal energy

Kinetic energy is associated with motion, but in two different ways. For a macroscopicobject such as a book or a ball, or a parcel of flowing water, it is simply given by ½ mv2.

But as we mentioned above, when an object is dropped onto the floor, or when anexothermic chemical reaction heats surrounding matter, the kinetic energy gets dispersedinto the molecular units in the environment. This "microscopic" form of kinetic energy, unlike that of a speeding bullet, iscompletely random in the kinds of motions it exhibits and in its direction. We refer to this as "thermalized" kinetic energy,or more commonly simply as thermal energy. We observe the effects of this as a rise in the temperature of thesurroundings. The temperature of a body is direct measure of the quantity of thermal energy is contains.

http://en.wikipedia.org/wiki/Muscles

http://en.wikipedia.org/wiki/Walking



Thermal energy is never completely recoverable

Once kinetic energy is thermalized, only a portion of it can be converted back into potential energy. The remainder simplygets dispersed and diluted into the environment, and is effectively lost.

To summarize, then:

Potential energy can be converted entirely into kinetic energy..

Potential energy can also be converted, with varying degrees of efficiency,into electrical energy.

The kinetic energy of macroscopic objects can be transferred between objects (barring the effects of friction).

Once kinetic energy becomes thermalized, only a portion of it can be converted back into either potential energy or beconcentrated back into the kinetic energy of a macroscopic. This limitation, which has nothing to do with technology but is afundamental property of nature, is the subject of the second law of thermodynamics.

A device that is intended to accomplish the partial transformation of thermal energy into organized kinetic energy is known as aheat engine.

2 Energy scales and units

Energy scales are always arbitrary

You might at first think that a book sitting on the table has zero kinetic energy since it is not moving. But if you think aboutit, the earth itself is moving; it is spinning on its axis, it is orbiting the sun, and the sun itself is moving away from the otherstars in the general expansion of the universe. Since these motions are normally of no interest to us, we are free to adopt anarbitrary scale in which the velocity of the book is measured with respect to the table; on this so-called laboratorycoordinate system, the kinetic energy of the book can be considered zero.

We do the same thing with potential energy. If the book is on the table, its potential energy with respect to the surface of thetable will be zero. If we adopt this as our zero of potential energy, and then push the book off the table, its potential energywill be negative after it reaches the floor.

Energy units

Energy is measured in terms of its ability to perform work or to transfer heat. Mechanical work is done when a force fdisplaces an object by a distance d: w = f × d. The basic unit of energy is the joule. One joule is the amount of work done when a force of 1 newton acts over adistance of 1 m; thus 1 J = 1 N-m. The newton is the amount of force required to accelerate a 1-kg mass by 1 m/sec2, so thebasic dimensions of the joule are kg m2 s–2. The other two units in wide use. the calorie and the BTU (British thermal unit)are defined in terms of the heating effect on water. Because of the many forms that energy can take, there are acorrespondingly large number of units in which it can be expressed, a few of which are summarized below.

1 calorie will raise the temperature of 1 g of water by 1 C°. The“dietary” calorie is actually 1 kcal. An average young adultexpends about 1800 kcal per day just to stay alive.

(you should know this definition)

1 cal = 4.184 J

1 BTU (British Thermal Unit) will raise the temperatureof 1 lb of water by 1F°. 1 BTU = 1055 J

The erg is the c.g.s. unit of energy and a very small 1 J = 107 ergs

http://www.chem1.com/acad/webtext/thermeq/TE3.html



one; the work done when a 1-dyne force acts over adistance of 1 cm.

1 erg = 1 d-cm = 1 gcm2 s–2

The electron-volt is even tinier: 1 e-v is the workrequired to move a unit electric charge (1 C) through apotential difference of 1 volt.

1 J = 6.24 × 1018 e-v

The watt is a unit of power, which measures the rate ofenergy flow in J sec–1. Thus the watt-hour is a unit ofenergy. An average human consumes energy at a rateof about 100 watts; the brain alone runs at about 5watts.

1 J = 2.78 × 10–4 watt-hr1 w-h = 3.6 kJ

The liter-atmosphere is a variant of force-displacement work associated with volume changes ingases.

1 L-atm = 101.325 J

The huge quantities of energy consumed by cities andcountries are expressed in quads; the therm is asimilar but smaller unit.

1 quad = 1015 Btu =1.05 × 1018 J

If the object is to obliterate cities or countries withnuclear weapons, the energy unit of choice is the tonof TNT equivalent.

1 ton of TNT = 4.184GJ(by definition)

In terms of fossil fuels, we have barrel-of-oilequivalent, cubic-meter-of-natural gas equivalent, andton-of-coal equivalent.

1 bboe = 6.1 GJ1 cmge = 37-39 mJ1 toce = 29 GJ

3 Heat and workHeat and work are both measured in energy units, so they must both represent energy. How do they differ from eachother, and from just plain “energy” itself?

Heat and work are processes and cannot be stored

In our daily language, we often say that "this object contains a lot of heat", but this kind of talk is a no-no inthermodynamics! It's ok to say that the object is "hot", meaning that its temperature is high.

The term "heat" has a special meaning in thermodynamics: it is a process in which a body (the contents of a teakettle, for example) acquires or loses energy as a direct consequence of its having a different temperqture than itssurroundings (the rest of the world).

Thermal energy can only flow from ahigher temperature to a lower

temperature. It is this flow thatconstitutes "heat".

Use of the term "flow" of heat recalls the 18th-century notion that heat is anactual substance called “caloric” that could flow like a liquid.

Heat is transferred by conduction or radiation

Transfer of thermal energy can be accomplished by bringing two bodies into physical contact (the kettle on top of



the stove, or through an electric heating element inside the kettle). Anothermechanism of thermal energy transfer is by radiation; a hot object willconvey energy to any body in sight of it via electromagnetic radiation in theinfrared part of the spectrum. In many cases, a combination of modes will beactive:

Thus when you place a can of beer in the refrigerator, bothprocesses are operative: the can radiates heat to the cold surfacesaround it, and absorbs it by direct conduction from the ambientair.

So what is work?

Work refers to the transfer of energy some means that does not depend on temperature difference.

Work, likeenergy, cantake variousforms, themostfamiliarbeing mechanical and electrical. Mechanical work arises when an objectmoves a distance Δx against an opposing force f: w = f Δx N-m; 1 N-m =1 J.

Electrical work is done when a body having a charge q moves through a potential difference ΔV.

Work, like heat, exists only when energy is being transferred.

When two bodies are placed in thermal contact and energy flows from thewarmer body to the cooler one,we call the process “heat”. A transfer of energy

to or from a system by any means other than heat is called “work”.

Interconvertability of heat and work

Work can be completely converted into heat (by friction, for example), but heat can only bepartially converted to work. Conversion of heat into work is accomplished by means of a heatengine, the most common example of which is an ordinary gasoline engine. The science ofthermodynamics developed out of the need to understand the limitations of steam-driven heatengines at the beginning of the Industrial Age. A fundamental law of Nature, the Second Law ofThermodynamics, states that the complete conversion of heat into work is impossible. Somethingto think about when you purchase fuel for your car!

What you should be able to doMake sure you thoroughly understand the following essential ideas which have been presented above. It is especiallyimportant that you know the precise meanings of all the green-highlighted terms in the context of this topic.

The potential energy of an object relates to its location, but there is one additional requirement that must be satisfied forpotential energy be present. Explain and give an example.

Distinguish between the nature of kinetic energy that is associated with macroscopic bodies and that is found inmicroscopic objects such as atoms and molecules.

http://www.chem1.com/acad/webtext/thermeq/TE3.html

http://en.wikipedia.org/wiki/Thermodynamics



Describe the meaning and origins of "chemical" energy.

Define the calorie.

Heat and work are both expressed in energy units, but they differ from "plain" energy in a fundamental way. Explain.

... and state the distinction between heat and work.



Concept Map

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2/24/2015 Chemical thermodynamics: the First Law


Chem1 General Chemistry Virtual Textbook → Chemical Energetics → First Law

The First Law of Thermodynamics

Chemical Energy: an introduction to thermodynamics - 2"Energy cannot be created or destroyed"— this fundamental law of nature,more properly known as conservation of energy, is familiar to anyone whohas studied science. Under its more formal name of the First Law ofThermodynamics, it governs all aspects of energy in science andengineering applications. It's special importance in Chemistry arises fromthe fact that virtually all chemical reactions are accompanied by theuptake or release of energy.

This lesson is the first in a series on thermodynamics. Please make sure you havethoroughly mastered this lesson before you go on to any of the others in this unit.

One of the interesting things about thermodynamics is that although it deals with matter, it makes no assumptions aboutthe microscopic nature of that matter. Thermodynamics deals with matter in a macroscopic sense; it would be valid evenif the atomic theory of matter were wrong. This is an important quality, because it means that reasoning based onthermodynamics is unlikely to require alteration as new facts about atomic structure and atomic interactions come tolight.

1 A thermodynamic view of the worldIn thermodynamics, we must be very precise in our use of certain words. The two mostimportant of these are system and surroundings. A thermodynamic system is that partof the world to which we are directing our attention. Everything that is not a part of thesystem constitutes the surroundings. The system and surroundings are separated by aboundary. If our system is one mole of a gas in a container, then the boundary is simplythe inner wall of the container itself. The boundary need not be a physical barrier; forexample, if our system is a factory or a forest, then the boundary can be wherever wewish to define it. We can even focus our attention on the dissolved ions in an aqueoussolution of a salt, leaving the water molecules as part of the surroundings. The singleproperty that the boundary must have is that it be clearly defined, so we can unambiguously say whether a given part ofthe world is in our system or in the surroundings.

If matter is not able to pass across the boundary, then the system is said to be closed; otherwise, it is open.A closed system may still exchange energy with the surroundings unless the system is an isolated one, inwhich case neither matter nor energy can pass across the boundary. The tea in a closed Thermos bottleapproximates a closed system over a short time interval.

Properties and the state of a system

The properties of a system are those quantities such as the pressure, volume, temperature, and its composition, whichare in principle measurable and capable of assuming definite values. There are of course many properties other thanthose mentioned above; the density and thermal conductivity are two examples. However, the pressure, volume, andtemperature have special significance because they determine the values of all the other properties; they are therefore



known as state properties because if their values are known then the system is in a definite state.

Change of state: the meaning of Δ

In dealing with thermodynamics, we must be able to unambiguously define the change in the state of a system when itundergoes some process. This is done by specifying changes in the values of the different state properties using thesymbol Δ (delta) as illustrated here for a change in the volume:

ΔV = Vfinal – Vinitial (1-1)

We can compute similar delta-values for changes in P, V, ni (the number of moles of component i), and the other stateproperties we will meet later.

2 Internal energy and the First LawInternal energy is simply the totality of all forms of kinetic and potential energy of the system. Thermodynamics makesno distinction between these two forms of energy and it does not assume the existence of atoms and molecules. Butsince we are studying thermodynamics in the context of chemistry, we can allow ourselves to depart from “pure”thermodynamics enough to point out that the internal energy is the sum of the kinetic energy of motion of themolecules, and the potential energy represented by the chemical bonds between the atoms and any other intermolecularforces that may be operative.

How can we know how much internal energy a system possesses? Theanswer is that we cannot, at least not on an absolute basis; all scales of energy are arbitrary. The best we can do ismeasure changes in energy. However, we are perfectly free to define zero energy as the energy of the system in somearbitrary reference state, and then say that the internal energy of the system in any other state is the difference betweenthe energies of the system in these two different states.

The First Law

This law is one of the most fundamental principles of the physical world. Also known as the Law of Conservation ofEnergy, it states that energy can not be created or destroyed; it can only be redistributed or changed from one form toanother.

A way of expressing this law that is generally more useful in Chemistry is that any change in the internal energy of asystem is given by the sum of the heat q that flows across its boundaries and the work w done on the system by thesurroundings.

important ⇒ ΔU = q + w (2-1)must know this!

This says that there are two kinds of processes, heat and work, that can lead to a change in the internal energy of asystem. Since both heat and work can be measured and quantified, this is the same as saying that any change in theenergy of a system must result in a corresponding change in the energy of the world outside the system- in other words,energy cannot be created or destroyed.

There is an important sign convention for heat and work that you are expected toknow. If heat flows into a system or the surroundings to do work on it, the internalenergy increases and the sign of q or w is positive. Conversely, heat flow out of thesystem or work done by the system will be at the expense of the internal energy, andwill therefore be negative. (Note that this is the opposite of the sign convention thatwas commonly used in much of the pre-1970 literature.)

The full significance of Eq. 1 cannot be grasped without understanding that



U is a state function. This means that a given change in internal energy ΔU can follow an infinite variety of pathwayscorresponding to all the possible combinations of q and w that can add up to a given value of ΔU.

As a simple example of how this principle can simplify our understanding of change, consider twoidentical containers of water initially at the same temperature. We place a flame under one until itstemperature has risen by 1°C. The water in the other container is stirred vigorously until its temperaturehas increased by the same amount. There is now no physical test by which you could determine whichsample of water was warmed by performing work on it, by allowing heat to flow into it, or by somecombination of the two processes. In other words, there is no basis for saying that one sample of waternow contains more “work”, and the other more “heat”. The only thing we can know for certain is that bothsamples have undergone identical increases in internal energy, and we can determine the value of simplyby measuring the increase in the temperature of the water.

There seems to be no end of schemes perpetrated by cranks, kooks (and perhapseven a few crooks!) to foist off onto the science-naïve public, crackpot schemes toobtain "free energy" from various sources, usually in blissful ignorance of the FirstLaw. Schemes for using water as a fuel are especially popular, as can be seen onthe many Web sites promoting devices that electrolytically decompose water tocreate H2/O2 mixtures that are given exotic names such as "Aquafuel" and"Brown's Gas" or "HHO" .) These hucksters fail to mention that somebody has topay for the electricity used to operate these goofy devices!

3 Pressure-volume workThe kind of work most frequently associated with chemical change occurs when the volume of the system changesowing to the disappearance or formation of gaseous substances. This is sometimes called expansion work or PV-work,and it can most easily be understood by reference to the simplest form of matter we can deal with, the hypothetical idealgas.

The figure shows a quantity of gas confined in a cylinder by means of a moveable piston. Weights placed on top of thepiston exert a force f over the cross-section area A, producing a pressure P = f / A which is exactly countered by thepressure of the gas, so that the piston remains stationary. Now suppose that we heat the gas slightly; according toCharles’ law, this will cause the gas to expand, so the piston will be forced upward by a distanceΔx. Since this motion is opposed by the force x, a quantity of work f Δx will be done by the gas on the piston. Byconvention, work done by the system (in this case, the gas) on the surroundings is negative, so the work is given by

w = – f Δx (3-1)

http://bingofuel.online.fr/bingofuel/html/aquagen.htm

http://www.brownsgas.ws/



When dealing with a gas, it is convenient to think in terms of the more relevant quantities pressure and volume ratherthan force and distance. We can accomplish this by multiplying the second term by A/A which of course leaves itunchanged:

(3-2)

By grouping the terms differently, but still not changing anything, we obtain

(3-3)

Since pressure is force per unit area and the product of the length A and the area has the dimensions of volume, thisexpression becomes

w = –P ΔV (3-4)

It is important to note that although P and V are state functions, the work isnot (that's why we denote it by a lower-case w.) As is shown farther below, the quantity of work done will depend onwhether the same net volume change is realized in a single step (by setting the external pressure to the final pressure P),or in multiple stages by adjusting the restraining pressure on the gas to successively smaller values approaching the finalvalue of P.

Problem Example 1Find the amount of work done on the surroundings when 1 liter of an ideal gas, initially at a pressure of 10 atm, isallowed to expand at constant temperature to 10 liters by a) reducing the external pressure to 1 atm in a single step, b)reducing P first to 5 atm, and then to 1 atm, c) allowing the gas to expand into an evacuated space so its total volume is10 liters.

Solution: First, note that ΔV, which is a state function, is the same for each path:V2 = (10/1) × (1 L) = 10 L, so ΔV = 9 L.

For path (a), w = –(1 atm)× (9 L) = –9 L-atm.

For path (b), the work is calculated for each stage separately:w = –(5 atm) × (2–1 L) – (1 atm) × (10–2 L) = –13 L-atm

For path (c) the process would be carried out by removing all weights from the piston in Fig. 1 so that the gas expands to10 L against zero external pressure. In this case w = (0 atm) × 9 L = 0; that is, no work is done because there is no forceto oppose the expansion.

Adiabatic and isothermal processes

When a gas expands, it does work on the surroundings; compression of a gas to a smaller volume similarly requires thatthe surroundings perform work on the gas. If the gas is thermally isolated from the surroundings, then the process is saidto occur adiabatically. In an adiabatic change, q = 0, so the First Law becomes ΔU = 0 + w. Since the temperature of thegas changes with its internal energy, it follows that adiabatic compression of a gas will cause it to warm up, whileadiabatic expansion will result in cooling.

In contrast to this, consider a gas that is allowed to slowly excape from a container immersed in a constant-temperaturebath. As the gas expands, it does work on the surroundings and therefore tends to cool, but the thermal gradient thatresults causes heat to pass into the gas from the surroundings to exactly compensate for this change. This is called anisothermal expansion. In an isothermal process the internal energy remains constant and we can write the First Law as0 = q + w, or q = –w, illustrating that the heat flow and work done exactly balance each other.

Because no thermal insulation is perfect, truly adiabatic processes do not occur. However, heat flow does take time, so acompression or expansion that occurs more rapidly than thermal equilibration can be considred adiabatic for practicalpurposes.



If you have ever used a hand pump to inflate a bicycle tire, you may have noticed thatthe bottom of the pump barrel can get quite warm. Although a small part of thiswarming may be due to friction, it is mostly a result of the work you (thesurroundings) are doing on the system (the gas.)

Adiabatic expansion and contractions are especially important in understanding the behavior ofthe atmosphere. Although we commonly think of the atmosphere as homogeneous, it is reallynot, due largely to uneven heating and cooling over localized areas. Because mixing and heattransfer between adjoining parcels of air does not occur rapidly, many common atmosphericphenomena can be considered at least quasi-adiabatic. A more detailed exposition of this topic is given in Part 5 of thisunit.

Reversible processes

From Problem Example 1 we see that when a gas expands into a vacuum (Pexternal = 0) the work done is zero. This isthe minimum work the gas can do; what is the maximum work the gas can perform on the surroundings? To answer this,notice that more work is done when the process is carried out in two stages than in one stage; a simple calculation willshow that even more work can be obtained by increasing the number of stages— that is, by allowing the gas to expandagainst a series of successively lower external pressures. In order to extract the maximum possible work from theprocess, the expansion would have to be carried out in an infinite sequence of infinitessimal steps. Each step yields anincrement of work P ΔV which can be expressed as (RT/V) dV and integrated:

(3-5)

Although such a path (which corresponds to what is called a reversible process) cannot be realized in practice, it can beapproximated as closely as desired.

http://www.chem1.com/acad/webtext/energetics/CE-5.html#TW



Bear in mind why q is so important:the heat flow into or out of thesystem is directly measurable. ΔU,being "internal" to the system, is notdirectly observable.

Even though no real process can take place reversibly (it would take an infinitely long time!), reversible processes playan essential role in thermodynamics. The main reason for this is that qrev and wrev are state functions which areimportant and are easily calculated. Moreover, many real processes take place sufficiently gradually that they can betreated as approximately reversible processes for easier calculation.

These plots illustrate the effects ofvarious degrees of reversibility on theamount of work done when a gasexpands, and the work that must bedone in order to restore it to its initialstate by recompressing it. The work,in each case, is proportional to theshaded area on the plot.

Each expansion-compression cycleleaves the gas unchanged, but in allbut the one in the bottom row, thesurroundings are forever altered,having expended more work incompressing the gas than wasperformed on it when the gasexpanted.

Only when the processes are carriedout in an infinite number of steps willthe system and the surroundings berestored to their initial states— this isthe meaning of thermodynamicreversibility.

4 Heat changes at constant pressure: the EnthalpyFor a chemical reaction that performs no work on the surroundings, the heat absorbed is the same as the change ininternal energy: q = ΔU. But many chemical processes do involve work in one form or another:

If the total volume of the reaction products exceeds that of the reactants, then the process performs work on the surroundingsin the amount PΔV, in which P is the pressure exerted by the surroundings (usually the atmosphere) on the system.

A reaction that drives an electrical current through an external circuit performs electrical work on the surroundings.

For an isothermal process, pressure-volume work affects the heat q

We will consider only pressure-volume work in this lesson. If the process takes place at a constant pressure, then thework is given by PΔV and the change in internal energy will be

ΔU = q – PΔV (4-1)

Thus the amount of heat that passes between the system and thesurroundings is given by

q = ΔU + PΔV (4-2)

This means that if an exothermic reaction is accompanied by a net increase involume under conditons of constant pressure, some additional heat additional to ΔU must be absorbed in order to supplythe energy expended as work done on the surroundings if the temperature is to remain unchanged (isothermal process.)

For most practical purposes, changes in the volume of the system are only significant if the reaction is accompanied bya difference in the moles of gaseous reactants and products.



Remember the sign convention: a flow ofheat or performance of work that suppliesenergy is positive; if it consumes energy,it is negative. Thus work performed bythe surroundings diminishes the energyof the surroundings (wsurr < 0) andincreases the energy of the system (wsys> 0).

For example, in the reaction H2(g) + ½ O2(g) → H2O(g), the total volume of the system decreases from that correpondingto 1.5 moles of reactants to 1 mole of products. If we define this quantity as Δng , then for this reaction,

Δng  = (1 – 1.5) mol = –0.5 mol

This corresponds to a net contraction (negative expansion) of the system, meaning that the surroundings perform workon the system. The molar volume of an ideal gas at 25° C and 1 atm is

(298/273) × (22.4 L mol–1) = 24.5 L mol–1

and the work done (by the surroundings on the system) is

(1 atm) (–0.5 mol)(24.5 L mol–1) = –12.2 L-atm.

Thus the energy of the system itself is +12.2 L-atm.

Using the conversion factor 1 J = 101.3 J, and bearing in mind thatwork performed on the system supplies energy to the system, thiswork increased the energy of the system by

(101.3 J/L-atm)(12.2 L-atm) = 1136 J = 1.24 kJ

Problem Example 2The above reaction H2(g) + ½ O2(g) → H2O(g) is carried out at a constant pressure of 1 atm and a constant temperature of25° C. What quantity of heat q will cross the system boundary (and in which direction?) For this reaction, the change ininternal energy is ΔU = –240.59 kJ/mol.

Solution: The reaction itself (that is, the re-arrangement of the atoms from reactants to products releases q = –240.59 kJof heat. The work performed by the surroundings supplies an additional energy of w = 1.24 kJ to the system. In order tomaintain the constant 25° temperature, an equivalent quantity of heat must be released: q = (–240.59 + 1.24) k J = –241.83 kJ

About "constant" pressure and temperature processes

This terminology can be somewhat misleading unless you bear in mind that theconditions ΔP and ΔT refer to the differences between the inital and final states ofthe system — that is, before and after the reaction.

During the time the reaction is in progress, the temperature of the mixture will riseor fall, depending on whether the process is exothermic or endothermic. Butbecause ΔT is a state function, its value is independent of what happens "inbetween" the initial state (reactants) and final state (products). The same is trueof ΔV.

Enthalpy hides work and saves it too!

Because most chemical changes we deal with take place at constant pressure, it would be tedious to have to explicitlydeal with the pressure-volume work details that were described above. Fortunately, chemists have found a way aroundthis; they have simply defined a new state function that incorporates and thus hides within itself any terms relating toincidental kinds of work (P-V, electrical, etc.)

Since both ΔP and ΔV in Eq 4-2 are state functions, then qP , the heat thatis absorbed or released when a process takes place at constant pressure, must also be a state function and is known asthe enthalpy change ΔH.

important ⇒ ΔH ≡ qP = ΔU + PΔV (4-3)



Since most processes that occur in the laboratory, on the surface of the earth, and in organisms do so undera constant pressure of one atmosphere, Eq 4-3 is the form of the First Law that is of greatest interest tomost of us most of the time.

Problem Example 3Hydrogen chloride gas readily dissolves in water, releasing 75.3 kJ/mol of heat in the process. If one mole of HCl at 298K and 1 atm pressure occupies 24.5 liters, find ΔU for the system when one mole of HCl dissolves in water under theseconditions.

Solution: In this process the volume of liquid remains practically unchanged, so ΔV = –24.5 L. The work done is

w = –PΔV = –(1 atm)(–24.5 L) = 24.6 L-atm

(The work is positive because it is being done on the system as its volume decreases due to the dissolution of the gas

into the much smaller volume of the solution.) Using the conversion factor 1 L-atm = 101.33 J mol–1 and substituting inEq. 3 (above) we obtain

ΔU= q +PΔV = –(75300 J) + [101.33 J/L-atm) × (24.5 L-atm)] = –72.82 kJ

In other words, if the gaseous HCl could dissolve without volume change, the heat released by the process (75.3 kJ)would cause the system’s internal energy to diminish by 75.3 kJ. But the disappearance of the gaseous phase reduces thevolume of the system. This is equivalent to compression of the system by the pressure of the atmosphere performingwork on it and consuming part of the energy that would otherwise be liberated, reducing the net value of ΔU to –72.82kJ.

5 The Heat CapacityFor systems in which no change in composition (chemical reaction) occurs, things are even simpler: to a verygood approximation, the enthalpy depends only on the temperature. This means that the temperature of such asystem can serve as a direct measure of its enthalpy. The functional relation between the internal energy and thetemperature is given by the heat capacity measured at constant pressure:

(5-1)

(or ΔH/ΔT if you don’t care for calculus!) An analogous quantity relates the heat capacity at constant volume tothe internal energy:

(5-2)

The difference between CP and CV is of importance only when the volume of the system changessignificantly— that is, when different numbers of moles of gases appear on either side of thechemical equation. For reactions involving only liquids and solids, Cp and Cv are for all practicalpurposes identical.

Heat capacity can be expressed in joules or calories permole per degree (molar heat capacity), or in joules or calories per gram per degree; the latter is calledthe specific heat capacity or just the specific heat.

The greater the heat capacity of a substance, the smallerwill be the effect of a given absorption or loss of heat on

its temperature.



What you should be able to doMake sure you thoroughly understand the following essential concepts that have been presented above.

Define: system, surroundings, state properties, change of state (how the latter is calculated).

Write out the equation that defines the First Law, and explain its physical meaning.

Describe the meaning of a pathway in thermodynamics, and how it relates to state functions.

Comment on the meaning of pressure-volume work: how is it calculated? What kinds of chemical reactions involve P-Vwork?

Define isothermal and adiabatic processes, and give examples of each.

Using the expansion of a gas as an example, state the fundamental distinction between reversible and irreversible changes interms of the system + surroundings.

Explain how enthalpy change relates to internal energy, and how it can be observed experimentally.

Define heat capacity; explain its physical significance, and why there is a difference between Cp and Cv.

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2/24/2015 Chemical energy and enthalpy


Chem1 General Chemistry Virtual Textbook→ Chemical Energetics →Chemical energy

Molecules as energy carriers and converters

Chemical Energetics and thermodynamics - 3All molecules at temperatures above absolue zero possessthermal energy— the randomized kinetic energy associatedwith the various motions the molecules as a whole, and also theatoms within them, can undergo. Polyatomic molecules alsopossess potential energy in the form of chemical bonds.Molecules are thus both vehicles for storing and transportingenergy, and the means of converting it from one form toanother when the formation, breaking, or rearrangement of thechemical bonds within them is accompanied by the uptake orrelease of heat.

1 - Chemical energy: potential + kinetic

When you buy a liter of gasoline for your car, a cubic meter of natural gas to heatyour home, or a small battery for your flashlight, you are purchasing energy in achemical form. In each case, some kind of a chemical change will have to occurbefore this energy can be released and utilized: the fuel must be burned in thepresence of oxygen, or the two poles of the battery must be connected through anexternal circuit (thereby initiating a chemical reaction inside the battery.) Andeventually, when each of these reactions is complete, our source of energy will beexhausted; the fuel will be used up, or the battery will be “dead”.

Where did the energy go? It could have gone to raise the temperature of theproducts, to perform work in expanding any gaseous products or to push electronsthrough a circuit. The remainder will reside in the chemical potential energyassociated with the products of the reaction.

Chemical substances are made of atoms, or more generally, of positively charged nuclei surrounded by negativelycharged electrons. A molecule such as dihydrogen, H2, is held together by electrostatic attractions mediated by theelectrons shared between the two nuclei. The total potential energy of the molecule is the sum of the repulsions betweenlike charges and the attractions between electrons and nuclei:

PEtotal = PEelectron-electron + PEnucleus-nucleus + PEnucleus-electron (1-1)

In other words, the potential energy of a molecule depends on the time-averaged relative locations of its constituentnuclei and electrons. This dependence is expressed by the familiar potential energy curve which serves as an importantdescription of the chemical bond between two atoms.

http://www.chem1.com/acad/webtext/chembond/cb01.html#POT



Translation refers to movement ofan object as a complete unit.Translational motions of molecules insolids or liquids are restricted to veryshort distances comparable to thedimensions of the moleculesthemselves, whereas in gases themolecules typically travel hundreds ofmolecular diameters betweencollisions.

In gaseous hydrogen, for example, the molecules will be moving freely fromone location to another; this is called translational motion, and the moleculestherefore possess translational kinetic energy KEtrans = mv2/2, in which v stands for the average velocity of the molecules; you may recall from yourstudy of gases that v, and therefore KEtrans, depends on the temperature.

Kinetic energy of vibration and rotation

In addition to translation, molecules composed of two or more atoms canpossess other kinds of motion. Because a chemical bond acts as a kind of spring, the two atoms in H2 will have a naturalvibrational frequency. In more complicated molecules, many different modes of vibration become possible, and theseall contribute a vibrational term KEvib to the total kinetic energy. Finally, a molecule can undergo rotational motionswhich give rise to a third term KErot. Thus the total kinetic energy of a molecule is the sum

KEtotal = KEtrans + KEvib + KErot (1-2)

The total energy of the molecule (its internal energy U) is just the sum

U = KEtotal + PEtotal (1-3)

Although this formula is simple and straightforward, it cannot take us very far in understanding and predicting thebehavior of even one molecule, let alone a large number of them. The reason, of course, is the chaotic and unpredictablenature of molecular motion. Fortunately, the behavior of a large collection of molecules, like that of a large population ofpeople, can be described by statistical methods.



monatomic diatomic triatomic

He 20.5 CO 29.3 H2O 33.5

Ne 20.5 N2 29.5 D2O 34.3

Ar 20.5 F2 31.4 CO2 37.2

Kr 20.5 Cl2 33.9 CS2 45.6

Table 1Molar heat capacities (kJ mol–1 K–1) of some gaseous substances at

constant pressure.

2 - How molecules take up thermal energyAs noted above, the heat capacity of a substance is a measure of how sensitively its temperature is affected by a changein heat content; the greater the heat capacity, the less effect a given flow of heat q will have on the temperature.

We also pointed out that temperature is a measure of the average kinetic energy due to translational motions ofmolecules. If vibrational or rotational motions are also active, these will also accept thermal energy and reduce theamount that goes into translational motions. Because the temperature depends only on the latter, the effect of the otherkinds of motions will be to Treduce the dependence of the internal energy on the temperature, thus raising the heatcapacity of a substance.

Molecular complexity and heat capacity

Whereas monatomic molecules can only possess translationalthermal energy, two additional kinds of motions become possiblein polyatomic molecules.

A linear molecule has an axis that defines two perpendiculardirections in which rotations can occur; each represents anadditional degree of freedom, so the two together contribute a totalof ½ R to the heat capacity.

Vibrational and rotational motions are not possible for monatomicspecies such as the noble gas elements, so these substances havethe lowest heat capacities. Moreover, as you can see in the leftmostcolumn of Table 1, their heat capacities are all the same. This

reflects the fact that translational motions are the same for all particles; all such motions can be resolved into threedirections in space, each contributing one degree of freedom to the molecule and ½ R to its heat capacity. (R is the gasconstant, 8.314 J K–1).

For a non-linear molecule, rotations are possible along all three directions of space, so these molecules have a rotationalheat capacity of 3/2 R. Finally, the individual atoms within a molecule can move relative to each other, producing avibrational motion. A molecule consisting of N atoms can vibrate in 3N –6 different ways or modes. Each vibrationalmode contributes R (rather than ½ R) to the total heat capacity. (These results come from advanced mechanics and willnot be proven here.)

type of motion →

translation rotation vibration

monatomic 3/2R 0 0

diatomic 3/2 R R R

polyatomic 3/2 R 3/2 R 3N – 6

separation betweenadjacent levels,kJ mol–1.

6.0 × 10–17 J(O2)

373 J (HCl) 373 J (HCl)

Table 2: Contribution of molecular motions to heat capacity



Monatomic molecules have the smallest heat capacities

Now we are in a position to understand why more complicated molecules have higher heat capacities. The total kineticenergy of a molecule is the sum of those due to the various kinds of motions:

KEtotal = KEtrans + KErot + KEvib (2-1)

When a monatomic gas absorbs heat, all of the energy ends up in translational motion, and thus goes to increase itstemperature. In a polyatomic gas, by contrast, the absorbed energy is partitioned among the other kinds of motions; sinceonly the translational motions contribute to the temperature, the temperature rise is smaller, and thus the heat capacity islarger.

There is one very significant complication, however: classical mechanics predicts that the energy is always partitionedequally between all degrees of freedom. Experiments, however, show that this is observed only at quite hightemperatures. The reason is that these motions are all quantized. This means that only certain increments of energy arepossible for each mode of motion, and unless a certain minimum amount of energy is available, a given mode will not beactive at all and will contribute nothing to the heat capacity.

Translational energy levels are effectively a continuum

The shading indicates the average thermal energy available att 300 K.Only those levels within this rage will have significant occupancy asindicated by the thickness of the lines in the two rightmost columns. At300K, only the lowest vibrational state and the first few rotational stateswill be active. Most of the thermal energy will be confined to thetranslational levels whose minute spacing (10–17 J) causes them to appearas a continuum.

← Heatcapacity ofdihydrogenas a function of temperature. This plot istypical of those for other polyatomic molecules, and showsthe practical consequences of the spacings of the variousforms of thermal energy. Thus translational motions areavailable at virtually all temperatures, but contributions toheat acapacity by rotational or vibrational motions canonly develop at temperatures sufficiently large to excitethese motions.

It turns out that translational energy levels are spaced soclosely that they these motions are active almost down to

absolute zero, so all gases possess a heat capacity of at least 3/2 R at all temperatures. Rotational motions do not getstarted until intermediate temperatures, typically 300-500K, so within this range heat capacities begin to increase withtemperature. Finally, at very high temperatures, vibrations begin to make a significant contribution to the heat capacity

The strong intermolecular forces of liquids and many solids allow heat to be channeled into vibrational motionsinvolving more than a single molecule, further increasing heat capacities. One of the well known “anomalous” propertiesof liquid water is its high heat capacity (75 J mol–1 K–1) due to intermolecular hydrogen bonding, which is directlyresponsible for the moderating influence of large bodies of water on coastal climates.



Enthalpy was introduced in the previouslesson on the First Law. If you are notsure of the difference between theenthalpy H and internal energy U, pleasereview this lesson before proceeding.

Heat capacities of metals

Metallic solids are a rather special case. In metals, the atoms oscillate about their equilibrium positions in a ratheruniform way which is essentially the same for all metals, so they should all have about the same heat capacity. That thisis indeed the case is embodied in the Law of Dulong and Petit. In the 19th century these workers discovered that themolar heat capacities of all the metallic elements they studied were around to 25 J mol–1 K–1, which is close to whatclassical physics predicts for crystalline metals. This observation played an important role in characterizing newelements, for it provided a means of estimating their molar masses by a simple heat capacity measurement.

3 Standard enthalpy changeUnder the special conditions in which the pressure is 1 atm and the reactants andproducts are at a temperature of 298 K,ΔH becomes the standard enthalpy change ΔH°.

Chemists usually refer to the "enthalpy change of a reaction" as simply the"enthalpy of reaction", or even more simply as the "heat of reaction". But studentsare allowed to employ this latter shortcut only if they are able to prove that theyknow the meaning of enthalpy.

Since most changes that occur in the laboratory, on the surface of the earth, and inorganisms are subjected to an approximately constant pressure of "oneatmosphere" and reasonably salubrious temperatures, most reaction heats quotedin the literature refer to ΔH°. But the high pressures and extreme temperaturesfrequently encountered by chemical engineers, geochemists, and practicioners ofchemical oceanography, often preclude the convenience of the "standard" values.

The rearrangement of atoms that occurs in a chemical reaction is virtually always accompanied by the liberation orabsorption of heat. If the purpose of the reaction is to serve as a source of heat, such as in the combustion of a fuel, thenthese heat effects are of direct and obvious interest. We will soon see, however, that a study of the energetics of chemicalreactions in general can lead us to a deeper understanding of chemical equilibrium and the basis of chemical changeitself.

In chemical thermodynamics, we define the zero of the enthalpy andinternal energy as that of the elements as they exist in their stable

forms at 298K and 1 atm pressure.

Thus the enthalpies H of Xe(g), O2(g) and C(diamond) are all zero, as are those of H2 and Cl2 in the reaction

H2(g) + Cl2(g) → 2 HCl(g)

The enthalpy of two moles of HCl is smaller than that of the reactants, so the difference is released as heat. Such areaction is said to be exothermic. The reverse of this reaction would absorb the same quantity of heat from thesurroundings and be endothermic.

In comparing the internal energies and enthalpies of different substances as we have been doing here, it is important tocompare equal numbers of moles, because energy is an extensive property of matter. However, heats of reaction arecommonly expressed on a molar basis and treated as intensive properties.



Changes in enthalpy and internal energy

We can characterize any chemical reaction by the change in the internal energy or enthalpy:

ΔH = Hfinal – Hinitial (3-1)

The significance of this can hardly be exaggerated because ΔH, being a state function, is entirely independent of how thesystem gets from the initial state to the final state. In other words, the value of ΔH or ΔU for a given change in state isindependent of the pathway of the process.

Consider, for example, the oxidation of a lump of sugar to carbon dioxide and water:

C12H22O11 + 12 O2(g) → 12 CO2(g) + 11 H2O(l)

This process can be carried out in many ways, for example by burning the sugar in air, or by eating the sugar and lettingyour body carry out the oxidation. Although the mechanisms of the transformation are completely different for these twopathways, the overall change in the enthalpy of the system (the atoms of carbon, hydrogen and oxygen that wereoriginally in the sugar) will be identical, and can be calculated simply by looking up the standard enthalpies of thereactants and products and calculating the difference

ΔH = [12 × H(CO2)] + [11 × H(H2O)] – H(C12H22O11) = –5606 kJ

The same quantity of heat is released whether the sugar is burnt in the air or oxidized in a series of enzyme-catalyzedsteps in your body.

Enthalpy increases with temperature

When the temperature of a substance is raised, it absorbs heatThe enthalpy of a system increases with the temperature bythe amount ΔH = Cp ΔT. The defining relation

ΔH = ΔU + P ΔV (3-4 in previous lesson)

tells us that this change is dominated by the internal energy, subject to a slight correction for the work associated withvolume change. Heating a substance causes it to expand, making ΔV positive and causing the enthalpy to increaseslightly more than the internal energy. Physically, what this means is that if the temperature is increased while holdingthe pressure constant, some extra energy must be expended to push back the external atmosphere while the systemexpands. The difference between the dependence of U and H on temperature is only really significant for gases, since thecoefficients of thermal expansion of liquids and solids are very small.

http://www.chem1.com/acad/webtext/energetics/CE-4.html#SEC2



Enthalpy of phase changes

A plot of the enthalpy of a system as a function of its temperature is called an enthalpy diagram. The slope of the line isgiven by Cp. The enthalpy diagram of a pure substance such as water shows that this plot is not uniform, but isinterrupted by sharp breaks at which the value of Cp is apparently infinite, meaning that the substance can absorb or loseheat without undergoing any change in temperature at all. This, of course, is exactly what happens when a substanceundergoes a phase change; you already know that the temperature the water boiling in a kettle can never exceed 100until all the liquid has evaporated, at which point the temperature of the steam will rise as more heat flows into thesystem.

A plot of the enthalpy of carbontetrachloride as a function of itstemperature provides a concise view of itsthermal behavior. The slope of the line is given by theheat capacity Cp. All H-vs.-C plots show sharp breaks atwhich the value of Cp is apparently infinite, meaning thatthe substance can absorb or lose heat without undergoingany change in temperature at all. This, of course, isexactly what happens when a substance undergoes aphase change; you already know that the temperature ofthe water boiling in a kettle can never exceed 100°C untilall the liquid has evaporated, at which point thetemperature (of the steam) will rise as more heat flowsinto the system.

The lowest-temperature discontinuity on the CCl4diagram corresponds to a solid-solid phase transitionassociated with a rearrangement of molecules in the

crystalline solid.

What you should be able to doMake sure you thoroughly understand the following essential concepts that have been presented above.

Describe the sources of potential energy and kinetic energy contained in a molecule.

Describe the nature of "thermal" energy, and how it relates to other forms of kinetic energy and to temperature.

Explain why the simplest molecules (monatomic and diatomic) have smaller heat capacities than polyatomic molecules.

Similarly, explain why the dependence of heat capacity on the temperature is different for monatomic and polyatomiocmolecules.



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