Chapter 18: Reaction Rates and Equilibrium

Section 18.1: Rates of Reaction

The speed of chemical reactionsChemical reactions take place at a variety of different speeds

How do you calculate speed? Speed is the distance traveled over a period of time.

Example of calculating average speedWhen Dr Collings did the Lima marathon last year (42 km), he completed the race in 4 hrs and 13 minutes. He passed the first quarter mark after 57 minutes, the halfway mark after 1hr 55 minutes, the three quarter mark after 3 hours.

What was his average speed throughout the race?Which was faster, his average speed in the first half or the second half?Which quarter of the race was he fastest in?

What is the relationship between Speed and rate?

A rate is a measure of how something changes in a given amount of time

Speed is an example of a rate

In a chemical reaction, the reaction rate is expressed as the change in the amount of a reactant or product over time

Reaction progressAs a reaction progresses, the number of reactants decreases and the number of products increases

Collision Theory● Collision theory

relates kinetic energy and reaction rate

● When atoms, ions or molecules collide

● When the particles have enough kinetic energy, they can react and form products

● When they do not have enough energy, they do not react

Activation energy● This is the minimum amount of energy that colliding particles need to react● A barrier the reactants must cross before the product can form● Activated complex - an unstable arrangement of atoms that exists at the top

of the activation-energy barrier

What can affect the rate of a reaction?● Temperature - Raising the

temperature speeds up the rate of reaction, lowering the temperature slows it down - why?

● At higher temperature particles move faster and collide more often

○ More have enough energy to get over the activation energy barrier

Reaction rates continued…..

Concentration - More particles in a confined space leads to increased numbers of collisions, and a higher reaction rate

Effect of particle size

The greater the surface area, the faster the reaction rate

A higher surface area maximises the rate at which collisions take place at the surface of reactants

This can be done through either reducing particle size or dissolving reactants

What caused this explosion?

What is a catalyst?A catalyst increases the rate of reaction without being used up in the reaction - by lowering the activation energy

This is often more effective than increasing temperature

Enzymes are natural catalysts found in the human body

Inhibitors block the actions of the catalyst

The progress of Chemical Reactions

Section 18.2

Rate lawsThe rate of a reaction depends in part on the concentrations of the reactants.Suppose there were a reaction with only one reactant and one product.A -> B

The rate at which A forms B can be expressed as the change in A (ΔA) with time

Rate laws continuedThe rate of disappearance of A is proportional to the concentration of A.

The proportionality can be expressed as the concentration of A, [A], multiplied by a constant, k.

This equation is a rate law, an expression for the rate of a reaction in terms of the concentration of the reactants.

What about if there is more than 1 reactant?The specific rate constant (k) for a reaction is a proportionality constant relating the concentrations of reactants to the rate of the reaction.

aA + bB -> cC + dD

For the reaction of A with B, the rate of reaction is dependent on the concentrations of both A and B.

What does this graph show?

The specific rate constant● In the rate law, the concentrations are multiplied by the specific rate constant

(k)● K relates the concentrations of reactants to the concentrations of products● The value of k depends on the reaction and the experimental conditions, such

as temperature● It can only be determined experimentally● If products form quickly k is large, ● If products form slowly k is small

What does a chemical equation tell you? What does it leave out?An equation does not tell you the path of a reaction from start to finish

Most chemical reactions are made up of multiple steps - the reaction mechanism

We can show the route reactions take using reaction progress curves

Are they always so straight forwards?● No, most reactions are not one step

reactions● In a complex (multistep) reaction,

there are peaks for each activated complex, and a valley for each intermediate

● An intermediate is a product of one one step in a reaction mechanism, and a reactant in the next

● Intermediates do not appear in the chemical equation

The rate determining stepIn a multistep reaction, one step will be slower than the others

The overall rate of reaction depends on the rate of the slowest step

Reversible reactionsSection 18.3

Do reactions always occur in one direction?● Based on reactions that you have been exposed to, you may think that this is

the case, but in actual fact this is not the case● Some reactions are reversible● A Reversible reaction is one where reactants change to products and

products change to reactions at the same time● It is important to pay attention to the direction of the arrow, to determine which

is the forward reaction and which is the reverse reaction● 2SO2(g) + O2(g) → 2SO3(g)● 2SO2(g) + O2(g) ← 2SO3(g)

Reversible reactions…..The two reactions can be combined into one by using a double arrow

Establishing EquilibriumWhat happens then when you mix a sulfur dioxide and oxygen in a sealed container?

Establishing EquilibriumThe forward reaction begins, and initially the rate of the reverse reaction is zero as no sulfur trioxide has forme. Once the sulfur trioxide begins to form the reverse reaction begins, but is slow at first.

As more sulfur trioixde forms the reverse reaction speeds up, and the rate of the forward reaction slows down because sulfur dioxide and oxygen are being used up

Eventually the rates of the forward and reverse reactions are equal, and the reaction has reached a state of balance: Chemical Equilibrium

What happens at Equilibrium? ● At equilibrium the reactions have not

stopped● An equilibrium is dynamic, meaning

the reactions continue taking place● The rates of the forward and reverse

reactions are equal● When a store opens, for example -

you only get people moving one way, yet later in the day, people move in and out at an equal rate - just like an equilibrium

Are concentrations equal at equilibrium? ● No - not necessarily!● Equilibrium only means equal rates of reaction, not equal concentrations● The Equilibrium Position is the relative concentrations of reactants and

products at equilibrium○ It tells you which reaction is more likely to take place○ If a mixture is 1 % A and 99 % B, then the formation of B is favored, yet f the mixture is 99% A

and 1 % B, then the formation of A is favored

● This can be represented by different length equilibrium arrows ● Almost all reactions are reversible under the right conditions, yet often one

reaction direction is so favored that the other set cannot be measured● When no reactants are measured the reaction has gone to completion● When no products are measured, no reaction has taken place

So what happens at equilibrium?At Chemical equilibrium, both the forward and reverse reactions continue . Because the rates are equal, no net change occurs in the concentration of the reaction components.

Le Chatelier’s Principle● Equilibrium systems have a delicate balance

○ Changing conditions can upset this balance

● Once disturbed, the system will work to get back to equilibrium - this equilibrium can be in a different position; a shift in equilibrium occurs

● Le Chatelier’s principle states that when a stress is applied to a system in equilibrium, the system changes in a way that relieves the stress

● Examples of stresses: ○ Changes in concentration○ Changes in temperature○ Changes in pressure

The effect of changing concentration

● If more CO2 is added, the reverse reaction speeds up. As more H2CO3 forms the forward reaction then speeds up until equilibrium is restored at a new position

● Adding a product pushes the equilibrium in the direction of the reactant● If CO2 is removed the equilibrium will move in the direction of the product● If you complete removing a product the reaction wlil go to completion

In summary...

H2CO3(aq) CO2(aq) + H2O(l)

Add CO2Direction of shift

H2CO3(aq) CO2(aq) + H2O(l)Remove CO2

Direction of shift

The effect of temperatureIncreasing the temperature causes the equilibrium position of a reaction to shift in the direction that absorbs heat.

In this example the reverse reaction is endothermic, and therefore works to reduce the stress in the system - equilibrium shifts in the direction of the reactants

N2(g) + 3H2(g) 2NH3(g) + heatAdd heat

Direction of shift

Remove heat (cool)Direction of shift

The effect of pressureEquilibrium systems in which some reactants and products are gases can be affected by a change in pressure.

A shift will occur only if there are an unequal number of moles of gas on each side of the equation.

N2(g) + 3H2(g) 2NH3(g)Add pressure

Direction of shift

Reduce pressureDirection of shift

The effect of pressure….

● You can predict which way the equilibrium position will shift by comparing the number of molecules of reactants and products.

● When two molecules of ammonia form, four molecules of reactants are used up.● A shift toward ammonia (the product) will reduce the number of molecules.

N2(g) + 3H2(g) 2NH3(g)

The effect of catalystsCatalysts speed up the time it takes for a system to reach equilibrium

Catalysts do not affect the amounts of reactants and products at equilibrium

The energy path for a reverse reaction is the opposite of the energy path for the forward reaction

Adding a catalyst lowers the energy path by the same amount for both reactions

Equilibrium constants● The equilibrium position is expressed as a number, which relates the number

of products to the number of reactants at equilibrium● The equilibrium constant is the ratio of the concentration of products to the

concentration of reactants at equilibrium● Each concentration is is raised to a power equal to the number of moles of

that substance in the balanced equation

aA + bB cC + dD

Keq = [C]c x [D]d[A]a x [B]b

Values of Keq

● The concentration of products is always the numerator

● The concentration of reactants is always the numerator

● As units can sometimes cancel out, equilibrium constants are reported without a unit

● A large value for the equilibrium constant means the equilibrium mixture is mostly product

● A small value for the equilibrium constant means the mixture is mostly reactant

● If the temperature of a system changes the Keq values will also change

Keq = [C]c x [D]d[A]a x [B]b

Solubility Equilibrium Section 18.4

The solubility product constant● Something that dissolves in water is described as being soluble● Something that does not dissolve in water is insoluble● Compounds containing carbonate or phosphate ions are generally

insoluble● Some general rules exist for whether something will be soluble in

water….

Compounds of the alkali metals and of ammonium ions

InsolubleCarbonates, phosphates, and sulfites

Alkali metal sulfides and hydroxides are soluble. Compounds of Ba, Sr, and Ca are slightly soluble.

Most are insoluble

Sulfides and hydroxides

Compounds of Ag and some compounds of Hg and Pb

SolubleChlorides, bromides, and iodides

Compounds of Pb, Ag, Hg, Ba, Sr, and CaSolubleSulfates

Few exceptionsSolubleEthanoates, nitrates, chlorates, and perchlorates

Some lithium compoundsSolubleSalts of Group 1A metals and ammonia

ExceptionsSolubilityCompounds

Solubility of Ionic Compounds in Water

How do you describe solubility?Scientists use the solubility product constant (Ksp) to compare the solubilities of ionic compounds

Ksp is essentially an equilibrium constant based only on the concentration of dissolved ions on a solution

Ksp = [A]a × [B]b

ExampleSilver chloride is an example of compound that is very slightly soluble in water

An equilibrium is established between the solid and the dissolved ions in the saturated solution.

In this equation, the coefficient for each ion is 1. So the Ksp expression for the dissociation is written as:

Ksp = [Ag+] x [Cl-]

AgCl(s) Ag+(aq) + Cl–(aq)

KSp Examples

1.8 × 10–14

1.2 × 10–12

ChromatesPbCrO4Ag2CrO4

4.5 × 10–9

9.3 × 10–10

1.0 × 10–10

8.15 × 10–12

5.0 × 10–9

CarbonatesCaCO3SrCO3ZnCO3Ag2CO3BaCO3

4.0 × 10–20

8.0 × 10–37

8.0 × 10–51

3.0 × 10–23

8.0 × 10–19

1.0 × 10–27

3.0 × 10–28

SulfidesNiSCuSAg2SZnSFeSCdSPbS

3.0 × 10–34

3.0 × 10–16

6.5 × 10–6

7.1 × 10–12

7.9 × 10–16

6.3 × 10–7

1.1 × 10–10

2.4 × 10–5

1.8 × 10–10

5.0 × 10–13

8.3 × 10–17

1.7 × 10–5

2.1 × 10–6

7.9 × 10–9

3.6 × 10–8

3.9 × 10–11

HydroxidesAl(OH)3Zn(OH)2Ca(OH)2Mg(OH)2Fe(OH)2

SulfatesPbSO4BaSO4CaSO4

HalidesAgClAgBrAgI

PbCl2PbBr2PbI2PbF2CaF2

KspIonic compoundKspIonic compoundKsp

Ionic compound

Solubility Product Constants (Ksp) at 25oC

How are Kspvalues used?The smaller the value of the Ksp the lower the solubility of the compound

There is a wide range in possible Ksp values

The common ion effectCommon Ion - An ion that is found in more than one ionic compound in a solution

Common Ion effect - The lowering of the solubility of an ionic compound due to the addition of a common ion

What does this all mean?

Example….In a saturated solution of lead(II) chromate, an equilibrium is established between the solid lead(II) chromate and its ions in solution.

What would happen if you added some lead nitrate to this solution?

PbCrO4(s) Pb2+(aq) + CrO42–(aq)

How do we apply Le Chatelier's principle● Lead(II) nitrite is soluble in water, so adding Pb(NO3)2 causes the

concentration of lead ion to increase.● The lead(II) ion is a common ion in both ionic compounds in a solution● The addition of lead ions is a stress on the equilibrium.● Applying Le Châtelier’s principle, the stress can be relieved if the reaction

shifts to the left - PbCrO4 precipitates out● Adding the common ion essentially lowered the solubility of the lead(II)

chromate○ The common ion effect○ This requires the new ion to be more soluble than the original compound in solution

The yellow solid in the test tube, which is PbCrO4, cannot dissolve because the solution is saturated with Pb2+ and CrO4

2– ions.

When some Pb(NO3)2 is added, the excess lead ions combine with the chromate ions in solution to form additional solid PbCrO4.

Why is all this useful? ● Combining all of this, it is possible to predict whether a precipitate will form

when two solutions are mixed● A precipitate will form if the product of the concentrations of two ions in the

mixture is greater than the Ksp value for the compound formed from the ions.● Example - Does a precipitate form when 0.5 L of 0.008 M Na2SO4 is mixed

with 0.5 L of 0.002 M Ba(NO3)2? The Ksp for BaSO4 is 1.1 × 10–10.● As you combine the two, the volume has doubled, therefore the concentration

of Ba2+ and SO42+ have halved.

● 0.001 x 0.004 is 4 x 10-6, greater than the Kspfor BaSO4 so a precipitate forms

Free energy and EntropySection 18.5

Can something spontaneously combust? Sometimes, this is possible, if there are the correct conditions in the system

What is meant by the term free energy? ● Free energy is the energy in a chemical reaction that is available to do

work○ This does not mean that it is all used to do work, just that it can be○ For example - in an internal combustion engine, 30 % of free energy is used to move the car,

whereas 70 % is lost as heat and friction○ This is therefore not very efficient

● An efficient process uses the least amount of energy, time or money to produce a result

○ No process is ever 100 % efficient

Spontaneous vs Nonspontaneous reactions● There are two types of reactions: ● Spontaneous reactions: a reaction that favors the formation of products

at the stated conditions○ These release free energy

● Nonspontaneous reactions: A reaction that does not favor the formation of products at the stated conditions

○ This type of reaction produces very little energy

How does this relate to reversible reactions?In nearly all reversible reactions one reaction is favored over the other:

Do spontaneous reactions occur quickly? ● Not necessarily● Spontaneous and nonspontaneous are terms that have nothing to do with

rate ● Some spontaneous reactions are so slow that they appear to not be taking

place○ Example - table sugar and oxygen○ Without heat takes thousands of year, with heat produces carbon dioxide and water

● Therefore changing the conditions not only affects reaction rate, but whether a reaction can take place or not

● Conditions determine whether a reaction is spontaneous or nonspontaneous

Can an endothermic system/process be spontaneous?

Ice melting is an endothermic process

Enthalpy alone does not determine whether a change is spontaneous or nonspontaneous

The other factor is Entropy - a measure of the disorder in a system

The law of disorderThis states that the natural tendency is for systems to move in the direction of increasing disorder or randomness

Reactions in which entropy increases as reactants form products tend to be favored

How to increase entropy in a systemThere are 4 ways that changes to a system can increase the entropy

1: State of matter - gas has more entropy than liquid or solid

Parts of a wholeEntropy increases when a substance is divided into parts

Number of molecules ENtropy increases when the total number of product molecules is greater than the number of reactant molecules

TemperatureThe higher the temperature, the higher the entropy

Relationship between Enthalpy and Entropy● The size and direction of enthalpy and entropy changes determines

whether a reaction is spontaneous or not● If one change is favorable, and one change is not, whether a reaction occurs

depends upon whether the unfavorable change is offset by the favorable one● When ice melts, it is endothermic - an unfavorable change● Yet, the change in entropy is favorable - reaching states of increased

disorder, therefore ice melting is spontaneous ● An endothermic reaction that leads to a decrease in energy is never

spontaneous

NoDecreasesIncreases (endothermic)

Only if unfavorable entropy change is offset by favorable enthalpy change

Decreases (less disorder in products than in reactants)

Decreases (exothermic)

Only if unfavorable enthalpy change is offset by favorable entropy change

IncreasesIncreases (endothermic)

YesIncreases (more disorder in products than in reactants)

Decreases (exothermic)

Is the reaction spontaneous?Entropy changeEnthalpy change

How Enthalpy Changes and Entropy ChangesAffect Reaction Spontaneity

Gibbs free energyThis is the term often used to describe free energy - named after the scientist who discovered this property

The symbol is G

Free energy can be either released or absorbed, and is calculated by the following equation:

A positive ΔG value = nonspontaneous reaction

A negative ΔG value = spontaneous reaction

ΔG = ΔH – TΔS