Heat ProblemsHeat Problems

There are a few problems that deal There are a few problems that deal with heat:with heat:– Heat as enthalpyHeat as enthalpy– Specific heatSpecific heat– Heat of fusionHeat of fusion– Heat of vaporizationHeat of vaporization

EnthalpyEnthalpy

EnthalpyEnthalpy is the total is the total energyenergy of a system of a system It is represented by a It is represented by a HH.. If the pressure remains If the pressure remains constantconstant, the , the

enthalpyenthalpy increase of a sample of matter increase of a sample of matter equals the equals the energyenergy as as heatheat that is that is received.received.

This remains true even during a This remains true even during a chemicalchemical reaction or a change of reaction or a change of statestate occurs. occurs.

It also indicates the It also indicates the totaltotal kinetickinetic energy energy of the particles in a sampleof the particles in a sample

So to calculate Enthalpy, we So to calculate Enthalpy, we have to visit have to visit molar heat molar heat

capacitycapacity Molar heat capacityMolar heat capacity of a pure substance is the of a pure substance is the energyenergy as as heatheat needed to increase the needed to increase the temperature of temperature of 1 mol1 mol of a substance by of a substance by 1K1K

It is symbolized by It is symbolized by CC It has a unit of It has a unit of J/(molJ/(mol..K)K) Formula:Formula: q=nC q=nCTT HeatHeat = (amount in = (amount in molesmoles) () (molar heat molar heat capacity) capacity)

(change in(change in temperature temperature)) Note: moles are used so you may have to do Note: moles are used so you may have to do

some gram to mole problems.some gram to mole problems. Table 1Table 1 on on Page 343Page 343 has many Molar Heat has many Molar Heat

Capacities of Elements and Compounds.Capacities of Elements and Compounds.

ExamplesExamples The molar heat capacity of tungsten is The molar heat capacity of tungsten is

24.2 J/(mol24.2 J/(mol..K).K). Calculate the energy as Calculate the energy as heat needed to increase the temperature heat needed to increase the temperature of 0.40 mol of tungsten by 10.0 K.of 0.40 mol of tungsten by 10.0 K.

Suppose a sample of water increased in Suppose a sample of water increased in temperature by 3.5 K when the sample temperature by 3.5 K when the sample absorbed 856 J of energy as heat. absorbed 856 J of energy as heat. Calculate the number of moles of water if Calculate the number of moles of water if the molar heat capacity is 50.5 J /(molthe molar heat capacity is 50.5 J /(mol..K). K). What is the mass of that water?What is the mass of that water?

Molar Enthalpy ChangeMolar Enthalpy Change Since enthalpy “equals the energy as Since enthalpy “equals the energy as heatheat that that

is received”, we can rewrite the heat equation is received”, we can rewrite the heat equation to:to:

H = nCH = nCTT EnthalpyEnthalpy change = (moles)( change = (moles)(molar heatmolar heat

capacity) (change in capacity) (change in temperaturetemperature)) The enthalpy change for The enthalpy change for oneone mole of a pure mole of a pure

substance is known as the substance is known as the molar enthalpy molar enthalpy change.change.

ExamplesExamples

The molar heat capacity of Al(s) is The molar heat capacity of Al(s) is 24.2 J/K24.2 J/K..mol. Calculate the molar mol. Calculate the molar enthalpy change when Al(s) is cooled enthalpy change when Al(s) is cooled from 128.5 from 128.5 C to 22.6 C to 22.6 C.C.

Lead has a molar heat capacity of Lead has a molar heat capacity of 26.4 J/K26.4 J/K..mol. What molar enthalpy mol. What molar enthalpy change occurs when lead is cooled change occurs when lead is cooled from 302 from 302 C to 275 C to 275 C?C?

Molar Heat Capacity is related Molar Heat Capacity is related to to Specific HeatSpecific Heat

Specific heatSpecific heat is the energy as heat needed to is the energy as heat needed to raise the raise the temperaturetemperature of one of one gramgram of substance of substance by one by one KelvinKelvin..

Symbolized by Symbolized by ccpp

This is why an iron gets hot faster than a pot of This is why an iron gets hot faster than a pot of waterwater

There are two equations that involve specific There are two equations that involve specific heatheat

1) 1) Molar MassMolar Mass (g/mol) x (g/mol) x ccpp (J/K (J/K..g) = g) = CC (J/K (J/K..mol)mol)

2) 2) q = m x cq = m x cpp x x T T

Example ProblemExample Problem

If the molar heat capacity of nitrogen (NIf the molar heat capacity of nitrogen (N22) is ) is 29.1 (J/K29.1 (J/K..mol), what is nitrogen’s specific heat?mol), what is nitrogen’s specific heat?

Calculate the specific heat of a Calculate the specific heat of a substance if a 35 g sample absorbs 48 J substance if a 35 g sample absorbs 48 J as the temperature is raised from 293 K as the temperature is raised from 293 K to 313 Kto 313 K

ccpp= 48 J/[35gx(313K-293K)]= 48 J/[35gx(313K-293K)]

= 0.069 J/gK= 0.069 J/gK

Two more heat equationsTwo more heat equations

Heat of Heat of fusionfusion (L (Lff))– Heat involved in melting or freezing a substanceHeat involved in melting or freezing a substance

Heat of Heat of vaporizationvaporization (L (Lvv))– Heat involved in evaporation or condensing a Heat involved in evaporation or condensing a

substancesubstance As a phase change occurs, all energy is As a phase change occurs, all energy is

being used for the change so the being used for the change so the temperature will not change.temperature will not change.

So, during a phase change, heat equals the So, during a phase change, heat equals the massmass (m) times a (m) times a valuevalue (L) for that material (L) for that material ((q=m x Lq=m x L))

Example ProblemExample Problem

If the heat of fusion of water is 80 If the heat of fusion of water is 80 cal/g, what is the amount of heat cal/g, what is the amount of heat energy required to change 15.0 energy required to change 15.0 grams of ice at 0grams of ice at 0C to 15.0 grams of C to 15.0 grams of water at 0water at 0C?C?

How do they all fit together?How do they all fit together?This is Figure 17 from page 394 from the book

As heat is added, temperature increases linearly (q=nCT)T)

Except, when a phase change occurs, because all the heat is going into changing the phase (q=m Lq=m L, note no , note no TT))

Try Practice Problems Try Practice Problems 2-4 on page 612-4 on page 61

1.1. 0.385 J/gK0.385 J/gK

2.2. 329 K329 K

3.3. 3.6 kJ3.6 kJ