Calorimetry and Hess’s Law

Experiment 3

Experiment 3

Goal: To determine heat capacities and

enthalpy changes

Method: Measure heat transferred to/from

various processes using a simple calorimeter

Use Hess’s Law

Definitions

Thermodynamics:The study of heat and its transformations

Energy:The capacity to do work or to produce heat

System:The part of the universe of interest

Surroundings:Everything else (relevant to system)

Universe:System + surroundings

First Law of Thermodynamics

w q

E EΔE initialfinalsys

Energy change in system

= heat disordered energy transferred

+ work

ordered energy transferred

Enthalpy, H

VpΔEqΔH p

Enthalpy change:– heat transferred at constant pressure– most processes on earth

Often:Often: H H EE

Enthalpy change

At constant pressure:

VpE ΔH

p qΔH p

Vi

Vf

V

p

Generally small

Enthalpy changes

1. Thermal enthalpyhigher T greater H

2. Phase enthalpyHsolid < Hliquid < Hgas

3. Chemical (reaction) enthalpyexothermic: heat released

endothermic: heat absorbed

Calorimetry at Constant Pressure

Coffee Cup Calorimeter

q T

qp = CT

H = CT

C: heat capacity

Heat flow (qp)

Heat Capacity

Amount of energy to raise the temperature of a substance 1°C (1 K)Depends on material’s amount and type

c, specific heat capacity: units – energy per gram.oC

C, molar heat capacity: units – energy per mole.oC

CCg

energygTmcqΔH o

op

CCmol

energymolTnCqΔH o

op

Enthalpy of phase change

No T at a phase change water vaporizes/condenses at 100°C

Hvap = –Hcond

water “fuses”/melts at 0°C

Hfus = –Hmelt

q amount and type

Units1. htransition: energy/g

2. Htransition: energy/mol

mol

energymolHnΔH transitionmeasures

g

energyghmΔH transitionmeasured

Measuring H (qp)

Perfect calorimeter is adiabatic:

rcalorimetesample q q

Heat gained/lost by sample = heat lost/gained by calorimeter

~No heat transfer from calorimeter to environment

0 rcalorimetesample q q

so0contentsrcalorimeteΔH

Basic Calorimeter Setup

Overview1: Calorimeter calibration each pair

Heat capacity of calorimeter

2: Determine heat of fusion (Hf) of water one pair in Heat required to melt ice small group

3: Determine specific heats of metals other pair in qmetal = Hmetal = mmetal

.cmetal.Tmetal small group

4: Determine heats of reaction (Hrxn) 1) Mg + 2HCl MgCl2 + H2 one pair 2) MgO + 2HCl MgCl2 + H2O other pair Overall) Mg + ½ O2 MgO

EVERYONE does individual report containing results for all FOUR parts of the lab

Part 1 Calorimeter Calibration

Mass dry calorimeter mcal

Add 100 mL room temp H2O

Mass and record temperature mcw,Tcw

Add 100 mL of 35°C H2O Thw

Mass and record temperature mall,Tf

Find heat capacity of calorimeter Ccal

fromwarm water

tocool water + calorimeter

heat

Calculations

0 H H ΔH rcalorimetecool waterhot water

0

TTC

TTc m TTcm

cwfrcalorimete

cwfcwcwhwfhwhw

loss (T dec)

gain(T inc)

gain(T inc)

cwater: 4.184 J/g.°C

Calibration Example Data

mass Tinitial Tfinal

Empty calorimeter 5.00 g 21.2oC28.0oC

Cool water 100. g 21.2oC 28.0oC

Warm water 100. g 35.0°C 28.0oCcwater: 4.184 J/g.°C

! Stop here and calculate your calorimeter’s heat capacity !It should be between 5 and 200 J/oC.If it’s negative or too large, repeat the calibration.

C

Jrcalorimete

orcalorimete

o

Cg

Jo

Cg

J

o

oo

.C

C..C C...g.C...g.

312

022102822102818441000350281844100

Part 2 Heat of Fusion of Ice

Mass dry calorimeter mcal

Add 100 mL water to calorimeter Mass and record temperature mRT,TRT

Add 25 g solid ice Tice = 0°C

Record lowest temperature Tf

Mass mall

fromroom T water &

calorimeter

tomelting ice & heating ice

heat

Calculations

0 H H H ΔH warm icemelt icercalorimeteRTwater

00

CTcmΔh m

TTC TTcmo

ficeicefusice

RTfrcalorimeteRTfRTRT

loss (T dec)

gain(T inc)

gain(T inc)

loss (T dec)

Convert hfus to fus in kJ/mol

Lit value is 6.02 kJ/mol

Heat of Fusion Example Data

mass Tinitial Tfinal

Empty calorimeter5.00 g 21.2°C1.9oC

Water 100. g 21.2°C1.9oC

Ice 25.0 g 0.0°C 1.9oC

C

Jfus

o

C

Jo

Cg

J

o

Cg

Jfus

o

oo

o

h

C... C...g.

C...g.g.h

325

022191312221911844100

0091184425025

molkJ

gkJ

molg.

gJ

fus .H 86510001

10218325

Part 3 Specific Heats of Metals

Mass metal mmetal10-30 g

Heat in large test tube in boiling water bath 30 min Thw

(start at beginning) Mass dry calorimeter mcal

Add 100 mL water Mass and record temperature

mw+cal, TRT

Slide metal into calorimeter Record highest temperature Tf

fromhot metal

towater + calorimeter

heat

Calculations

0 H H H rcalorimetecool watermetal

0

RTfrcalorimete

RTfRTwhwfmetmet

TT C

TTcm TTcm

loss (T dec)

gain(T inc)

gain(T inc)

Convert cmet to required units

Metals/Specific Heat Example Data

mass Tinitial Tfinal

Empty calorimeter5.00 g 21.2°C 22.6°C

Water 100. g 21.2°C 22.6°C

Hot metal 20.0 g 100.°C 22.6°C

Cg

Jmetal

o

C

Jo

Cg

Jometal

o

oo

.c

C...C...g.C..cg.

3900

022162231222162218441000100622020

copperforisthis.c molJ

molg.

Cg

J.metal o 8241

55633900

Metal heat capacities

Law of Dulong and Petit:Cmetal (per mol) = 3R = 24.94

J/K.molwhere R = 8.314 J/K.mol

Compare your value

Measured values:water 75.29 J/K. molCu 24.44 J/K. molAl 24.35 J/K. mol

Compare your value

Part 4 Heat of Chemical Reaction (a)

Mg + 2 HCl MgCl2 + H2 Ha

Mass empty calorimeter mcal

Add 25 mL HCl to 50 mL water Mass and record temperature mRT,TRT

Mass 0.10 – 0.15 g Mg; add mMg

Record highest temperature Tf

fromreaction

towater &

calorimeter

heat

Part 4 Heat of Chemical Reaction (b)

MgO + 2 HCl MgCl2 + H2O Hb

Mass empty calorimeter mcal

Add 25 mL HCl to 50 mL water Mass and record temperature

mRT,TRT

Mass 0.30 g MgO; add mMgO

Record highest temperature Tf

fromreaction

towater &

calorimeter

heat

Calculations

0 H H H rcalorimetecool waterrxn

01

1

TTC

TTcm HMM

m

frcalorimete

fcwcwrxnMg

Mg

loss (T dec)

gain(T inc)

gain(T inc)

#mol reactant

Calculations

0 H H H rcalorimetecool waterrxn

01

1

TTC

TTcm HMM

m

frcalorimete

fcwcwrxnMgO

MgO

loss (T dec)

gain(T inc)

gain(T inc)

#mol reactant

Mg/HCl Example Data

mass Tinitial Tfinal

Empty calorimeter5.00 g 21.2°C28.1oC

Acidic H2O 75.0 g (mL)21.2°C 28.1oC

Mg metal 0.12 g

Assume the heat capacity of the solution is that of water (big assumption)

Literature value: -462kJ/mol (compare your value)

gMgJ

a

o

C

Jo

Cg

Ja

.h

C...C...g.gMg.h oo

618779

022112831222112818441275120

HCl/MgforisthisH molkJ

JkJ

molg.

gMgJ.

a 45710001

13124618779

MgO/HCl Example Data

mass Tinitial Tfinal

Empty calorimeter5.00 g 21.2°C24.6oC

Acidic H2O 75.0 g (mL)21.2°C 24.6oC

MgO powder 0.30 g

Assume the heat capacity of the solution is that of water (big assumption)

Literature value: -146kJ/mol (compare your value)

gMgO

Jb

o

C

Jo

Cg

Jb

h

C...C...g.gMgO.h oo

1113

022162431222162418443075300

HCl/MgOforisthisH molkJ

JkJ

molg.

gMgOJ

b 15010001

131401113

Part 4 Heat of Chemical Reaction

Mg + ½ O2 MgO

Use:Mg + 2 HCl MgCl2 + H2 Ha

MgO+ 2 HCl MgCl2 + H2O Hb

H2 + ½ O2 H2O Hc

Hc = -285.8 kJ

Part 4 - Hess’s Law

Hrxn = [Hindividual rxns]

A B HAB

B C HBC

A + B B + C

A C HAC = HAB+ HBC

Part 4 Hess’s Law Application

Heat of Reaction for Mg combustion

Mg + 2 H+ Mg2+ + H2 ΔHa

Mg2+ + H2O MgO + 2 H+ –ΔHb

H2 + ½ O2 H2O ΔHc

Mg + ½ O2 MgO ΔHcomb(or form)

compare to lit value (-601 kJ)

Part 4 Example CalculationHeat of Reaction for Mg combustion

Mg + 2 H+ Mg2+ + H2 –457 kJ/mol

Mg2+ + H2O MgO + 2 H+ +150 kJ/mol

H2 + ½ O2 H2O –286 kJ/mol

Mg + ½ O2 MgO –593 kJ/molcompare to lit value (-601 kJ)

ReportAbstractResults Sample calculations including:

Calorimeter heat capacity (part 1) Heat of fusion of ice (part 2) Specific heats of metals – Cu and Al

(part 4) Heats of reactions (part 4)

Discussion/review questions