Chem 1050
Thermochemistry
Fall 2010
Text: Petrucci Herring Madura Bissonnette 10 th Edition Chapter 7
Exercises:
1, 5, 7, 9, 13, 15, 17, 19, 21, 23, 27, 29, 31, 33, 35, 37, 39, 41, 45, 47, 49, 51, 53, 55,
57, 65, 67, 69, 71, 73, 75, 79, 81, 93
Text: Petrucci Harwood Herring Madura 9 th Edition Chapter 7
Exercises:
1, 3, 5, 7, 11, 13, 15, 17, 19, 21, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 51, 53,
55, 57, 59, 61, 63, 65, 67, 69, 71, 75, 81
Integrative and Advanced Exercises: 91
Additional Problems:
A.
First Law of Thermodynamics:
1.
Calculate the change in internal energy DU of a system if it
(a)
(b)
absorbs 405 J of heat and does 760 J of work on the surroundings.
loses 192 J of heat and has 104 J of work done on it by the surroundings.
2.
A gas is compressed from a volume of 5.00 L to 3.00 L by an external pressure of 2.00 atm and
at the same time gains 275 J of heat. Calculate DU of the gas. 1 L atm = 101.3 J
3.
A 0.400 mol sample of argon expands from an initial pressure of 2.95 bar against an atmospheric
pressure of 0.800 bar at a constant temperature of 25 ºC until its pressure is the same as
atmospheric pressure. During the expansion it loses 350 J of heat. Calculate DU of the argon.
Hint: Calculate the initial and final volumes of the argon. 1 L bar = 100 J.
4.
Calculate the work done when 75.0 g H2O(l) vaporizes to steam at 100.0°C against an
atmospheric pressure of 1.00 atm. The density of H2O(l) can be assumed to be 1.00 g mLG1.
Hint: The steam escapes the boiling liquid at a pressure equal to the external pressure.
B.
Stoichiometric relationship between heat of reaction (and phase changes) and amounts of
reactants consumed and products formed
1
5.
Consider the following equation for the oxidation of IG to I2 by permanganate ion:
6IG(aq) + 2MnO 4G(aq) + 4H2O(l) → 3I2(s) + 2MnO 2(s) + 8OHG(aq) )H = !363.2 kJ
(a)
(b)
(c)
6.
Determine the molar enthalpy change for the reaction per mole of IG consumed and
also per mole of I2 formed.
How much heat is released when 0.100 mol of IG is consumed?
How many grams of I2 are formed when 779.4 J of heat is evolved?
Methyl alcohol, CH3OH, is sometimes added to gasoline to reduce the air pollution from cars. The
equation representing its combustion is as follows:
2CH3OH (l) + 3O2(g) → 2CO2(g) + 4H2O(l)
)H = !1453.0 kJ
Calculate the heat released when 1.000 L of methyl alcohol (density = 0.7914 g mLG1) is burned
completely in excess oxygen.
7.
Metallic iron can be produced from its oxide Fe3O4, called magnetite, in the thermite reaction with
aluminum metal:
3Fe3O4(s) + 8Al(s) → 4Al2O3(s) + 9Fe(s)
In an experiment, 157.2 g of magnetite reacted with excess aluminum releasing 757.6 kJ of heat.
Calculate the value of )H for the reaction as described by the equation given above, exactly as
written. (i.e. for 3 mol Fe3O4 consumed.)
8.
How much heat would be required to vaporize 98.7 g methanol at its boiling point of 64.0°C? The
heat of vaporization )Hvap of methanol is 35.3 kJ molG1.
CH3OH(l) → CH3OH(g) )H = +35.3 kJ
9.
Sodium chloride melts at 801°C. Calculate the mass of sodium chloride that can be melted by the
addition of 391 kJ of heat if the heat of fusion of sodium chloride )Hfus is 28.5 kJ molG1.
NaCl(s) → NaCl(l) )H = + 28.5 kJ
10.
Lead melts at 327°C. At that temperature, 148 J of heat is required to melt 6.00 g of lead.
Pb(s) → Pb(l)
(a)
(b)
Calculate the latent heat of fusion in J gG1 of lead.
Calculate the heat of fusion )Hfus in kJ molG1 of lead.
C.
Specific heat, heat capacity and temperature change
11.
Calculate the heat required to increase the temperature of 380 g of diamond, which has a specific
heat of 0.502 J gG1 KG1, from 30.0°C to 3000°C. Note: diamond has a melting point of greater
than 3550°C.
2
12.
When a block of copper absorbs 727.5 kJ of heat, its temperature rises from 20.5°C to 324.3°C.
(a)
(b)
Calculate the heat capacity of the block in kJ KG1 and kJ °CG1.
If the specific heat of copper is 0.385 J gG1 °CG1, calculate the mass of the block.
13.
A student has 5.00 gram samples of iron and gold. Both metals, initially at 20.0°C, are heated with
1.00 x 102 joules of energy. Which metal sample achieves the highest temperature? Data: specific
heat of iron = 0.444 J gG1 KG1 specific heat of gold = 0.129 J gG1 KG1. Note: No calculation
is necessary, but )T can be easily calculated for both metal samples.
14.
(a)
Calculate the heat required to change the temperature of a solution with a heat capacity of
4.62 kJ KG1 from 25.0°C to 32.4°C.
(b)
If the volume of the solution is doubled, does its heat capacity change?
D.
Applications of Calorimetry
NOTES:
1.
2.
For each problem, clearly indicate all assumptions made.
Problems 15, 16, 17, 21-23 require the specific heat capacity of water, 4.184 J gG1 °CG1 as
additional data. Problems 21 and 22 require the density of water, 1.00 g mLG1. On a test or exam,
such data will be provided with the periodic table. You will be expected to look them up as
needed.
15.
A 129 g sample of brass at 95.0°C is added to 44.6 g of water initially at 25.0°C in a styrofoam
cup calorimeter. The final temperature of the brass and water is 40.0°C. Calculate the specific
heat of brass in J gG1 °CG1.
16.
550 grams of aluminum (c = 0.900 J gG1 KG1) at 80.0°C is added to 675 grams of water in a
styrofoam cup at a temperature of 23.8°C. Calculate the final temperature of the water and
aluminum.
17.
A 855 g sample of copper (c = 0.385 J gG1 °CG1) is removed from an oven and plunged into 450
g of water in an insulated container. The temperature of the water increased from 23.2°C to
39.8°C. Calculate the original temperature of the oven.
18.
(a)
(b)
19.
Calculate )U for the combustion of propane at 25 °C given
Explain the difference between )H and )U of a reaction.
Differentiate between )H for a reaction in kJ for a chemical equation exactly as written and
)Hm in kJ molG1 of substance. Which is an intensive property and which is an extensive
property? How can one be converted to the other?
C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(l)
3
)H° = !2219.9 kJ at 25°C and 1 atm
20.
For the reaction C2H4(g) + H2(g) → C2H6(g)
)H° = !146.79 kJ at 525°C and 1 atm. Calculate )U° for the reaction at 525°C and 1 atm.
21.
A 0.199 g sample of menthol (C10H20O) was burned in a bomb calorimeter which has a total heat
capacity of 4602 J KG1. The temperature rose from 22.17°C to 23.92°C. Calculate )Um and
)Hm of combustion in kJ molG1 of menthol at 25°C.
Given: C10H20O(s) +
22.
29
2
O2(g) → 10 CO2(g) + 10 H2O(l)
The heat capacity of a bomb calorimeter can be determined by burning an accurate mass of a
substance whose heat of combustion is known. Burning a 1.500 g sample of methane, CH4, in an
bomb calorimeter increased the temperature from 21.110°C to 23.300°C. Calculate the total heat
capacity of the calorimeter in kJ KG1. Hint: Find )Um in kJ molG1 CH4 first.
CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l)
23.
)Hm° = !890.3 kJ molG1 at 25°C and 1 atm.
Calculate the mass of hexane C6H14(l) which, when burned in an excess of oxygen in a bomb
calorimeter whose total heat capacity is 12.05 kJ °CG1, will increase the temperature of the
calorimeter and its contents by 12.18°C.
2 C6H14(l) + 19 O2(g) → 12 CO2(g) + 14 H2O(l)
24.
A 100.0 mL sample of 0.400 mol LG1 HCl(aq) is added to 150.0 mL of 0.300 mol LG1 NH3(aq)
in a coffee cup calorimeter and the temperature of the resulting solution rises from 23.92°C to
26.07°C.
HCl(aq) + NH3(aq) → NH4Cl(aq)
(a)
(b)
(c)
25.
)H° = !8326 kJ at 25°C and 1 atm
Determine the limiting reagent.
Calculate the enthalpy change )Hm for the reaction in kJ molG1 of the limiting reagent.
Calculate DHm in kJ molG1 of the excess reagent. (only the amount of the excess reagent
which actually reacts is relevant!)
The value of )H for the following reaction is determined in a coffee cup calorimeter:
CaO(s) + 2HCl(aq) → CaCl2(aq) + H2O(l)
1.1216 g of CaO(s) are added to 100.0 mL of 1.00 mol LG1 HCl(aq)
The temperature rises from 24.94°C to 34.18°C.
(a)
(b)
Determine the limiting reagent
Find the value of )Hm in kJ molG1 for both the limiting and excess reagents..
4
26.
Consider the process for the dissolution of KClO 3 in water:
KClO 3(s) → K+(aq) + ClO 3G(aq)
)H° = +42.0 kJ molG1 of KClO 3
In an experiment, a student dissolves 2.00 g of KClO 3 in 50.0 g of water in a coffee cup
calorimeter.
If the initial temperature of the water is 25.00°C, calculate the final temperature of the
KClO 3(aq). Hint: Calculate the temperature change ()T) that occurs first. This will simplify the
calculations.
E.
Hess's law and heats of formation
27.
Determine the value of )H° for the following reaction: CH4(g) + 3Cl2(g) → CHCl3(l) +
3HCl(g)
Given:
2C(gr) + H2(g) + 3Cl2(g) → 2CHCl3(l)
2C(gr) + 4H2(g) → 2CH4(g)
½H2(g) + ½Cl2(g) → HCl(g)
28.
)H° = !268.94 kJ
)H° = !149.62 kJ
)H° = !92.31 kJ
Given the following data:
2C2H6(g) + 7O2(g) → 4CO2(g) + 6H2O(l)
)H° = !3120 kJ
C(gr) + O2(g) → CO2(g)
)H° = !394 kJ
2H2(g) + O2(g) → 2H2O(l)
)H° = !572 kJ
Calculate )H° for the following reaction:
2C(gr) + 3H2(g) → C2H6(g)
29.
Acetylene gas C2 H2 can be produced by the reaction of calcium carbide CaC2 with water
according to the following balanced equation:
CaC2(s) + 2H2O(l) → Ca(OH)2(s) + C2H2(g)
Determine the value of )Ho for this reaction using the thermochemical equations provided below:
Ca(s) + 2C(gr) → CaC2(s)
)Ho = !62.8 kJ
Ca(s) + ½O2(g) → CaO(s)
)Ho = !635.5 kJ
CaO(s) + H2O(l) → Ca(OH)2(s)
)Ho = !65.2 kJ
2C2H2(g) + 5O2(g) → 4CO2(g) + 2H2O(l)
)Ho = !2600 kJ
C(gr) + O2(g) → CO2(g)
)Ho = !393.5 kJ
5
30.
Calculate the heat of formation )Hf o of liquid hydrazine N2H4(l) from the following data:
2NH3(g) + 3 N2O(g) → 4N2(g) + 3H2O(l)
)Ho = !1010 kJ
N2O(g) + 3H2(g) → N2H4(l) + H2O(l)
)Ho = !317.0 kJ
2NH3(g) + ½O2(g) → N2H4(l) + H2O(l)
)Ho = !143.0 kJ
H2(g) + ½O2(g) → H2O(l)
)Ho = !286.0 kJ
Hint: Write the reaction for the formation of one mole at N2H4(l) from its elements in their
standard states.
31.
Calculate the value of )Ho for each of the following reactions using Hess's law and the heat of
formation data provided in the table below:
(a)
2ClF 3(g) + 2NH3(g) → N2(g) + 6HF(g) + Cl2(g)
(b)
3Al(s) + 3NH4ClO 4(s) → Al2O3(s) + AlCl3(s) + 3NO(g) + 6H2O(g)
Substance
DHfo/kJ molG1
Substance
DHfo/kJ molG1
HF(g)
!271.1
NO(g)
+90.25
NH3(g)
!46.11
NH4ClO 4(s)
!295.0
ClF 3(g)
!169.0
Al2O3(s)
!1675.7
H2O(g)
!241.818
AlCl3(s)
!704.0
F.
Miscellaneous problems
32.
0.4089 g of benzoic acid C7H6O2 are burned in a bomb calorimeter containing 900.00 g of H2O.
The heat capacity of the bomb calorimeter without water is 1506.7 J KG1. The temperature rises
from 24.02°C to 27.64°C. Find the )Um and )Hm of combustion for benzoic acid in kJ molG1.
33.
Given the following data:
Substance
DHfo/kJ molG1
B5H9(l)
+80.9
H2O(l)
!285.8
B2O3(s)
!1272.8
6
(a)
Find )Ho for the following reaction as written using Hess's law:
2B5H9(l) + 12O2(g) → 9H2O(l) + 5B2O3(s)
(b)
(c)
34.
Determine )Ho per mole of B5H9 consumed and per mole of B2O3 formed.
How many grams of B5H9 must be burned to heat 750.0 grams of water from 20.0°C to
70.0°C?.
Given the following information, solve for )Hfo H2S(g) using Hess's law.
)Hfo HNO3(l) = !174.10 kJ molG1 )Hfo H2O(l) = !285.830 kJ molG1
)Hfo NO(g) = +90.25 kJ molG1
3H2S(g) + 2HNO3(l) → 2NO(g) + 4H2O(l) + 3S(s)
35.
)H° = !552.7 kJ
One version of an ice calorimeter measures heats of reaction at constant volume by determining
the amount of ice that melts at a constant temperature of 0°C. A sealed bomb containing 5.40 g
Al and 19.89 g CuO is placed in an ice calorimeter containing 6.427 kg of ice and 6.692 kg of
H2O(l) at 0°C. The reaction is set off by remote control and it is found that 6.126 kg of ice and
6.993 kg of H2O(l) remain after melting stops. The balanced equation for the reaction is as follows:
2Al(s) + 3CuO(s) → Al2O3(s) + 3Cu(s)
(a)
(b)
(c)
(d)
(e)
Determine the limiting reagent
How much ice melts?
How much heat in kJ is needed to melt the ice in part (b) if the molar heat of fusion of ice
is 6.008 kJ molG1?
Assuming that all the heat of reaction is used to melt ice, calculate )Um and )Hm per mole
of the limiting reagent.
Find )H for the reaction exactly as written.
36.
The boiling point and freezing point of ethyl alcohol, C2H5OH, are 78.7°C and !117.3°C
respectively. The specific heat of ethyl alcohol(l) = 2.46 J g KG1. The heat of vaporization )HVAP
and the heat of fusion )HFUS are 39.3 kJ molG1 and 7.61 kJ molG1 respectively. How many joules
of heat are needed to change 75.0 g of solid C2 H5 OH at !117.3°C to gaseous C2H5OH at
78.7°C?
37.
An ice cube with a mass of 50.0 g is dropped into 150.9 g of hot water at 75.0 °C in a Styrofoam
cup. Calculate the final temperature of the water in the cup after thermal equilibrium is reached if
the molar enthalpy of fusion of ice is 6.008 kJ molG1.
38.
Write balanced thermochemical equations for the following. Express )Ho in kJ for each
equation exactly as written.
(a)
heat of formation of K2CO3(s)
)Hfo = !1146 kJ molG1 of K2CO3(s)
(b)
heat of neutralization of H2S(aq)
(using NaOH(aq) as the base)
)Hmo = !32.4 kJ molG1 of H2S(g)
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(c)
heat of solution of NH4Cl(s)
)Hmo = +15.13 kJ molG1 of NH4Cl(s)
(d)
heat of combustion of C2H6(g)
)Hmo = !1371 kJ molG1 of C2H6(g)
(e)
heat of fusion of BaBr2
)Hmo = +25.1 kJ molG1 of BaBr2(s)
(f)
heat of vaporization of CH3CHO
)Hmo = +29 kJ molG1 of CH3CHO(l)
39.
Define or explain: internal energy, enthalpy, state function, path dependent function, heat, pressurevolume work, enthalpy of formation, reference form of an element, standard state of solids, liquids,
gases, first law of thermodynamics, law of conservation of energy. See text for answers.
40.
Define and give several examples of each: intensive and extensive properties.
Answers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
18
(a) DU = !355 J
(b) DU = !88 J
w = 405 J DU = 680 J
DV = 9.03 L w = !723 J DU = !1073 J
w = !12.9 kJ
(a)
)Hm = !60.53 kJ molG1 of IG
)Hm = !121.7 kJ molG1 of I2
(b)
!6.053 kJ
(c)
1.634 g I2
q(combustion) = !1.794 x 104 kJ
i.e. 1.794 x 104 kJ evolved.
!3348 kJ
109 kJ
802 g NaCl
(a) 24.7 J g G1 (b) 5.10 kJ molG1
5.67 x 102 kJ
(a) 2.395 kJ KG1 or 2.395 kJ °CG1 (b) 6.220 x 103 g Cu
TF(Fe) = 65.0°C TF(Au) = 175°C
(a) 34.2 kJ
(b) Doubling the volume of the solution doubles its mass. The heat capacity will
double as its mass doubles. C(new) = 9.24 kJ °CG1
0.395 J gG1 °CG1
TF = 32.0°C
oven T = 134.7°C
(a) )U = Uproducts ! Ureactants = qv (heat exchanged with surroundings at constant volume)
)H = Hproducts ! Hreactants = qp (heat exchanged with surroundings at constant pressure)
Note: H and U are system properties, heat is not.
(b)
)H in kJ the heat (enthalpy) of reaction for an equation exactly as written, is an extensive
property dependent on the molar amounts of reactants consumed and products formed.
Hence doubling all the co!efficients in the equation doubles the value of )H. )H in kJ
molG1 of substance is an intensive property (a constant).
)H(kJ) = < (co!efficient of substance in moles) x )Hm (kJ molG1 of substance).
8
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
)U = !2214.9 kJ
)U = !153.43 kJ
)Um = ! 6.32 x 103 kJ molG1 )Hm = !6.34 x 103 kJ molG1
C = 38.0 kJ KG1
mass hexane = 3.045 g
!56.2 kJ molG1 HCl !56.2 kJ molG1 NH3
!194 kJ molG1 CaO !97.0 kJ molG1 HCl
21.72°C
)H° = !336.6 kJ
)H° = !86 kJ
)Ho = !125 kJ
)Ho = +50.5 kJ
(a) )Ho = !1196.4 kJ (b) )Ho = !2674.9 kJ
)Um = !3226 kJ molG1 and )Hm = !3227 kJ molG1
(a) !9098 kJ (b) !4549 kJ molG1 B5H9, !1820 kJ molG1 B2O3 (c) 2.18 g B5H9
!20.6 kJ molG1 H2S(g)
(a) CuO is L.R. (b) 301 g ice (c) qv = 100 kJ (d) )Um = )Hm = !401 kJ molG1 of CuO
(e) )H = !1.20 x 103 kJ
1.12 x 105 J
Final temperature of water = 36.5°C
(a)
2 K(s) + C(gr) + 32 O2(g) → K2CO3(s)
)Ho = !1146 kJ
or
4 K(s) + 2 C(gr) + 3 O2(g) → 2 K2CO3(s)
)Ho = !2292 kJ
(b)
H2S(aq) + 2 NaOH(aq) → Na2S(aq) + 2 H2O(l) )Ho = !32.4 kJ
(c)
NH4Cl(s) → NH4Cl(aq)
)Ho = +15.13 kJ
(d)
or
(e)
(f)
40.
C2H6(g) + 72 O2(g) → 2 CO2(g) + 3 H2O(l)
2 C2H6(g) + 7O2(g) → 4 CO2(g) + 6 H2O(l)
BaBr2(s) → BaBr2(l)
CH3CHO(l) → CH3CHO(g)
)Ho = !1371 kJ
)Ho = !2742 kJ
)Ho = +25.1 kJ
)Ho = +29 kJ
Intensive (independent of amount) e.g. all molar quantities i.e molar heat capacities, molar
enthalpy changes, density, all concentration terms, specific heat capacities, percent composition
of a compound.
Extensive (depend on amount) )H of a reaction for an equation exactly as written, mass, heat,
moles, volume, )U of a reaction for an equation exactly as written, heat capacity.
Note: The true SI unit for enthalpy (heat) of reaction as an extensive property is kJ molG 1 of
reaction. Our text, Petrucci 10th edition, drops the molG1 of reaction in Chapter 7.
Physical chemists differentiate between enthalpy (heat) of reaction as an extensive property
and as an intensive property (molar enthalpy change), which appears to have the same
units, kJ molG1, by using the subscript “m” for molar enthalpy change i.e. )Hm and
sometimes by using the bar notation ∆H .
Developed by Dr. Chris Flinn
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