10: Thermodynamics
- Page ID
- 285680
Energy
Exercise \(\PageIndex{1.1}\)
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Express the quantity of 422 J in calories.
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Express the quantity of 3.225 kJ in calories.
- Answer
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- 101 cal
\(422 J\left ( \frac{1 calorie}{4.184 } \right )=101 calorie\)
- 770.8 cal
Exercise \(\PageIndex{1.2}\)
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Express the quantity 55.69 cal in joules.
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Express the quantity 965.3 kcal in joules.
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Express the quantity 965.3 Cal in joules.
- Answer
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- 233.0 joules
\(55.69 cal\left ( \frac{4.184 J}{1 cal} \right )=233.0 J\)
- 4.039 x 106 joules
- 4.039 x 106 joules (Cal is kcal)
Heat Capacity
Exercise \(\PageIndex{2.1}\)
The specific heat capacity of water(liquid) is 4.18 J/g⋅°C. What is the molar specific heat capacity of this substance? The molar mass of water is 18.01 g/mol.
- Answer
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75.3 J/mol * °C
\(c_{m}=\frac{4.18 J}{\left ( \frac{1}{18.01} mol * °C\right )}=75.2818 J/mol * °C\)
Exercise \(\PageIndex{2.2}\)
Exactly 149.6 J will raise the temperature of 10.0 g of a metal from 25.0 °C to 60.0 °C. What is the specific heat capacity of the metal?
- Answer
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0.427 J/(g *°C)
Exercise \(\PageIndex{2.3}\)
A 100 g sample of each of the following metals is heated from 35°C to 45°C. Which metal absorbs the lowest amount of heat energy?
Metal Specific Heat Capacity
Copper 0.385 J/(g*°C)
Magnesium 1.02 J/(g*°C)
Mercury 0.138 J/(g*°C)
Silver 0.237 J/(g*°C)
Lead 0.129 J/(g*°C)
- Answer
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Lead
Exercise \(\PageIndex{2.4}\)
35.0 kJ raises the temperature of an gold object from 22oC to its melting point of 1064.18oC. What is the mass of the gold object?
- Answer
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\[q=mc\Delta T \] [\ m=\frac{q}{c\left ( T_f-T_i \right )}\] \[=\frac{35kJ\left ( \frac{1000J}{kJ} \right )}{\frac{0.129J}{g\cdot ^{o} C}\left (1064.18^{o}C-22^{o}C \right )}=260. g \nonumber\]
Exercise \(\PageIndex{2.5}\)
What is the specific heat capacity in cal/goC of a substance if it takes 5.09 kJ to raise a 30.1 g mass sample of the material from 25.0 to 400.0oC?
- Answer
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\[q=mc\Delta T\\c=\frac{q}{m\left ( T_f-T_i \right )}=\frac{5.09kJ\left ( \frac{1000J}{kJ} \right )\left ( \frac{cal}{4.184J} \right )}{30.1g\left (400.0^{o}C-25.0^{o}C \right )}=0.108\left ( \frac{cal}{g\cdot^{o}C} \right ) \nonumber\]
Exercise \(\PageIndex{2.6}\)
What is the final temperature if 20.0kJ is added to a 340 g of gold at 25.0oC?
- Answer
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\[q=mc\Delta T \\ T_F = T_i+\frac{q}{mc} \\ = 25.0^o+\frac{20.0kJ}{0.340kg(0.108)( \frac{kcal}{kg \cdot^oC)}}=545^oC\nonumber \]
Exercise \(\PageIndex{2.7}\)
35.0 kJ raises the temperature of a 260.0g object from 22oC to its melting point of 1064.18oC. Could the object be gold?
- Answer
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\[q=mc\Delta T\\c=\frac{q}{m\left ( T_f-T_i \right )}=\frac{35.0kJ\left ( \frac{1000J}{kJ} \right )\left ( \frac{cal}{4.184J} \right )}{260.0g\left (1064.18.0^{o}C-25.0^{o}C \right )}=0.108\left ( \frac{cal}{g\cdot^{o}C} \right ) \\=0.0309 \\ \text{wrong heat capacity, can not be gold}\nonumber\]
Exercise \(\PageIndex{2.8}\)
How much heat is required to be removed from water for it to cool the temperature of 1.00 liter of water (density = 0.9982g/mL) from 25.0oC to 32.0oF?
- Answer
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\[q=mc\Delta T= 1.00L\left ( 0.9982\frac{kg}{L} \right )4.18J\frac{kJ}{kg \cdot^oC}\left ( 0.00^oC-25.0^oC \right )\\q=-104kJ\]
Exercise \(\PageIndex{2.9}\)
How much heat is required to be removed from ice to cool 1.00 liter of water (density = 0.9982g/mL) from its freezing point to -5.00oC?
- Answer
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\[q=mc\Delta T= 1.00L\left ( 0.9982\frac{kg}{L} \right )2.06\frac{kJ}{kg \cdot^oC}\left ( -5^oC-0^oC \right )\\q=-10.3kJ\]
Energy and Phase Changes
Exercise \(\PageIndex{1}\)
How much energy is needed to convert 5.88 g of ice at 0.00 °C to liquid water at 85.0 °C?
Specific heat capacity (ice) = 2.10 J/g*°C
Specific heat capacity (liquid water) = 4.18 J/g*°C
Heat of fusion = 333 J/g
- Answer
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4.05 * 103 J
\(q_{1} = m\Delta H_{f} = \left ( 5.88 g \right )\left ( 333 J/g \right ) = 1958.04 J\)
\(q_{2} = mc\Delta T = \left ( 5.88 g \right )\left ( 4.18 J/g*°C \right )\left ( 85 °C - 0 °C \right ) = 2089.164 J\)
qTotal = q1 + q2 = 1958.04 J + 2089.164 J = 4047.204 J
Exercise \(\PageIndex{2}\)
Calculate the energy in the form of heat (in kJ) required to convert 125 grams of liquid water at 20.0 °C to steam at 115 °C. Assume that no energy in the form of heat is transferred to the environment. (Heat of fusion = 333 J/g; heat of vaporization = 2256 J/g; specific heat capacities: liquid water = 4.184 J/g*°C, steam = 1.92 J/g*°C)
- Answer
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3.28 * 102 kJ
Exercise \(\PageIndex{3}\)
Calculate the energy in the form of heat (in kJ) required to change 81.5 g of liquid water at 30.6 °C to ice at –13.5 °C. Assume that no energy in the form of heat is transferred to the environment. (Heat of fusion = 333 J/g; heat of vaporization = 2256 J/g; specific heat capacities: ice = 2.06 J/g*°C, liquid water = 4.184 J/g*°C)
- Answer
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-39.8 kJ
Exercise \(\PageIndex{4}\)
What is the minimum mass of ice at 0.0 °C that must be added to 2.50 kg of water to cool the water from 28.0 °C to 9.0 °C? (Heat of fusion = 333 J/g; specific heat capacities: ice = 2.06 J/g*°C, liquid water = 4.184 J/g*°C)
- Answer
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m = 536 g
\(mc\Delta T = mc\Delta T + m\Delta H_{f}\)
\((2500g)(4.184 J/g*°C)(28 °C - 9 °C) = x(4.184 J/g*°C)(9 °C - 0 °C)+ x(333 J/g)\)
\(198740 = x370.656\)
\(x = \frac{198740}{370.656}\)
x = 536.184 g
Exercise \(\PageIndex{5}\)
How much heat is required to be removed from 1.00L water to freeze it at it's freezing point
- Answer
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\[\Delta H=-n\Delta H_f=1.00L\left ( 998.2\frac{g}{L} \right )\frac{mol_{H_2O}}{18.015g}\left ( \frac{6.01kJ}{mol_{H_2O}} \right )= 332kJ\]
First Law of Thermodynamics
Exercise \(\PageIndex{1}\)
If a 55.8 g piece of silver at 75.8°C is placed in 150.0 g of water at 35.2°C, what is the final temperature? Assume that no heat is transferred to the surroundings.
- Answer
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36.0 °C
\((mc_{s}(T_{final}-T_{initial}))_{Ag} + (mc_{s}(T_{final}-T_{initial}))_{H_{2}O} = 0\)
\((55.8 g)(0.240 J/g*°C)(T_{final} - 75.8°C) + (150 g)(4.184 J/g*°C)(T_{final} - 35.2 °C) = 0\)
\(T_{final}(13.392 J/g*°C) -1015.1136 J + T_{final}(627.6 J/g*°C) - (22091.52 J) = 0\)\(T_{final}(640.992 J/g*°C) = 23106.6336 J\)
\(T_{final} = 36.048 °C\)
Exercise \(\PageIndex{2}\)
If a 105.3 g piece of copper pipe at 63.8°C is placed in 94.7 g of water at 27.0°C, what is the final temperature? Assume that no heat is transferred to the surroundings.
- Answer
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30.4 °C
Enthalpy of Reaction
Exercise \(\PageIndex{1}\)
Decide whether each of these reactions is exothermic or endothermic:
- When two chemicals mix their temperature rises
- A solid burns brightly and releases heat, light and sound
- When two chemicals are mixed their temperatures drops
- Two chemicals will only react if you heat them continually
- Plants take in light energy for photosynthesis
- Answer
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- exothermic
- exothermic
- endothermic
- endothermic
- endothermic
Exercise \(\PageIndex{2}\)
What quantity, in moles, of hydrogen is consumed when 185.6 kJ of energy is evolved from the combustion of a mixture of H2(g) and O2(g)?
H2(g) + O2(g) → H2O(l); ΔrH° = –285.8 kJ/mol-rxn
- Answer
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0.6494 moles
\(\frac{185.6 kJ}{285.8 kJ/mol} = 0.649405 moles\)
Exercise \(\PageIndex{3}\)
The following reaction of iron oxide with aluminum is an exothermic reaction.
Fe2O3(s) + 2 Al(s) → 2 Fe(s) + Al2O3(s)
The reaction of 7.50 g of Fe2O3 with excess Al(s) evolves 31.5 kJ of energy in the form of heat. Calculate the enthalpy change per mole of Fe2O3.
- Answer
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-6.71*102 kJ*mol-1 (heat evolved, negative sign)
Exercise \(\PageIndex{4}\)
How much heat is liberated at constant pressure if 0.675 g of calcium carbonate reacts with 45.1 mL of 0.498 M hydrochloric acid?
CaCO3(s) + 2HCl(aq) → CaCl2(aq) + H2O(l) + CO2(g); ΔrH° = –15.2 kJ/mol-rxn
- Answer
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ΔH = -0.103 kJ
Enthalpy Calculations
Hess's Law And Enthalpy of Reaction
Exercise \(\PageIndex{1}\)
What is the overall chemical equation that results from the sum of the given steps?
2 C(s) + 2 H2O(g) → 2 CO(g) + 2 H2(g)
CO(g) + H2O(g) → CO2(g) + H2(g)
CO(g) + 3 H2(g) → CH4(g) + H2O(g)
- Answer
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2 C(s) + 2 H2O(g) → CO2(g) + CH4(g)
Exercise \(\PageIndex{2}\)
Determine the heat of evaporation of carbon disulfide,
CS2(l) → CS2(g)
given the enthalpies of reaction below.
C(s) + 2 S(s) → CS2(l) ΔrH° = +89.4 kJ/mol-rxn
C(s) + 2 S(s) → CS2(g) ΔrH° = +116.7 kJ/mol-rxn
- Answer
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+27.3 kJ
Reverse (1) and add to (2) ΔHrxn = -ΔH1 + ΔH2
(1) CS2(l) →
C(s)+2 S(s)= -89.4 kJ/mol + 116.7 kJ/mol = 27.3 kJ/mol(2)
C(s)+2 S(s)→ CS2(g)
CS2 (l) → CS2 (g)
Enthalpy of Formation
Exercise \(\PageIndex{3}\)
Determine the standard enthalpy of formation of Fe2O3(s) given the thermochemical equations below.
Fe(s) + 3 H2O(l) → Fe(OH)3(s) + 3/2 H2(g) ΔrH° = +160.9 kJ/mol-rxn
H2(g) + 1/2 O2(g) → H2O(l) ΔrH° = –285.8 kJ/mol-rxn
Fe2O3(s) + 3 H2O(l) → 2 Fe(OH)3(s) ΔrH° = +288.6 kJ/mol-rxn
- Answer
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–824.2 kJ/mol-rxn
- (Fe(s) + 3 H2O(l) → Fe(OH)3(s) + 3/2 H2(g) ΔrH° = +160.9 kJ/mol-rxn) * 2
2 Fe(s) + 6 H2O(l) → 2 Fe(OH)3(s) + 3 H2(g) ΔrH° = +321.8 kJ/mol-rxn
- (H2(g) + 1/2 O2(g) → H2O(l) ΔrH° = –285.8 kJ/mol-rxn) * 3
3 H2(g) + 3/2 O2(g) → 3 H2O(l) ΔrH° = –857.4kJ/mol-rxn
- (Fe2O3(s) + 3 H2O(l) → 2 Fe(OH)3(s) ΔrH° = +288.6 kJ/mol-rxn) Reverse Equation or ( * -1)
2 Fe(OH)3(s) → Fe2O3(s) + 3 H2O(l) ΔrH° = -288.6 kJ/mol-rxn
- Add the equations and ΔrH°.
2 Fe(s) +
6 H2O(l)→2 Fe(OH)3(s)+3 H2(g)ΔrH° = +321.8 kJ/mol-rxn3 H2(g)+ 3/2 O2(g) →3 H2O(l)ΔrH° = –857.4kJ/mol-rxn2 Fe(OH)3(s)→ Fe2O3(s) +3 H2O(l)ΔrH° = -288.6 kJ/mol-rxn
2 Fe(s) + 3/2 O2(g) → Fe2O3(s) ΔHf = -824.2 kJ/mol
Exercise \(\PageIndex{4}\)
Determine the standard enthalpy of formation of calcium carbonate from the thermochemical equations given below.
Ca(OH)2(s) → CaO(s) + H2O(l) ΔrH° = 65.2 kJ/mol-rxn
Ca(OH)2(s) + CO2(g) → CaCO3(s) + H2O(l) ΔrH° = −113.8 kJ/mol-rxn
C(s) + O2(g) → CO2(g) ΔrH° = −393.5 kJ/mol-rxn
2 Ca(s) + O2(g) → 2 CaO(s) ΔrH° = −1270.2 kJ/mol-rxn
- Answer
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−1207.6 kJ/mol-rxn
Enthalpy of Reaction from Standard Enthalpies of Formation
Exercise \(\PageIndex{5}\)
Calculate ΔrH° for the combustion of ammonia, using standard molar enthalpies of formation:
4 NH3(g) + 7 O2(g) → 4 NO2(g) + 6 H2O(l)
Molecule ΔfH° (kJ/mol-rxn)
NH3(g) –45.9
NO2(g) +33.1
H2O(l) –285.8
- Answer
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–1398.8 kJ/mol-rxn
ΔH°rxn = Σ ΔH°f(products) - Σ ΔH°f(reactants)
= [(4 * ΔH°f(NO2)) + (6 * ΔH°f(H2O))] - [(4 * ΔH°f(NH3)) + (7 * ΔH°f(O2))]
= [(4 * 33.1) + (6 * -285.8)] - [(4 * -45.9) + (7 * 0)]
= -1398.8 kJ/mol-rxn
Exercise \(\PageIndex{6}\)
What is ΔrH° for the following phase change?
LiF(s) → LiF(l)
Substance ΔH°f (kJ/mol-rxn)
LiF(s) –616.93
LiF(l) –598.65
- Answer
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18.28 kJ/mol-rxn