Enthalpy - Summary - UCalgary Chemistry Textbook

Key Concepts and Summary

If a chemical change is carried out at constant pressure and the only work done is caused by expansion or contraction, $q$ for the change is called the enthalpy change with the symbol $ΔH$, or $ΔH°$ for reactions occurring under standard state conditions at 298 K. The value of ΔH for a reaction in one direction is equal in magnitude, but opposite in sign, to ΔH for the reaction in the opposite direction, and ΔH is directly proportional to the quantity of reactants and products. The standard enthalpy of formation, $ΔH_f°$ is the enthalpy change accompanying the formation of 1 mole of a substance from the elements in their most stable states at 1 bar and 298.15 K. If the enthalpies of formation are available for the reactants and products of a reaction, the enthalpy change can be calculated using Hess’s law: If a process can be written as the sum of several stepwise processes, the enthalpy change of the total process equals the sum of the enthalpy changes of the various steps.

Key Equations

$ΔU=q+w$

$ΔH°_{reaction}=∑n×ΔH_f°_{(products)}−∑n×ΔH_f°_{(reactants)}$

Practice Questions

Calculate the enthalpy of solution (ΔH for the dissolution) per mole of CaCl₂.

Solution

81 kJ mol⁻¹

Although the gas used in an oxyacetylene torch is essentially pure acetylene, the heat produced by combustion of one mole of acetylene in such a torch is likely not equal to the enthalpy of combustion of acetylene listed in the table on this page. Considering the conditions for which the tabulated data are reported, suggest an explanation.

How much heat is produced by burning 4.00 moles of acetylene under standard state conditions?

Solution

5204.4 kJ

How much heat is produced by combustion of 125 g of methanol under standard state conditions?

How many moles of isooctane must be burned to produce 100 kJ of heat under standard state conditions?

Solution

$1.83×10^{-2}$ mol

What mass of carbon monoxide must be burned to produce 175 kJ of heat under standard state conditions?

When 2.50 g of methane burns in oxygen, 125 kJ of heat is produced. What is the enthalpy of combustion per mole of methane under these conditions?

Solution

–802 kJ mol⁻¹

How much heat is produced when 100 mL of 0.250 M HCl (density, 1.00 g/mL) and 200 mL of 0.150 M NaOH (density, 1.00 g/mL) are mixed?

HCl (a q) + NaOH (a q) ⟶ NaCl (a q) + H_{2} O (l) Δ H ° = −58 kJ

If both solutions are at the same temperature and the heat capacity of the products is 4.19 J/g °C, how much will the temperature increase? What assumption did you make in your calculation?

A sample of 0.562 g of carbon is burned in oxygen in a bomb calorimeter, producing carbon dioxide. Assume both the reactants and products are under standard state conditions, and that the heat released is directly proportional to the enthalpy of combustion of graphite. The temperature of the calorimeter increases from 26.74 °C to 27.93 °C. What is the heat capacity of the calorimeter and its contents?

Solution

15.5 kJ/ºC

Before the introduction of chlorofluorocarbons, sulfur dioxide (enthalpy of vaporization, 6.00 kcal/mol) was used in household refrigerators. What mass of SO₂ must be evaporated to remove as much heat as evaporation of 1.00 kg of CCl₂F₂ (enthalpy of vaporization is 17.4 kJ/mol)?

The vaporization reactions for SO₂ and CCl₂F₂ are

{SO}_{2} (l) ⟶ {SO}_{2} (g)

and

{CCl}_{2} F (l) ⟶ {CCl}_{2} F_{2} (g),

respectively.

Homes may be heated by pumping hot water through radiators. What mass of water will provide the same amount of heat when cooled from 95.0 to 35.0 °C, as the heat provided when 100 g of steam is cooled from 110 °C to 100 °C.

Solution

7.43 g

Which of the enthalpies of combustion in in the table on this page are also standard enthalpies of formation?

Does the standard enthalpy of formation of H₂O(g) differ from ΔH° for the reaction

{2H}_{2} (g) + O_{2} (g) ⟶ 2 H_{2} O (g) ?

Solution

Yes. Water in this example is not in its standard state.

Joseph Priestly prepared oxygen in 1774 by heating red mercury(II) oxide with sunlight focused through a lens. How much heat is required to decompose exactly 1 mole of red HgO(s) to Hg(l) and O₂(g) under standard conditions?

How many kilojoules of heat will be released when exactly 1 mole of manganese, Mn, is burned to form Mn₃O₄(s) at standard state conditions?

Solution

459.6 kJ

How many kilojoules of heat will be released when exactly 1 mole of iron, Fe, is burned to form Fe₂O₃(s) at standard state conditions?

The following sequence of reactions occurs in the commercial production of aqueous nitric acid:

4 {NH}_{3} (g) + 5 O_{2} (g) ⟶ 4 NO (g) + 6 H_{2} O (l) Δ H = −907 kJ

2 NO (g) + O_{2} (g) ⟶ 2 {NO}_{2} (g) Δ H = −113 kJ

3 {NO}_{2} + H_{2} O (l) ⟶ 2 {HNO}_{3} (a q) + NO (g) Δ H = −139 kJ

Determine the total energy change for the production of one mole of aqueous nitric acid by this process.

Solution

−494 kJ/mol

Both graphite and diamond burn.

C (s, diamond) + O_{2} (g) ⟶ {CO}_{2} (g)

For the conversion of graphite to diamond:

C (s, graphite) ⟶ C (s, diamond) Δ H ° = 1.90 kJ

Which produces more heat, the combustion of graphite or the combustion of diamond?

From the molar heats of formation in this appendix, determine how much heat is required to evaporate one mole of water:

H_{2} O (l) ⟶ H_{2} O (g)

Solution

44.01 kJ/mol

Which produces more heat?

Os (s) ⟶ 2 O_{2} (g) ⟶ {OsO}_{4} (s)

Os (s) ⟶ 2 O_{2} (g) ⟶ {OsO}_{4} (g)

for the phase change

{OsO}_{4} (s) ⟶ {OsO}_{4} (g) Δ H = 56.4 kJ

Calculate

Δ H °

for the process

Sb (s) + \frac{5}{2} {Cl}_{2} (g) ⟶ {SbCl}_{5} (s)

from the following information:

\begin{array}{l} Sb (s) + \frac{3}{2} {Cl}_{2} (g) ⟶ {SbCl}_{3} (s) Δ H ° = −314 kJ \\ {SbCl}_{3} (s) + {Cl}_{2} (g) ⟶ {SbCl}_{5} (s) Δ H ° = −80 kJ \end{array}

Solution

−394 kJ

Calculate

Δ H °

for the process

Zn (s) + S (s) + 2 O_{2} (g) ⟶ {ZnSO}_{4} (s)

from the following information:

\begin{array}{l} Zn (s) + S (s) ⟶ ZnS (s) Δ H ° = −206.0 kJ \\ ZnS (s) + {2O}_{2} (g) ⟶ {ZnSO}_{4} (s) Δ H ° = −776.8 kJ \end{array}

Calculate ΔH for the process

{Hg}_{2} {Cl}_{2} (s) ⟶ 2 Hg (l) + {Cl}_{2} (g)

from the following information:

\begin{array}{l} Hg (l) + {Cl}_{2} (g) ⟶ {HgCl}_{2} (s) Δ H = −224 kJ \\ Hg (l) + {HgCl}_{2} (s) ⟶ {Hg}_{2} {Cl}_{2} (s) Δ H = −41.2 kJ \end{array}

Solution

265 kJ

Calculate the standard molar enthalpy of formation of NO(g) from the following data:

\begin{array}{l} N_{2} (g) + 2 O_{2} ⟶ 2 {NO}_{2} (g) Δ H ° = 66.4 kJ \\ 2NO (g) + O_{2} ⟶ 2 {NO}_{2} (g) Δ H ° = −114.1 kJ \end{array}

Solution

90.3 kJ/mol

Using the data in this appendix, calculate the standard enthalpy change for each of the following reactions:

(a)

N_{2} (g) + O_{2} (g) ⟶ 2 NO (g)

(b)

Si (s) + 2 {Cl}_{2} (g) ⟶ {SiCl}_{4} (g)

(c)

{Fe}_{2} O_{3} (s) + 3 H_{2} (g) ⟶ 2 Fe (s) + 3 H_{2} O (l)

(d)

2 LiOH (s) + {CO}_{2} (g) ⟶ {Li}_{2} {CO}_{3} (s) + H_{2} O (g)

Using the data in this appendix, calculate the standard enthalpy change for each of the following reactions:

(a)

Si (s) + 2 F_{2} (g) ⟶ {SiF}_{4} (g)

(b)

2 C (s) + 2 H_{2} (g) + O_{2} (g) ⟶ {CH}_{3} {CO}_{2} H (l)

(c)

{CH}_{4} (g) + N_{2} (g) ⟶ HCN (g) + {NH}_{3} (g);

(d)

{CS}_{2} (g) + 3 {Cl}_{2} (g) ⟶ {CCl}_{4} (g) + S_{2} {Cl}_{2} (g)

Solution

(a) −1615.0 kJ mol⁻¹; (b) −484.3 kJ mol⁻¹; (c) 164.2 kJ; (d) −232.1 kJ

The following reactions can be used to prepare samples of metals. Determine the enthalpy change under standard state conditions for each.

(a)

2 {Ag}_{2} O (s) ⟶ 4 Ag (s) + O_{2} (g)

(b)

SnO (s) + CO (g) ⟶ Sn (s) + {CO}_{2} (g)

(c)

{Cr}_{2} O_{3} (s) + 3 H_{2} (g) ⟶ 2 Cr (s) + 3 H_{2} O (l)

(d)

2 Al (s) + {Fe}_{2} O_{3} (s) ⟶ {Al}_{2} O_{3} (s) + 2 Fe (s)

The decomposition of hydrogen peroxide, H₂O₂, has been used to provide thrust in the control jets of various space vehicles. Using the data in this appendix, determine how much heat is produced by the decomposition of exactly 1 mole of H₂O₂ under standard conditions.

2 H_{2} O_{2} (l) ⟶ 2 H_{2} O (g) + O_{2} (g)

Solution

−54.04 kJ mol⁻¹

Calculate the enthalpy of combustion of propane, C₃H₈(g), for the formation of H₂O(g) and CO₂(g). The enthalpy of formation of propane is −104 kJ/mol.

Calculate the enthalpy of combustion of butane, C₄H₁₀(g) for the formation of H₂O(g) and CO₂(g). The enthalpy of formation of butane is −126 kJ/mol.

Solution

−2660 kJ mol⁻¹

Both propane and butane are used as gaseous fuels. Which compound produces more heat per gram when burned?

The white pigment TiO₂ is prepared by the reaction of titanium tetrachloride, TiCl₄, with water vapor in the gas phase:

{TiCl}_{4} (g) + 2 H_{2} O (g) ⟶ {TiO}_{2} (s) + 4 HCl (g) .

How much heat is evolved in the production of exactly 1 mole of TiO₂(s) under standard state conditions?

Solution

67.1 kJ

Water gas, a mixture of H₂ and CO, is an important industrial fuel produced by the reaction of steam with red hot coke, essentially pure carbon:

C (s) + H_{2} O (g) ⟶ CO (g) + H_{2} (g) .

(a) Assuming that coke has the same enthalpy of formation as graphite, calculate

Δ H °

for this reaction.

(b) Methanol, a liquid fuel that could possibly replace gasoline, can be prepared from water gas and additional hydrogen at high temperature and pressure in the presence of a suitable catalyst:

2 H_{2} (g) + CO (g) ⟶ {CH}_{3} OH (g) .

Under the conditions of the reaction, methanol forms as a gas. Calculate

Δ H °

for this reaction and for the condensation of gaseous methanol to liquid methanol.

In the early days of automobiles, illumination at night was provided by burning acetylene, C₂H₂. Though no longer used as auto headlamps, acetylene is still used as a source of light by some cave explorers. The acetylene is (was) prepared in the lamp by the reaction of water with calcium carbide, CaC₂:

{CaC}_{2} (s) + 2 H_{2} O (l) ⟶ Ca {(OH)}_{2} (s) + C_{2} H_{2} (g) .

Calculate the standard enthalpy of the reaction. The

Δ H_{f}^{°}

of CaC₂ is −15.14 kcal/mol.

Solution

−122.8 kJ

From the data in [link], determine which of the following fuels produces the greatest amount of heat per gram when burned under standard conditions: CO(g), CH₄(g), or C₂H₂(g).

The enthalpy of combustion of hard coal averages −35 kJ/g, that of gasoline, $1.28×10^5$ kJ/gal. How many kilograms of hard coal provide the same amount of heat as is available from 1.0 gallon of gasoline? Assume that the density of gasoline is 0.692 g/mL (the same as the density of isooctane).

Solution

3.7 kg

Ethanol, C₂H₅OH, is used as a fuel for motor vehicles, particularly in Brazil.

(a) Write the balanced equation for the combustion of ethanol to CO₂(g) and H₂O(g), and, using the data in this appendix, calculate the enthalpy of combustion of 1 mole of ethanol.

(b) The density of ethanol is 0.7893 g/mL. Calculate the enthalpy of combustion of exactly 1 L of ethanol.

(c) Assuming that an automobile’s mileage is directly proportional to the heat of combustion of the fuel, calculate how much farther an automobile could be expected to travel on 1 L of gasoline than on 1 L of ethanol. Assume that gasoline has the heat of combustion and the density of n–octane, C₈H₁₈

(Δ H_{f}^{°} = −208.4 kJ/mol;

density = 0.7025 g/mL).

Among the substances that react with oxygen and that have been considered as potential rocket fuels are diborane [B₂H₆, produces B₂O₃(s) and H₂O(g)], methane [CH₄, produces CO₂(g) and H₂O(g)], and hydrazine [N₂H₄, produces N₂(g) and H₂O(g)]. On the basis of the heat released by 1.00 g of each substance in its reaction with oxygen, which of these compounds offers the best possibility as a rocket fuel? The

Δ H_{f}^{°}

of B₂H₆(g), CH₄(g), and N₂H₄(l) may be found in this appendix.

Solution

On the assumption that the best rocket fuel is the one that gives off the most heat, B₂H₆ is the prime candidate.

How much heat is produced when 1.25 g of chromium metal reacts with oxygen gas under standard conditions?

Ethylene, C₂H₄, a byproduct from the fractional distillation of petroleum, is fourth among the 50 chemical compounds produced commercially in the largest quantities. About 80% of synthetic ethanol is manufactured from ethylene by its reaction with water in the presence of a suitable catalyst.

C_{2} H_{4} (g) + H_{2} O (g) ⟶ C_{2} H_{5} OH (l)

Using the data in the table in this appendix, calculate ΔH° for the reaction.

Solution

−88.2 kJ

The oxidation of the sugar glucose, C₆H₁₂O₆, is described by the following equation:

C_{6} H_{12} O_{6} (s) + 6 O_{2} (g) ⟶ 6 {CO}_{2} (g) + 6 H_{2} O (l) Δ H = −2816 kJ

The metabolism of glucose gives the same products, although the glucose reacts with oxygen in a series of steps in the body.

(a) How much heat in kilojoules can be produced by the metabolism of 1.0 g of glucose?

(b) How many Calories can be produced by the metabolism of 1.0 g of glucose?

Propane, C₃H₈, is a hydrocarbon that is commonly used as a fuel.

(a) Write a balanced equation for the complete combustion of propane gas.

(b) Calculate the volume of air at 25 °C and 1.00 atmosphere that is needed to completely combust 25.0 grams of propane. Assume that air is 21.0 percent O₂ by volume. (Hint: We will see how to do this calculation in a later chapter on gases—for now use the information that 1.00 L of air at 25 °C and 1.00 atm contains 0.275 g of O₂ per liter.)

Δ H_{f}^{°}

of propane given that

Δ H_{f}^{°}

of H₂O(l) = −285.8 kJ/mol and

Δ H_{f}^{°}

of CO₂(g) = −393.5 kJ/mol.

(d) Assuming that all of the heat released in burning 25.0 grams of propane is transferred to 4.00 kilograms of water, calculate the increase in temperature of the water.

Solution

(a)

C_{3} H_{8} (g) + 5 O_{2} (g) ⟶ 3 {CO}_{2} (g) + 4 H_{2} O (l);

(b) 330 L; (c) −104.5 kJ mol⁻¹; (d) 75.4 °C

During a recent winter month in Sheboygan, Wisconsin, it was necessary to obtain 3500 kWh of heat provided by a natural gas furnace with 89% efficiency to keep a small house warm (the efficiency of a gas furnace is the percent of the heat produced by combustion that is transferred into the house).

(a) Assume that natural gas is pure methane and determine the volume of natural gas in cubic feet that was required to heat the house. The average temperature of the natural gas was 56 °F; at this temperature and a pressure of 1 atm, natural gas has a density of 0.681 g/L.

(b) How many gallons of LPG (liquefied petroleum gas) would be required to replace the natural gas used? Assume the LPG is liquid propane [C₃H₈: density, 0.5318 g/mL; enthalpy of combustion, 2219 kJ/mol for the formation of CO₂(g) and H₂O(l)] and the furnace used to burn the LPG has the same efficiency as the gas furnace.

(d) What mass of water is produced by combustion of the methane used to heat the house?

(e) What volume of air is required to provide the oxygen for the combustion of the methane used to heat the house? Air contains 23% oxygen by mass. The average density of air during the month was 1.22 g/L.

(f) How many kilowatt–hours (1 kWh = $3.6×10^6$ J) of electricity would be required to provide the heat necessary to heat the house? Note electricity is 100% efficient in producing heat inside a house.

(g) Although electricity is 100% efficient in producing heat inside a house, production and distribution of electricity is not 100% efficient. The efficiency of production and distribution of electricity produced in a coal-fired power plant is about 40%. A certain type of coal provides 2.26 kWh per pound upon combustion. What mass of this coal in kilograms will be required to produce the electrical energy necessary to heat the house if the efficiency of generation and distribution is 40%?