General Chemistry: Principles and Modern Applications

Ralph H. Petrucci, F. Geoffrey Herring, Jeffry D. Madura, Carey Bissonnette

Chapter 7 Thermochemistry - all with Video Answers

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Chapter Questions

04:18

Problem 1

Calculate the quantity of heat, in kilojoules, (a) required to raise the temperature of 9.25 Lof water from
22.0 to $29.4^{\circ} \mathrm{C} ;$ (b) associated with a $33.5^{\circ} \mathrm{C}$ decrease in temperature in a $5.85 \mathrm{kg}$ aluminum bar (specific heat capacity of aluminum $=0.903 \mathrm{Jg}^{-1} \mathrm{C}^{-1}$ ).

Bhumika Jayee

Numerade Educator

03:13

Problem 2

Calculate the final temperature that results when (a) a
12.6 g sample of water at $22.9^{\circ} \mathrm{C}$ absorbs $875 \mathrm{J}$ of heat;
(b) a 1.59 kg sample of platinum at $78.2^{\circ} \mathrm{C}$ gives off $1.05 \mathrm{kcal}$ of heat $\left(c_{p}=0.032 \mathrm{cal} \mathrm{g}^{-1} \mathrm{C}^{-1}\right)$

Brass has a density of $8.40 \mathrm{g} / \mathrm{cm}^{3}$ and a specific heat capacity of $0.385 \mathrm{J}$$g^{-1 \circ} C^{-1}$. $A 15.2 \mathrm{cm}^{3}$ piece of brass at an initial temperature of $163^{\circ} \mathrm{C}$ is dropped into an insulated container with $150.0 \mathrm{g}$ water initially at 22.4 ^ C. What will be the final temperature of the brass-water mixture?

Elham Kordzadeh

Numerade Educator

06:18

Problem 9

A $74.8 \mathrm{g}$ sample of copper at $143.2^{\circ} \mathrm{C}$ is added to an insulated vessel containing $165 \mathrm{mL}$ of glycerol, $\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3}(1)(d=1.26 \mathrm{g} / \mathrm{mL}),$ at $24.8^{\circ} \mathrm{C} .$ The final tem-
perature is $31.1^{\circ} \mathrm{C} .$ The specific heat capacity of copper is $0.385 \mathrm{Jg}^{-1} \mathrm{C}^{-1}$. What is the heat capacity of glycerol in $\mathrm{Jmol}^{-1 \circ} \mathrm{C}^{-1} ?$

How much heat, in kilojoules, is evolved in the complete combustion of (a) $1.325 \mathrm{gC}_{4} \mathrm{H}_{10}(\mathrm{g})$ at $25^{\circ} \mathrm{C}$ and 1 atm; (b) $28.4 \mathrm{LC}_{4} \mathrm{H}_{10}(\mathrm{g})$ at STP;
(c) $12.6 \mathrm{L} \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})$ at $23.6^{\circ} \mathrm{C}$ and $738 \mathrm{mmHg}$ ?Assume that the enthalpy of reaction does not change significantly with temperature or pressure. The complete combustion of butane, $\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g}),$ is represented by the equation $\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{g})+\frac{13}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{CO}_{2}(\mathrm{g})+5 \mathrm{H}_{2} \mathrm{O}(1)$
$$\Delta_{\mathrm{r}} H^{\circ}=-2877 \mathrm{kJ} \mathrm{mol}^{-1}$$

Kaylee Rushlau

Numerade Educator

10:05

Problem 16

Upon complete combustion, the indicated substances evolve the given quantities of heat. Write a balanced equation for the combustion of 1.00 mol of each substance, including the enthalpy of reaction, $\Delta_{\mathrm{r}} H$ for the reaction.
(a) $0.584 \mathrm{g}$ of propane, $\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{g}),$ yields $29.4 \mathrm{kJ}$
(b) $0.136 \mathrm{g}$ of camphor, $\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}(\mathrm{s}),$ yields $5.27 \mathrm{kJ}$
(c) 2.35 mL of acetone, $\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}(1)(d=$ $0.791 \mathrm{g} / \mathrm{mL}),$ yields $58.3 \mathrm{kJ}$

Elham Kordzadeh

Numerade Educator

08:39

Problem 17

The combustion of methane gas, the principall constituent of natural gas, is represented by the equation
$\mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(1)$
$$\Delta_{\mathrm{r}} H^{\circ}=-890.3 \mathrm{kJ} \mathrm{mol}^{-1}$$
(a) What mass of methane, in kilograms, must be burned to liberate $2.80 \times 10^{7} \mathrm{kJ}$ of heat?
(b) What quantity of heat, in kilojoules, is liberated in the complete combustion of $1.65 \times 10^{4} \mathrm{L}$ of $\mathrm{CH}_{4}(\mathrm{g})$ measured at $18.6^{\circ} \mathrm{C}$ and $768 \mathrm{mmHg} ?$
(c) If the quantity of heat calculated in part (b) could be transferred with $100 \%$ efficiency to water, what volume of water, in liters, could be heated from 8.8 to $60.0^{\circ} \mathrm{C}$ as a result?

Kaylee Rushlau

Numerade Educator

07:26

Problem 18

Refer to the Integrative Example. What volume of the synthesis gas, measured at STP and burned in an open flame (constant-pressure process), is required to heat 40.0 gal of water from 15.2 to $65.0^{\circ} \mathrm{C}$ ? (1 gal $=3.785$ L.)

Ronald Prasad

Numerade Educator

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Problem 19

The combustion of hydrogen-oxygen mixtures is used to produce very high temperatures (approximately $2500^{\circ} \mathrm{C}$ ) needed for certain types of welding operations. Consider the reaction to be
$$\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \Delta_{\mathrm{r}} H^{\circ}=-241.8 \mathrm{kJ} \mathrm{mol}^{-1}$$
What is the quantity of heat evolved, in kilojoules, when a $180 \mathrm{g}$ mixture containing equal parts of $\mathrm{H}_{2}$ and $\mathrm{O}_{2}$ by mass is burned?

Susan Hallstrom

Numerade Educator

06:36

Problem 20

Thermite mixtures are used for certain types of welding, and the thermite reaction is highly exothermic.
$\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Fe}(\mathrm{s})$
$$\Delta_{\mathrm{r}} H^{\circ}=-852 \mathrm{kJ} \mathrm{mol}^{-1}$$
$1.00 \mathrm{mol}$ of granular $\mathrm{Fe}_{2} \mathrm{O}_{3}$ and $2.00 \mathrm{mol}$ of granular Al are mixed at room temperature $\left(25^{\circ} \mathrm{C}\right),$ and a reaction is initiated. The liberated heat is retained within the products, whose combined specific heat capacity over a broad temperature range is about $0.8 \mathrm{Jg}^{-1 \circ} \mathrm{C}^{-1}$. (The melting point of iron is $1530^{\circ} \mathrm{C}$.) Show that the quantity of heat liberated is more than sufficient to raise the temperature of the products to the melting point of iron.

The enthalpy of vaporization for $\mathrm{N}_{2}(1)$ is $5.56 \mathrm{kJ} / \mathrm{mol}$ How much heat (in J) is required to produce $1.0 \mathrm{L}$ of $\mathrm{N}_{2}(\mathrm{g})$ at $77.36 \mathrm{K}$ and $1.0 \mathrm{atm} ?$

Elham Kordzadeh

Numerade Educator

01:12

Problem 35

A sample gives off 5228 cal when burned in a bomb calorimeter. The temperature of the calorimeter assembly increases by $4.39^{\circ} \mathrm{C}$. Calculate the heat capacity of the calorimeter, in kilojoules per degree Celsius.

The oxidation of $\mathrm{NH}_{3}(\mathrm{g})$ to $\mathrm{NO}(\mathrm{g})$ in the Ostwald process must be very carefully controlled in terms of temperature, pressure, and contact time with the catalyst. This is because the oxidation of $\mathrm{NH}_{3}(\mathrm{g})$ can yield any one of the products $\mathrm{N}_{2}(\mathrm{g}), \mathrm{N}_{2} \mathrm{O}(\mathrm{g}), \mathrm{NO}(\mathrm{g})$
and $\mathrm{NO}_{2}(\mathrm{g}),$ depending on conditions. Show that oxidation of $\mathrm{NH}_{3}(\mathrm{g})$ to $\mathrm{N}_{2}(\mathrm{g})$ is the most exothermic of the four possible reactions.

Ronald Prasad

Numerade Educator

05:53

Problem 118

In the Are You Wondering $7-1$ box, the temperature variation of enthalpy is discussed, and the equation $q_{p}=$ heat capacity $\times$ temperature change $=C_{p} \times \Delta T$ was introduced to show how enthalpy changes with temperature for a constant-pressure process. Strictly speaking, the heat capacity of a substance at constant pressure is the slope of the line representing the variation of enthalpy (H) with temperature, that is
$C_{p}=\frac{d H}{d T} \quad$ (at constant pressure)
where $C_{p}$ is the heat capacity of the substance in question. Heat capacity is an extensive quantity and heat capacities are usually quoted as molar heat capacities $C_{p, \mathrm{m}},$ the heat capacity of one mole of substance, which is an intensive property. The heat capacity at constant pressure is used to estimate the change in enthalpy due to a change in temperature. For infinitesimal changes in temperature,
$d H=C_{p} d T \quad$ (at constant pressure)
To evaluate the change in enthalpy for a particular temperature change, from $T_{1}$ to $T_{2}$, we write
$\int_{H\left(T_{1}\right)}^{H\left(T_{2}\right)} d H=H\left(T_{2}\right)-H\left(T_{1}\right)=\int_{T_{1}}^{T_{2}} C_{p} d T$
If we assume that $C_{p}$ is independent of temperature, then we recover equation (7.5)
$q_{p}=\Delta H=C_{p} \Delta T$
On the other hand, we often find that the heat capacity is a function of temperature; a convenient empirical expression is
$C_{p, \mathrm{m}}=a+b T+\frac{c}{T^{2}}$
What is the change in molar enthalpy of $\mathrm{N}_{2}$ when it is heated from $25.0^{\circ} \mathrm{C}$ to $100.0^{\circ} \mathrm{C}$ ? The molar heat capacity of nitrogen is given by
$C_{p, \mathrm{m}}=\left(28.58+3.77 \times 10^{-3} T-\frac{0.5 \times 10^{5}}{T^{2}}\right) \mathrm{Jmol}^{-1} \mathrm{K}^{-1}$

Refer to Example $7-5$ dealing with the work done by 0.100 mol He at $298 \mathrm{K}$ in expanding in a single step from 2.40 to 1.20 atm. Review also the two-step expansion $(2.40 \mathrm{atm} \longrightarrow 1.80 \mathrm{atm} \longrightarrow 1.20 \mathrm{atm})$
described on page 261 (see Figure $7-11$ ).
(a) Determine the total work that would be done if the He expanded in a series of steps, at 0.10 atm intervals, from 2.40 to 1.20 atm.
(b) Represent this total work on the graph below, in which the quantity of work done in the two-step expansion is represented by the sum of the colored rectangles.
(c) Show that the maximum amount of work would occur if the expansion occurred in an infinite number of steps. To do this, express each infinitesimal quantity of work as $d w=-P d V$ and use the methods of integral calculus (integration) to sum these quantities. Assume ideal behavior for the gas.
(d) Imagine reversing the process, that is, compressing the He from 1.20 to 2.40 atm. What are the maximum and minimum amounts of work required to produce this compression? Explain.
(e) In the isothermal compression described in part (d), what is the change in internal energy assuming ideal gas behavior? What is the value of $q ?$
(f) Using the formula for the work derived in part (c), obtain an expression for $q / T$. Is this new function a state function? Explain.

Construct a concept map to show the interrelationships between path-dependent and pathindependent quantities in thermodynamics.

Elham Kordzadeh

Numerade Educator