Chapter 6

Define energy, kinetic energy, potential energy, and internal energy.

Define the joule in terms of SI base units.

What is the original definition of the calorie? What is the present definition?

Describe the interconversions of potential and kinetic energy in a moving pendulum. A moving pendulum eventually comes to rest. Has the energy been lost? If not, what has happened to it?

Suppose heat flows into a vessel containing a gas. As the heat flows into the gas, what happens to the gas molecules? What happens to the internal energy of the gas?

Define an exothermic reaction and an endothermic reaction. Give an example of each.

The internal energy of a substance is a state function. What does this mean?

Under what condition is the enthalpy change equal to the heat of reaction?

How does the enthalpy change for an endothermic reaction occurring at constant pressure?

Why is it important to give the states of the reactants and products when giving an equation for \(\Delta H ?\)

If an equation for a reaction is doubled and then reversed, how is the value of \(\Delta H\) changed?

Define the heat capacity of a substance. Define the specific heat of a substance.

Describe a simple calorimeter. What measurements are needed to determine the heat of reaction?

What property of enthalpy provides the basis of Hess's law? Explain.

You discover that you cannot carry out a particular reaction for which you would like the enthalpy change. Does this mean that you will be unable to obtain this enthalpy change? Explain.

What is meant by the thermodynamic standard state?

What is meant by the reference form of an element? What is the standard enthalpy of formation of an element in its reference form?

What is meant by the standard enthalpy of formation of a substance?

Write the chemical equation for the formation reaction of \(\mathrm{H}_{2} \mathrm{~S}(g)\).

Is the following reaction the appropriate one to use in determining the enthalpy of formation of methane, \(\mathrm{CH}_{4}(g) ?\) Why or why not? $$ \mathrm{C}(g)+4 \mathrm{H}(g) \longrightarrow \mathrm{CH}_{4}(g) $$

What is a fuel? What are the fossil fuels?

Give chemical equations for the conversion of carbon in coal to methane, \(\mathrm{CH}_{4}\).

The equation for the combustion of \(2 \mathrm{~mol}\) of butane can be written $$ 2 \mathrm{C}_{4} \mathrm{H}_{10}(g)+\mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H<\mathrm{O} $$ Which of the following produces the least heat? a. Burning 1 mol of butane. b. Reacting \(1 \mathrm{~mol}\) of oxygen with excess butane. c. Burning enough butane to produce \(1 \mathrm{~mol}\) of carbon dioxide. d. Burning enough butane to produce 1 mol of water. e. All of the above reactions \((a, b, c\), and \(d)\) produce the same amount of heat.

A \(5.0-\mathrm{g}\) sample of water starting at \(60.0^{\circ} \mathrm{C}\) loses \(418 \mathrm{~J}\) of energy in the form of heat. What is the final temperature of the water after this heat loss? a. \(20 .{ }^{\circ} \mathrm{C}\) b. \(40 .{ }^{\circ} \mathrm{C}\) c. \(50 .{ }^{\circ} \mathrm{C}\) d. \(60 .{ }^{\circ} \mathrm{C}\) e. \(80 .{ }^{\circ} \mathrm{C}\)

Hypothetical elements \(\mathrm{A}_{2}\) and \(\mathrm{B}_{2}\) react according to the following equation, forming the compound \(\mathrm{AB}\). $$ \mathrm{A}_{2}(a q)+\mathrm{B}_{2}(a q) \longrightarrow 2 \mathrm{AB}(a q) ; \Delta H^{\circ}=+271 \mathrm{~kJ} / \mathrm{mol} $$ If solutions \(\mathrm{A}_{2}(a q)\) and \(\mathrm{B}_{2}(a q)\), starting at the same temperature, are mixed in a coffee-cup calorimeter, the reaction that occurs is a. exothermic, and the temperature of the resulting solution rises. b. endothermic, and the temperature of the resulting solution rises. c. endothermic, and the temperature of the resulting solution falls. d. exothermic, and the temperature of the resulting solution falls. e. exothermic or endothermic, depending on the original and final temperatures.

Part 1: In an insulated container, you mix 200. g of water at \(80^{\circ} \mathrm{C}\) with \(100 . \mathrm{g}\) of water at \(20^{\circ} \mathrm{C}\). After mixing, the temperature of the water is \(60^{\circ} \mathrm{C}\). a. How much did the temperature of the hot water change? How much did the temperature of the cold water change? Compare the magnitudes (positive values) of these changes. b. During the mixing, how did the heat transfer occur: from hot water to cold, or from cold water to hot? C. What quantity of heat was transferred from one sample to the other? d. How does the quantity of heat transferred to or from the hot-water sample compare with the quantity of heat transferred to or from the cold-water sample? e. Knowing these relative quantities of heat, why is the temperature change of the cold water greater than the magnitude of the temperature change of the hot water. f. A sample of hot water is mixed with a sample of cold water that has twice its mass. Predict the temperature change of each of the samples. g. You mix two samples of water, and one increases by \(20^{\circ} \mathrm{C}\), while the other drops by \(60^{\circ} \mathrm{C}\). Which of the samples has less mass? How do the masses of the two water samples compare? h. A 7 -g sample of hot water is mixed with a \(3-\mathrm{g}\) sample of cold water. How do the temperature changes of the two water samples compare? Part \(2:\) A sample of water is heated from \(10^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\). Can you calculate the amount of heat added to the water sample that caused this temperature change? If not, what information do you need to perform this calculation? Part 3: Two samples of water are heated from \(20^{\circ} \mathrm{C}\) to \(60^{\circ} \mathrm{C}\). One of the samples requires twice as much heat to bring about this temperature change as the other. How do the masses of the two water samples compare? Explain your reasoning.

a. A \(100 .-\mathrm{g}\) sample of water is placed in an insulated container and allowed to come to room temperature at \(21^{\circ} \mathrm{C}\). To heat the water sample to \(41^{\circ} \mathrm{C}\), how much heat must you add to it? b. Consider the hypothetical reaction, $$ 2 \mathrm{X}(a q)+\mathrm{Y}(l) \longrightarrow \mathrm{X}_{2} \mathrm{Y}(a q) $$ being run in an insulated container that contains \(100 . \mathrm{g}\) of solution. If the temperature of the solution changes from \(21^{\circ} \mathrm{C}\) to \(31^{\circ} \mathrm{C}\), how much heat does the chemical reaction produce? How does this answer compare with that in part a? (You can assume that this solution is so dilute that it has the same heat capacity as pure water.) C. If you wanted the temperature of \(100 . \mathrm{g}\) of this solution to increase from \(21^{\circ} \mathrm{C}\) to \(51^{\circ} \mathrm{C}\), how much heat would you have to add to it? (Try to answer this question without using a formula.) d. If you had added \(0.02\) mol of \(X\) and \(0.01\) mol of \(Y\) to form the solution in part b, how many moles of \(\mathrm{X}\) and \(\mathrm{Y}\) would you need to bring about the temperature change described in part c. e. Judging on the basis of your answers so far, what is the enthalpy of the reaction \(2 \mathrm{X}(a q)+\mathrm{Y}(l) \longrightarrow \mathrm{X}_{2} \mathrm{Y}(a q) ?\)

A small car is traveling at twice the speed of a larger car, which has twice the mass of the smaller car. Which car has the greater kinetic energy? (Or do they both have the same kinetic energy?)

A \(250-\mathrm{g}\) sample of water at \(20.0^{\circ} \mathrm{C}\) is placed in a freezer that is held at a constant temperature of \(-20.0^{\circ} \mathrm{C}\). Considering the water as the "system," answer the following questions: a. what is the sign of \(q_{\text {sys }}\) for the water after it is placed in the freezer? b. After a few hours, what will be the state of the water? c. How will the initial enthalpy for the water compare with the final enthalpy of the water after it has spent several hours in the freezer? d. What will the temperature of the water be after several hours in the freezer?

What is the enthalpy change for the preparation of one mole of liquid water from the elements, given the following equations? $$ \begin{aligned} &\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H_{f} \\ &\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H_{v a p} \end{aligned} $$

You have two samples of different metals, metal \(\mathrm{A}\) and metal \(\mathrm{B}\), each having the same mass. You heat both metals to \(95^{\circ} \mathrm{C}\) and then place each one into separate beakers containing the same quantity of water at \(25^{\circ} \mathrm{C}\). a. You measure the temperatures of the water in the two beakers when each metal has cooled by \(10^{\circ} \mathrm{C}\) and find that the temperature of the water with metal \(\mathrm{A}\) is higher than the temperature of the water with metal \(\mathrm{B}\). Which metal has the greater specific heat? Explain. b. After waiting a period of time, the temperature of the water in each beaker rises to a maximum value. In which beaker does the water rise to the higher value, the one with metal \(\mathrm{A}\) or the one with metal \(\mathrm{B} ?\) Explain.

A soluble salt, \(\mathrm{MX}_{2}\), is added to water in a beaker. The equation for the dissolving of the salt is: $$ \mathrm{MX}_{2}(s) \longrightarrow \mathrm{M}^{2+}(a q)+2 \mathrm{X}^{-}(a q) ; \quad \Delta H>0 $$ a. Immediately after the salt dissolves, is the solution warmer or colder? b. Indicate the direction of heat flow, in or out of the beaker, while the salt dissolves. c. After the salt dissolves and the water returns to room temperature, what is the value of \(q\) for the system?

Methane, \(\mathrm{CH}_{4}\), is a major component of marsh gas. When \(0.5000\) mol methane burns to produce carbon dioxide and liquid water, \(-445.1 \mathrm{~kJ}\) of heat is released. What is this heat in kilocalories?

Hydrogen sulfide, \(\mathrm{H}_{2} \mathrm{~S}\), is produced during decomposition of organic matter. When \(0.5500 \mathrm{~mol} \mathrm{H}_{2} \mathrm{~S}\) burns to produce \(\mathrm{SO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l),-309.1 \mathrm{~kJ}\) of heat is released. What is this heat in kilocalories?

A bullet weighing 245 grains is moving at a speed of \(2.52 \times 10^{3} \mathrm{ft} / \mathrm{s} .\) Calculate the kinetic energy of the bullet in joules and in calories. One grain equals \(0.0648 \mathrm{~g}\).

Chlorine dioxide, \(\mathrm{ClO}_{2}\), is a reddish yellow gas used in bleaching paper pulp. The average speed of a \(\mathrm{ClO}_{2}\) molecule at \(25^{\circ} \mathrm{C}\) is \(306 \mathrm{~m} / \mathrm{s}\). What is the kinetic energy (in joules) of a \(\mathrm{ClO}_{2}\) molecule moving at this speed?

Nitrous oxide, \(\mathrm{N}_{2} \mathrm{O}\), has been used as a dental anesthetic. The average speed of an \(\mathrm{N}_{2} \mathrm{O}\) molecule at \(25^{\circ} \mathrm{C}\) is \(379 \mathrm{~m} / \mathrm{s}\). Calculate the kinetic energy (in joules) of an \(\mathrm{N}_{2} \mathrm{O}\) molecule traveling at this speed.

The process of dissolving ammonium nitrate, \(\mathrm{NH}_{4} \mathrm{NO}_{3}\), in water is an endothermic process. What is the sign of \(q ?\) If you were to add some ammonium nitrate to water in a flask, would you expect the flask to feel warm or cool?

The decomposition of ozone, \(\mathrm{O}_{3}\), to oxygen, \(\mathrm{O}_{2}\), is an exothermic reaction. What is the sign of \(q ?\) If you were to touch a flask in which ozone is decomposing to oxygen, would you expect the flask to feel warm or cool?

Nitric acid, a source of many nitrogen compounds, is produced from nitrogen dioxide. An old process for making nitrogen dioxide employed nitrogen and oxygen. $$ \mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) $$ The reaction absorbs \(66.2 \mathrm{~kJ}\) of heat per \(2 \mathrm{~mol} \mathrm{NO}_{2}\) produced. Is the reaction endothermic or exothermic? What is the value of \(q\) ?

Hydrogen cyanide is used in the manufacture of clear plastics such as Lucite and Plexiglas. It is prepared from ammonia and natural gas \(\left(\mathrm{CH}_{4}\right)\). $$ 2 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g)+2 \mathrm{CH}_{4}(g) \longrightarrow 2 \mathrm{HCN}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) $$ The reaction evolves \(939 \mathrm{~kJ}\) of heat per \(2 \mathrm{~mol} \mathrm{HCN}\) formed. Is the reaction endothermic or exothermic? What is the value of \(q ?\)

When \(1 \mathrm{~mol}\) of iron metal reacts with hydrochloric acid at constant temperature and pressure to produce hydrogen gas and aqueous iron(II) chloride, \(89.1 \mathrm{~kJ}\) of heat evolves. Write a thermochemical equation for this reaction.

When 2 mol of potassium chlorate crystals decompose to potassium chloride crystals and oxygen gas at constant temperature and pressure, \(78.0 \mathrm{~kJ}\) of heat is given off. Write a thermochemical equation for this reaction.

When white phosphorus burns in air, it produces phosphorus(V) oxide. $$ \mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g) \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(s) ; \Delta H=-3010 \mathrm{~kJ} $$ What is \(\Delta H\) for the following equation? $$ \mathrm{P}_{4} \mathrm{O}_{10}(s) \longrightarrow \mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g) $$

Carbon disulfide burns in air, producing carbon dioxide and sulfur dioxide. $$ \mathrm{CS}_{2}(l)+3 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{SO}_{2}(g) ; \Delta H=-1077 \mathrm{~kJ} $$ What is \(\Delta H\) for the following equation? $$ \frac{1}{2} \mathrm{CS}_{2}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \frac{1}{2} \mathrm{CO}_{2}(g)+\mathrm{SO}_{2}(g) $$

Phosphoric acid, \(\mathrm{H}_{3} \mathrm{PO}_{4}\), can be prepared by the reactio of phosphorus(V) oxide, \(\mathrm{P}_{4} \mathrm{O}_{10}\), with water. $$ \frac{1}{4} \mathrm{P}_{4} \mathrm{O}_{10}(s)+\frac{3}{2} \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{4}(a q) ; \Delta H=-96.2 \mathrm{~kJ} $$ What is \(\Delta H\) for the reaction involving \(1 \mathrm{~mol}\) of \(\mathrm{P}_{4} \mathrm{O}_{10}\) ? $$ \mathrm{P}_{4} \mathrm{O}_{10}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{H}_{3} \mathrm{PO}_{4}(a q) $$

With a platinum catalyst, ammonia will burn in oxygen give nitric oxide, NO. $$ \begin{aligned} 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) & \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) \\ \Delta H &=-906 \mathrm{~kJ} \end{aligned} $$ What is the enthalpy change for the following reaction? $$ \mathrm{NO}(g)+\frac{3}{2} \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{NH}_{3}(g)+\frac{5}{4} \mathrm{O}_{2}(g) $$

Colorless nitric oxide, NO, combines with oxygen to form nitrogen dioxide, \(\mathrm{NO}_{2}\), a brown gas. $$ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g) ; \Delta H=-114 \mathrm{~kJ} $$ What is the enthalpy change per gram of nitric oxide?

Hydrogen, \(\mathrm{H}_{2}\), is used as a rocket fuel. The hydrogen is burned in oxygen to produce water vapor. $$ 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(g) ; \Delta H=-484 \mathrm{~kJ} $$ What is the enthalpy change per gram of hydrogen?

Ammonia burns in the presence of a copper catalyst to form nitrogen gas. $$ \begin{aligned} 4 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g) ; \\ \Delta H=-1267 \mathrm{~kJ} \end{aligned} $$ What is the enthalpy change to burn \(35.8 \mathrm{~g}\) of ammonia?