Chapter 6

Give definitions for (a) energy, (b) kinetic energy, and (c) potential energy.

State the equation used to calculate an object's kinetic energy. Define the symbols used in the equation. Which variable has a larger effect on kinetic energy when it is doubled?

State the law of conservation of energy. Describe how it explains the motion of a child on a swing.

A pendulum such as a swinging chandelier continuously converts kinetic energy to potential energy and back again. Describe how these energies vary during a single swing of the pendulum.

What is meant by the term chemical energy?

How does the potential energy change (increase, decrease, or no change) for each of the following? (a) Two electrons come closer together. (b) An electron and a proton become farther apart. (c) Two atomic nuclei approach each other. (d) A ball rolls downhill.

Why is heat considered a waste product in a car engine?

Define heat. How do heat and temperature differ?

How is internal energy related to molecular kinetic and potential energy? How is a change in internal energy defined for a chemical reaction?

Suppose the temperature of an object is raised from \(100^{\circ} \mathrm{C}\) to \(200^{\circ} \mathrm{C}\) by heating it with a Bunsen burner. Which of the following will be true? (a) The average molecular kinetic energy will increase. (b) The total kinetic energy of all the molecules will increase. (c) The number of fast-moving molecules will increase. (d) The number of slow-moving molecules will increase. (e) The chemical potential energy will decrease.

What is a state function? Give four examples that meet your definition.

What do the terms system and surroundings mean? What is the difference between an isolated system and a closed system? What is the universe in terms of thermodynamics?

What are the names of the thermal properties whose values can have the following units? (a) \(J \mathrm{~g}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) (b) \(J \mathrm{~mol}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) (c) \(J^{\circ} \mathrm{C}^{-1}\) (d) J

For samples with the same mass, which kind of substance needs more energy to undergo an increase of \(5^{\circ} \mathrm{C},\) something with a large specific heat or something with a small specific heat? Explain.

How do heat capacity and specific heat differ?

Suppose object \(A\) has twice the specific heat and twice the mass of object \(B\). If the same amount of heat is applied to both objects, how will the temperature change of \(A\) be related to the temperature change in \(B\) ?

In a certain chemical reaction, there is a decrease in the potential energy (chemical energy) as the reaction proceeds. (a) How does the total kinetic energy of the particles change? (b) How does the temperature of the reaction mixture change?

What term do we use to describe a reaction that liberates heat to its surroundings? How does the chemical energy change during such a reaction? What is the algebraic sign of \(q\) for such a reaction?

What term is used to describe a reaction that absorbs heat from the surroundings? How does the chemical energy change during such a reaction? What is the algebraic sign of \(q\) for such a reaction?

When gasoline burns, it reacts with oxygen in the air and forms hot gases consisting of carbon dioxide and water vapor. How does the potential energy of the gasoline and oxygen compare with the potential energy of the carbon dioxide and water vapor?

Write the equation that states the first law of thermodynamics. In your own words, what does this statement mean in terms of energy exchanges between a system and its surroundings?

How are heat and work defined?

Why are heat and work not state functions?

How is enthalpy defined?

What is the sign of \(\Delta H\) for an endothermic change?

If a system containing gases expands and pushes back a piston against a constant opposing pressure, what equation describes the work done on the system?

What distinguishes a thermochemical equation from an ordinary chemical equation?

Why are fractional coefficients permitted in a balanced thermochemical equation? If a formula in a thermochemical equation has a coefficient of \(\frac{1}{2}\), what does it signify?

What fundamental fact about \(\Delta H\) makes Hess's law possible?

What two conditions must be met by a thermochemical equation so that its standard enthalpy change can be given the symbol \(\Delta H_{\mathrm{f}}^{\circ}\) ?

If a car increases its speed from \(30 \mathrm{mph}\) to \(60 \mathrm{mph}\), by what factor does the kinetic energy of the car increase? By what factor will the kinetic energy change if the speed decreases to \(10 \mathrm{mph}\) ?

If the mass of a truck is doubled - for example, when it is loaded - by what factor does the kinetic energy of the truck increase? By what factor does the kinetic energy change if the mass is one-tenth of the original mass?

If the mass of a truck is doubled- for example, when it is loaded - by what factor does the kinetic energy of the truck increase? By what factor does the kinetic energy change if the mass is one-tenth of the original mass?

How much heat, in joules and in calories, must be removed from \(1.75 \mathrm{~mol}\) of water to lower its temperature from \(25.0^{\circ} \mathrm{C}\) to \(15.0^{\circ} \mathrm{C}^{?}\)

Calculate the molar heat capacity of iron in \(\mathrm{J} \mathrm{mol}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) Its specific heat is \(0.4498 \mathrm{Jg}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\).

What is the molar heat capacity of ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) in units of \(\mathrm{J} \mathrm{mol}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\), if its specific heat is \(0.586 \mathrm{cal} \mathrm{g}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1} ?\)

A vat of \(4.54 \mathrm{~kg}\) of water underwent a decrease in temperature from \(60.25^{\circ} \mathrm{C}\) to \(58.65^{\circ} \mathrm{C}\). How much energy in kilojoules left the water? (For this range of temperature, use a value of \(4.18 \mathrm{~J} \mathrm{~g}^{-1}{\underline{\phantom{xx}}}^{\circ} \mathrm{C}^{-1}\) for the specific heat of water.

A container filled with \(2.46 \mathrm{~kg}\) of water underwent a temperature change from \(25.24^{\circ} \mathrm{C}\) to \(27.31^{\circ} \mathrm{C}\). How much heat, measured in kilojoules, did the water absorb?

A \(1.000 \mathrm{~mol}\) sample of propane, a gas used for cooking in many rural areas, was placed in a bomb calorimeter with excess oxygen and ignited. The initial temperature of the calorimeter was \(25.000^{\circ} \mathrm{C}\) and its total heat capacity was \(97.13 \mathrm{~kJ}^{\circ} \mathrm{C}^{-1}\). The reaction raised the temperature of the calorimeter to \(27.282^{\circ} \mathrm{C}\). (a) Write the balanced chemical equation for the reaction in the calorimeter. (b) How many joules were liberated in this reaction? (c) What is the heat of reaction of propane with oxygen expressed in kilojoules per mole of \(\mathrm{C}_{3} \mathrm{H}_{8}\) burned?

Toluene, \(\mathrm{C}_{7} \mathrm{H}_{8}\), is used in the manufacture of explosives such as TNT (trinitrotoluene). A \(1.500 \mathrm{~g}\) sample of liquid toluene was placed in a bomb calorimeter along with excess oxygen. When the combustion of the toluene was initiated, the temperature of the calorimeter rose from \(25.000^{\circ} \mathrm{C}\) to \(26.413^{\circ} \mathrm{C}\). The products of the combustion were \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l),\) and the heat capacity of the calorimeter was \(45.06 \mathrm{~kJ}^{\circ} \mathrm{C}^{-1}\) (a) Write the balanced chemical equation for the reaction in the calorimeter. (b) How many joules were liberated by the reaction? (c) How many joules would be liberated under similar conditions if 1.000 mol of toluene was burned?

If a system does \(45 \mathrm{~J}\) of work and receives \(28 \mathrm{~J}\) of heat, what is the value of \(\Delta E\) for this change?

If a system has \(48 \mathrm{~J}\) of work done on it and absorbs \(22 \mathrm{~J}\) of heat, what is the value of \(\Delta E\) for this change?

Chargers for cell phones get warm while they are being used. Some of the energy that they are using is being used to power the cell phone and the rest is wasted as heat. If a cell phone battery needs \(235 \mathrm{~J}\) of energy and \(345 \mathrm{~J}\) are wasted as heat, how many joules are required to charge the cell phone?

If a battery can release \(535 \mathrm{~J}\) of energy and \(455 \mathrm{~J}\) are used for work, how much energy is released as heat?

One thermochemical equation for the reaction of carbon monoxide with oxygen is $$ 3 \mathrm{CO}(g)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g) \quad \Delta H^{\circ}=-849 \mathrm{~kJ} $$ (a) Write the thermochemical equation for the reaction of \(2.00 \mathrm{~mol}\) of \(\mathrm{CO}\) (b) What is the \(\Delta H^{\circ}\) for the reaction that produces \(1.00 \mathrm{~mol}\) of \(\mathrm{CO}_{2} ?\)

Magnesium burns in air to produce a bright light and is often used in fireworks displays. The combustion of magnesium can be described by the following thermochemical equation: \(2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s) \quad \Delta H^{\circ}=-1203 \mathrm{~kJ}\) How much heat (in kilojoules) is liberated by the combustion of \(6.54 \mathrm{~g}\) of magnesium?

Methane burns with oxygen to produce carbon dioxide and water as a gas. The balanced thermochemical equation is $$ \mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g) \atop \Delta H^{\circ}=-802 \mathrm{~kJ} $$ How much methane, in grams, must be burned to release \(432 \mathrm{~kJ}\) of heat?

Calculate \(\Delta H^{\circ}\) in kilojoules for the following reaction, the preparation of the unstable acid nitrous acid, \(\mathrm{HNO}_{2}\). $$ \mathrm{HCl}(g)+\mathrm{NaNO}_{2}(s) \longrightarrow \mathrm{HNO}_{2}(l)+\mathrm{NaCl}(s) $$ Use the following thermochemical equations \(2 \mathrm{NaCl}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{HCl}(g)+\mathrm{Na}_{2} \mathrm{O}(s)\) \(\Delta H^{\circ}=+507.31 \mathrm{~kJ}\) \(\mathrm{NO}(g)+\mathrm{NO}_{2}(g)+\mathrm{Na}_{2} \mathrm{O}(s) \longrightarrow 2 \mathrm{NaNO}_{2}(s)\) $$ \begin{aligned} \Delta H^{\circ} &=-427.14 \mathrm{~kJ} \\ \mathrm{NO}(g)+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{O}_{2}(g) & \\ \Delta H^{\circ} &=-42.68 \mathrm{~kJ} \end{aligned} $$ \(2 \mathrm{HNO}_{2}(l) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) \(\Delta H^{\circ}=+34.35 \mathrm{~kJ}\)

Given the following thermochemical equations, $$ 3 \mathrm{Mg}(s)+2 \mathrm{NH}_{3}(g) \longrightarrow \mathrm{Mg}_{3} \mathrm{~N}_{2}(s)+3 \mathrm{H}_{2}(g) $$ \(\Delta H^{\circ}=-371 \mathrm{~kJ}\) $$ \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) \longrightarrow \mathrm{NH}_{3}(g) \quad \Delta H^{\circ}=-46 \mathrm{~kJ} $$ calculate \(\Delta H^{\circ}\) (in kilojoules) for the following reaction: $$ 3 \mathrm{Mg}(s)+\mathrm{N}_{2}(g) \longrightarrow \mathrm{Mg}_{3} \mathrm{~N}_{2}(s) $$

Which of the following thermochemical equations can have \(\Delta H_{\mathrm{f}}^{\circ}\) for the heat of the reaction? If it cannot, then why not? (a) \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(a q) \longrightarrow \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(s)\) (b) \(\mathrm{C}+\mathrm{O}+2 \mathrm{~N}+4 \mathrm{H} \longrightarrow \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(a q)\) (c) \(\mathrm{C}(s,\) graphite \()+\frac{1}{2} \mathrm{O}_{2}(g)+\mathrm{N}_{2}(g)+4 \mathrm{H}_{2}(g) \longrightarrow\) \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(a q)\) (d) \(2 \mathrm{C}(s,\) graphite \()+\mathrm{O}_{2}(g)+2 \mathrm{~N}_{2}(g)+8 \mathrm{H}_{2}(g) \longrightarrow\) \(2 \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(a q)\)