Chapter 6

The flashlight in the photo does not use batteries. Instead you move a lever, which turns a geared mechanism and results finally in light from the bulb. What type of energy is used to move the lever? What type or types of energy are produced?

A solar panel is pictured in the photo. When light shines on the panel, a small electric motor propels the car. What types of energy are involved in this setup?

You are on a diet that calls for eating no more than 1200 Cal/day. How many joules would this be?

A 2 -in. piece of chocolate cake with frosting provides \(1670 \mathrm{kJ}\) of energy. What is this in dietary Calories (Cal)?

One food product has an energy content of 170 kcal per serving and another has \(280 \mathrm{kJ}\) per serving. Which food has a greater energy content per serving?

Which has a greater energy content, a raw apple or a raw apricot? Go to the USDA Nutrient Database on the World Wide Web for the information (http://www.nal.usda.gov/ fnic/foodcomp/). Report the energy content of the fruit in kcal and kJ.

The specific heat capacity of benzene \(\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)\) is \(1.74 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} . \text { What is its molar heat capacity (in } \mathrm{J} / \mathrm{mol} \cdot \mathrm{K}) ?\)

The specific heat capacity of copper is \(0.385 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\). What quantity of heat is required to heat 168 g of copper from \(-12.2^{\circ} \mathrm{C}\) to \(+25.6^{\circ} \mathrm{C} ?\)

The initial temperature of a 344 -g sample of iron is \(18.2^{\circ} \mathrm{C} .\) If the sample absorbs \(2.25 \mathrm{kJ}\) of heat, what is its final temperature?

After absorbing \(1.850 \mathrm{kJ}\) of heat, the temperature of a \(0.500-\mathrm{kg}\) block of copper is \(37^{\circ} \mathrm{C} .\) What was its initial temperature?

A 182 -g sample of gold at some temperature is added to 22.1 g of water. The initial water temperature is \(25.0^{\circ} \mathrm{C}\) and the final temperature is \(27.5^{\circ} \mathrm{C}\). If the specific heat capacity of gold is \(0.128 \mathrm{J} / \mathrm{g} \cdot \mathrm{K},\) what was the initial temperature of the gold?

One beaker contains \(156 \mathrm{g}\) of water at \(22^{\circ} \mathrm{C}\) and a second beaker contains \(85.2 \mathrm{g}\) of water at \(95^{\circ} \mathrm{C} .\) The water in the two beakers is mixed. What is the final water temperature?

When 108 g of water at a temperature of \(22.5^{\circ} \mathrm{C}\) is mixed with \(65.1 \mathrm{g}\) of water at an unknown temperature, the final temperature of the resulting mixture is \(47.9^{\circ} \mathrm{C}\) What was the initial temperature of the second sample of water?

A 13.8 -g piece of zinc was heated to \(98.8^{\circ} \mathrm{C}\) in boiling water and then dropped into a beaker containing \(45.0 \mathrm{g}\) of water at \(25.0^{\circ} \mathrm{C} .\) When the water and metal come to thermal equilibrium, the temperature is \(27.1^{\circ} \mathrm{C} .\) What is the specific heat capacity of zinc?

A 237 -g piece of molybdenum, initially at \(100.0^{\circ} \mathrm{C},\) is dropped into \(244 \mathrm{g}\) of water at \(10.0^{\circ} \mathrm{C} .\) When the system comes to thermal equilibrium, the temperature is \(15.3^{\circ} \mathrm{C}\) What is the specific heat capacity of molybdenum?

What quantity of heat is evolved when 1.0 L of water at \(0^{\circ} \mathrm{C}\) solidifies to ice? The heat of fusion of water is \(333 \mathrm{J} / \mathrm{g} .\)

The heat energy required to melt \(1.00 \mathrm{g}\) of ice at \(0^{\circ} \mathrm{C}\) is 333 J. If one ice cube has a mass of \(62.0 \mathrm{g},\) and a tray contains 16 ice cubes, what quantity of energy is required to melt a tray of ice cubes to form liquid water at \(0^{\circ} \mathrm{C} ?\)

What quantity of heat is required to vaporize \(125 \mathrm{g}\) of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) at its boiling point, \(80.1^{\circ} \mathrm{C} ?\) The heat of vaporization of benzene is \(30.8 \mathrm{kJ} / \mathrm{mol}\).

Chloromethane, \(\mathrm{CH}_{3} \mathrm{Cl}\), arises from the oceans and from microbial fermentation and is found throughout the environment. It is used in the manufacture of various chemicals and has been used as a topical anesthetic. What quantity of heat must be absorbed to convert \(92.5 \mathrm{g}\) of liquid to a vapor at its boiling point, \(-24.09^{\circ} \mathrm{C} ?\) The heat of vaporization of \(\mathrm{CH}_{3} \mathrm{Cl}\) is \(21.40 \mathrm{kJ} / \mathrm{mol}\).

The freezing point of mercury is \(-38.8^{\circ} \mathrm{C} .\) What quantity of heat energy, in joules, is released to the surroundings if \(1.00 \mathrm{mL}\) of mercury is cooled from \(23.0^{\circ} \mathrm{C}\) to \(-38.8^{\circ} \mathrm{C}\) and then frozen to a solid? (The density of liquid mercury is \(13.6 \mathrm{g} / \mathrm{cm}^{3} .\) Its specific heat capacity is \(0.140 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\) and its heat of fusion is \(11.4 \mathrm{J} / \mathrm{g} .\) )

Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) boils at \(78.29^{\circ} \mathrm{C} .\) What quantity of heat energy, in joules, is required to raise the temperature of 1.00 kg of ethanol from \(20.0^{\circ} \mathrm{C}\) to the boiling point and then to change the liquid to vapor at that temperature? (The specific heat capacity of liquid ethanol is \(2.44 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\) and its enthalpy of vaporization is \(855 \mathrm{J} / \mathrm{g} .\) )

A 25.0 -mL sample of benzene at \(19.9^{\circ} \mathrm{C}\) was cooled to its melting point, \(5.5^{\circ} \mathrm{C},\) and then frozen. How much heat was given off in this process? The density of benzene is \(0.80 \mathrm{g} / \mathrm{mL},\) its specific heat capacity is \(1.74 \mathrm{J} / \mathrm{g} \cdot \mathrm{K},\) and its heat of fusion is \(127 \mathrm{J} / \mathrm{g}\).

Nitrogen monoxide, a gas recently found to be involved in a wide range of biological processes, reacts with oxygen to give brown \(\mathrm{NO}_{2}\) gas. $$2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) \quad \Delta H_{\mathrm{rxn}}^{\circ}=-114.1 \mathrm{kJ}$$ Is this reaction endothermic or exothermic? If \(1.25 \mathrm{g}\) of NO is converted completely to \(\mathrm{NO}_{2}\), what quantity of heat is absorbed or evolved?

Calcium carbide, \(\mathrm{CaC}_{2}\), is manufactured by the reaction of CaO with carbon at a high temperature. (Calcium carbide is then used to make acetylene.) $$\mathrm{CaO}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \longrightarrow \mathrm{CaC}_{2}(\mathrm{s})+\mathrm{CO}(\mathrm{g})$$ $$\Delta H_{\mathrm{rxn}}^{\circ}=+464.8 \mathrm{kJ}$$ Is this reaction endothermic or exothermic? If \(10.0 \mathrm{g}\) of CaO is allowed to react with an excess of carbon, what quantity of heat is absorbed or evolved by the reaction?

Isooctane ( 2,2,4 -trimethylpentane), one of the many hydrocarbons that make up gasoline, burns in air to give water and carbon dioxide. $$\begin{array}{r}2 \mathrm{C}_{8} \mathrm{H}_{18}(\ell)+25 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 16 \mathrm{CO}_{2}(\mathrm{g})+18 \mathrm{H}_{2} \mathrm{O}(\ell) \\\\\Delta H_{\mathrm{rsn}}^{\circ}=-10,922 \mathrm{kJ} \end{array}$$ If you burn 1.00 L of isooctane (density \(=0.69 \mathrm{g} / \mathrm{mL}\) ), what quantity of heat is evolved?

Acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\), is made industrially by the reaction of methanol and carbon monoxide. $$\begin{aligned}\mathrm{CH}_{3} \mathrm{OH}(\ell)+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\ell) & \\\& \Delta H_{\mathrm{rxn}}^{\circ}=-355.9 \mathrm{kJ}\end{aligned}$$ If you produce \(1.00 \mathrm{L}\) of acetic acid (density \(=\) \(1.044 \mathrm{g} / \mathrm{mL})\) by this reaction, what quantity of heat is evolved?

Assume you mix \(100.0 \mathrm{mL}\) of \(0.200 \mathrm{M} \mathrm{CsOH}\) with \(50.0 \mathrm{mL}\) of \(0.400 \mathrm{M} \mathrm{HCl}\) in a coffee-cup calorimeter. The following reaction occurs: $$\mathrm{CsOH}(\mathrm{aq})+\mathrm{HCl}(\mathrm{aq}) \longrightarrow \mathrm{CsCl}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)$$ The temperature of both solutions before mixing was \(22.50^{\circ} \mathrm{C},\) and it rises to \(24.28^{\circ} \mathrm{C}\) after the acid-base reaction. What is the enthalpy change for the reaction per mole of CsOH? Assume the densities of the solutions are all \(1.00 \mathrm{g} / \mathrm{mL}\) and the specific heat capacities of the solutions are \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\).

You mix \(125 \mathrm{mL}\) of \(0.250 \mathrm{M} \mathrm{CsOH}\) with \(50.0 \mathrm{mL}\) of \(0.625 \mathrm{M} \mathrm{HF}\) in a coffee-cup calorimeter, and the temperature of both solutions rises from \(21.50^{\circ} \mathrm{C}\) before mixing to \(24.40^{\circ} \mathrm{C}\) after the reaction. $$\mathrm{CsOH}(\mathrm{aq})+\mathrm{HF}(\mathrm{aq}) \longrightarrow \mathrm{CsF}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)$$ What is the enthalpy of reaction per mole of CsOH? Assume the densities of the solutions are all \(1.00 \mathrm{g} / \mathrm{mL}\) and the specific heats of the solutions are \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\).

A piece of titanium metal with a mass of \(20.8 \mathrm{g}\) is heated in boiling water to \(99.5^{\circ} \mathrm{C}\) and then dropped into a coffee-cup calorimeter containing \(75.0 \mathrm{g}\) of water at \(21.7^{\circ} \mathrm{C} .\) When thermal equilibrium is reached, the final temperature is \(24.3^{\circ} \mathrm{C} .\) Calculate the specific heat capacity of titanium.

A piece of chromium metal with a mass of \(24.26 \mathrm{g}\) is heated in boiling water to \(98.3^{\circ} \mathrm{C}\) and then dropped into a coffee-cup calorimeter containing \(82.3 \mathrm{g}\) of water at 23.3 "C. When thermal equilibrium is reached, the final temperature is \(25.6^{\circ} \mathrm{C} .\) Calculate the specific heat capacity of chromium.

Adding \(5.44 \mathrm{g}\) of \(\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{s})\) to \(150.0 \mathrm{g}\) of water in a coffee-cup calorimeter (with stirring to dissolve the salt) resulted in a decrease in temperature from \(18.6^{\circ} \mathrm{C}\) to \(16.2^{\circ} \mathrm{C} .\) Calculate the enthalpy change for dissolving \(\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{s})\) in water, in \(\mathrm{kJ} / \mathrm{mol}\). Assume that the solution (whose mass is \(155.4 \mathrm{g}\) ) has a specific heat capacity of \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K} .\) (Cold packs take advantage of the fact that dissolving ammonium nitrate in water is an endothermic process.)

You should use care when dissolving \(\mathrm{H}_{2} \mathrm{SO}_{4}\) in water because the process is highly exothermic. To measure the enthalpy change, \(5.2 \mathrm{g} \mathrm{H}_{2} \mathrm{SO}_{4}(\ell)\) was added (with stirring) to 135 g of water in a coffee-cup calorimeter. This resulted in an increase in temperature from \(20.2^{\circ} \mathrm{C}\) to \(28.8^{\circ} \mathrm{C}\) Calculate the enthalpy change for the process \(\mathrm{H}_{2} \mathrm{SO}_{4}(\ell) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}),\) in \(\mathrm{k} \mathrm{J} / \mathrm{mol}\).

Sulfur \((2.56 \mathrm{g})\) is burned in a constant volume calorimeter with excess \(\mathrm{O}_{2}(\mathrm{g}) .\) The temperature increases from \(21.25^{\circ} \mathrm{C}\) to \(26.72^{\circ} \mathrm{C} .\) The bomb has a heat capacity of \(923 \mathrm{J} / \mathrm{K},\) and the calorimeter contains \(815 \mathrm{g}\) of water. Calculate the heat evolved, per mole of \(\mathrm{SO}_{2}\) formed, for the reaction $$\mathrm{S}_{8}(\mathrm{s})+8 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 8 \mathrm{SO}_{2}(\mathrm{g})$$

Suppose you burn 0.300 g of \(C\) (graphite) in an excess of \(\mathrm{O}_{2}(\mathrm{g})\) in a constant volume calorimeter to give \(\mathrm{CO}_{2}(\mathrm{g})\). $$\mathrm{C}(\text { graphite })+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})$$ The temperature of the calorimeter, which contains \(775 \mathrm{g}\) of water, increases from \(25.00^{\circ} \mathrm{C}\) to \(27.38^{\circ} \mathrm{C} .\) The heat capacity of the bomb is \(893 \mathrm{J} / \mathrm{K}\). What quantity of heat is evolved per mole of carbon?

A 0.692 -g sample of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) is burned in a constant volume calorimeter. The temperature rises from \(21.70^{\circ} \mathrm{C}\) to \(25.22^{\circ} \mathrm{C} .\) The calorimeter contains \(575 \mathrm{g}\) of water and the bomb has a heat capacity of \(650 \mathrm{J} / \mathrm{K}\). What quantity of heat is evolved per mole of glucose?

An "ice calorimeter" can be used to determine the specific heat capacity of a metal. A piece of hot metal is dropped onto a weighed quantity of ice. The quantity of heat transferred from the metal to the ice can be determined from the amount of ice melted. Suppose you heat a 50.0 -g piece of silver to \(99.8^{\circ} \mathrm{C}\) and then drop it onto ice. When the metal's temperature has dropped to \(0.0^{\circ} \mathrm{C},\) it is found that \(3.54 \mathrm{g}\) of ice has melted. What is the specific heat capacity of silver?

A \(9.36-\) g piece of platinum is heated to \(98.6^{\circ} \mathrm{C}\) in a boiling water bath and then dropped onto ice. (See Study Question 41.) When the metal's temperature has dropped to \(0.0^{\circ} \mathrm{C},\) it is found that \(0.37 \mathrm{g}\) of ice has melted. What is the specific heat capacity of platinum?

The enthalpy changes for the following reactions can be measured: $$\begin{aligned}&\mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\\\&&\Delta H^{\circ}=-802.4 \mathrm{kJ}\end{aligned}$$ $$\begin{aligned}&\mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})+\frac{3}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\\\&&\Delta H^{\circ}=-676 \mathrm{kJ} \end{aligned}$$ (a) Use these values and Hess's law to determine the enthalpy change for the reaction $$\mathrm{CH}_{4}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})$$ (b) Draw an energy level diagram that shows the relationship between the energy quantities involved in this problem.

The enthalpy changes of the following reactions can be measured: $$\begin{aligned}\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow & 2 \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \\\& \Delta H^{\circ}=-1411.1 \mathrm{kJ}\end{aligned}$$ $$\begin{aligned}\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\ell) & \\\\\Delta H^{\circ}=-1367.5 \mathrm{kJ}\end{aligned}$$ (a) Use these values and Hess's law to determine the enthalpy change for the reaction $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)$$ (b) Draw an energy level diagram that shows the relationship between the energy quantities involved in this problem.

Enthalpy changes for the following reactions can be determined experimentally: $$\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g}) \quad \Delta H^{\circ}=-91.8 \mathrm{kJ}$$ $$\begin{array}{r}4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\\\\Delta H^{\circ}=-906.2 \mathrm{kJ}\end{array}$$ $$\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \quad \Delta H^{\circ}=-241.8 \mathrm{kJ}$$ Use these values to determine the enthalpy change for the formation of \(\mathrm{NO}(\mathrm{g})\) from the elements (an enthalpy change that cannot be measured directly because the reaction is reactant-favored). $$\frac{1}{2} \mathrm{N}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{NO}(\mathrm{g}) \quad \Delta H^{\circ}=?$$

You wish to know the enthalpy change for the formation of liquid PCl grom the elements. $$\mathrm{P}_{4}(\mathrm{s})+6 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{PCl}_{3}(\ell) \quad \Delta H^{\circ}=?$$ The enthalpy change for the formation of \(\mathrm{PCl}_{5}\) from the elements can be determined experimentally, as can the enthalpy change for the reaction of \(\mathrm{PCl}_{3}(\ell)\) with more chlorine to give \(\mathrm{PCl}_{5}(\mathrm{s}):\) $$\begin{array}{cc}\mathrm{P}_{4}(\mathrm{s})+10 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{PCl}_{5}(\mathrm{s}) & \Delta H^{\circ}=-1774.0 \mathrm{kJ} \\\\\mathrm{PCl}_{3}(\ell)+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{PCl}_{5}(\mathrm{s}) & \Delta H^{\circ}=-123.8 \mathrm{kJ}\end{array}$$ Use these data to calculate the enthalpy change for the formation of 1.00 mol of \(\mathrm{PCl}_{3}(\ell)\) from phosphorus and chlorine.

The standard enthalpy of formation of solid barium oxide, \(\mathrm{BaO},\) is \(-553.5 \mathrm{kJ} / \mathrm{mol},\) and the enthalpy of formation of barium peroxide, \(\mathrm{BaO}_{2},\) is \(-634.3 \mathrm{kJ} / \mathrm{mol}\). (a) Calculate the standard enthalpy change for the following reaction. Is the reaction exothermic or endothermic? $$\mathrm{BaO}_{2}(\mathrm{s}) \longrightarrow \mathrm{BaO}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g})$$ (b) Draw an energy level diagram that shows the relationship between the enthalpy change of the decomposition of \(\mathrm{BaO}_{2}\) to \(\mathrm{BaO}\) and \(\mathrm{O}_{2}\) and the enthalpies of formation of \(\mathrm{BaO}(\mathrm{s})\) and \(\mathrm{BaO}_{2}(\mathrm{s})\).

The enthalpy change for the oxidation of styrene, \(\mathbf{C}_{8} \mathrm{H}_{8}\) is measured by calorimetry. $$\begin{aligned}\mathrm{C}_{8} \mathrm{H}_{8}(\ell)+10 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 8 \mathrm{CO}_{2}(\mathrm{g})+4 \mathrm{H}_{2} \mathrm{O}(\ell) & \\\& \Delta H_{\mathrm{rsn}}^{\circ}=-4395.0 \mathrm{kJ}\end{aligned}$$ Use this value, along with the standard heats of formation of \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\ell),\) to calculate the enthalpy of formation of styrene, in \(\mathrm{kJ} / \mathrm{mol}\).

The following terms are used extensively in thermodynamics. Define each and give an example. (a) exothermic and endothermic (b) system and surroundings (c) specific heat capacity (d) state function (e) standard state (f) enthalpy change, \(\Delta H\) (g) standard enthalpy of formation

For each of the following, tell whether the process is exothermic or endothermic. (No calculations are required.) (a) \(\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) (b) \(2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (c) \(\mathrm{H}_{2} \mathrm{O}\left(\ell, 25^{\circ} \mathrm{C}\right) \longrightarrow \mathrm{H}_{2} \mathrm{O}\left(\ell, 15^{\circ} \mathrm{C}\right)\) (d) \(\mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

For each of the following, define a system and its surroundings and give the direction of heat transfer between system and surroundings. (a) Methane is burning in a gas furnace in your home. (b) Water drops, sitting on your skin after a dip in a swimming pool, evaporate. (c) Water, at \(25^{\circ} \mathrm{C},\) is placed in the freezing compartment of a refrigerator, where it cools and eventually solidifies. (d) Aluminum and \(\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})\) are mixed in a flask sitting on a laboratory bench. A reaction occurs, and a large quantity of heat is evolved.

Which of the following are state functions? (a) the volume of a balloon (b) the time it takes to drive from your home to your college or university (c) the temperature of the water in a coffee cup (d) the potential energy of a ball held in your hand

Define the first law of thermodynamics using a mathematical equation and explain the meaning of each term in the equation.

What does the term "standard state" mean? What are the standard states of the following substances at \(298 \mathrm{K}: \mathrm{H}_{2} \mathrm{O}\) \(\mathrm{NaCl}, \mathrm{Hg}, \mathrm{CH}_{4} ?\)

A piece of lead with a mass of \(27.3 \mathrm{g}\) was heated to \(98.90^{\circ} \mathrm{C}\) and then dropped into \(15.0 \mathrm{g}\) of water at \(22.50^{\circ} \mathrm{C} .\) The final temperature was \(26.32^{\circ} \mathrm{C} .\) Calculate the specific heat capacity of lead from these data.