Chapter 5

Define the terms system and surroundings. What does it mean to say that a system and its surroundings are in thermal equilibrium?

What determines the directionality of energy transfer as heat?

Identify whether the following processes are exothermic or endothermic. (a) combustion of methane (b) melting of ice (c) raising the temperature of water from \(25^{\circ} \mathrm{C}\) to \(100^{\circ} \mathrm{C}\) (d) heating \(\operatorname{CaCO}_{3}(\mathrm{s})\) to form \(\mathrm{CaO}(\mathrm{s})\) and \(\mathrm{CO}_{2}(\mathrm{g})\)

Identify whether the following processes are exothermic or endothermic. (a) the reaction of \(\mathrm{Na}(\mathrm{s})\) and \(\mathrm{Cl}_{2}(\mathrm{g})\) (b) cooling and condensing gaseous \(N_{2}\) to form liquid \(\mathrm{N}_{2}\) (c) cooling a soft drink from \(25^{\circ} \mathrm{C}\) to \(0^{\circ} \mathrm{C}\) (d) heating \(\mathrm{HgO}(\mathrm{s})\) to form \(\mathrm{Hg}(\ell)\) and \(\mathrm{O}_{2}(\mathrm{g})\)

The molar heat capacity of mercury is \(28.1 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K}\) What is the specific heat capacity of this metal in \(\mathrm{J} / \mathrm{g} \cdot \mathrm{K}\) ?

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

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

How much energy as heat is required to raise the temperature of \(50.00 \mathrm{mL}\) of water from \(25.52^{\circ} \mathrm{C}\) to \(28.75^{\circ} \mathrm{C} ?\) (Density of water at this temperature = \(0.997 \mathrm{g} / \mathrm{mL} .)\)

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 energy as heat, what is its final temperature?

After absorbing \(1.850 \mathrm{kJ}\) of energy as 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 was added to 22.1 g of water. The initial water temperature was \(25.0^{\circ} \mathrm{C},\) and the final temperature was \(27.5^{\circ} \mathrm{C} .\) 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 sample?

When \(108 \mathrm{g}\) 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 came to thermal equilibrium, the temperature was \(27.1^{\circ} \mathrm{C} .\) What is the specific heat capacity of zinc?

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

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

The 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 \(0^{\circ} \mathrm{C} ?\)

How much energy 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 microbial fermentation and is found throughout the environment. It is also produced industrially, is used in the manufacture of various chemicals, and has been used as a topical anesthetic. How much energy is required 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 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 J/g \(\cdot\) K and its heat of fusion is \(11.4 \mathrm{J} / \mathrm{g} .\) )

What quantity of energy, in joules, is required to raise the temperature of \(454 \mathrm{g}\) of tin from room temperature, \(25.0^{\circ} \mathrm{C},\) to its melting point, \(231.9^{\circ} \mathrm{C},\) and then melt the tin at that temperature? (The specific heat capacity of tin is \(0.227 \mathrm{J} / \mathrm{g} \cdot \mathrm{K},\) and the heat of fusion of this metal is \(59.2 \mathrm{J} / \mathrm{g} .\) )

Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH},\) boils at \(78.29^{\circ} \mathrm{C} .\) How much energy, in joules, is required to raise the temperature of \(1.00 \mathrm{kg}\) 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 energy was given off as heat in this process? (The density of benzene is \(0.80 \mathrm{g} / \mathrm{mL},\) its specific heat capacity is \(1.74 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}, \text { and its heat of fusion is } 127 \mathrm{J} / \mathrm{g} .)\)

Calcium carbide, \(\mathrm{CaC}_{2}\), is manufactured by the reaction of CaO with carbon at a high temperature. (Calcium carbidCalcium 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.)e is then used to make acetylene.) \(\begin{aligned} \mathrm{CaO}(\mathrm{s})+3 \mathrm{C}(\mathrm{s}) \rightarrow \mathrm{CaC}_{2}(\mathrm{s}) &+\mathrm{CO}(\mathrm{g}) \\ & \Delta_{\mathrm{r}} H^{\circ}=+464.8 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} \end{aligned}\) Is this reaction endothermic or exothermic? What is the enthalpy change if \(10.0 \mathrm{g}\) of \(\mathrm{CaO}\) is allowed to react with an excess of carbon?

Acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\), is made industrially by the reaction of methanol and carbon monoxide. \(\begin{aligned} \mathrm{CH}_{3} \mathrm{OH}(\ell)+\mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}(\ell) & \\ \Delta_{\mathrm{r}} H^{\circ}=-134.6 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} \end{aligned}\) What is the enthalpy change for producing \(1.00 \mathrm{L}\) of acetic acid \((d=1.044 \mathrm{g} / \mathrm{mL})\) by this reaction?

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: \(\mathrm{CsOH}(\mathrm{aq})+\mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{CsCl}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)\) 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 \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\)

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 \(23.3^{\circ} \mathrm{C} .\) 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 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.) (IMAGE CAN'T COPY)

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, \(5.2 \mathrm{g}\) of concentrated \(\mathrm{H}_{2} \mathrm{SO}_{4}(\ell)\) 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 \(\mathrm{H}_{2} \mathrm{SO}_{4}(\ell) \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}),\) in \(\mathrm{kJ} / \mathrm{mol}\)

Suppose you burned \(0.300 \mathrm{g}\) of \(\mathrm{C}(\mathrm{s})\) in an excess of \(\mathrm{O}_{2}(\mathrm{g})\) in a constant volume calorimeter to give \(\mathrm{CO}_{2}(\mathrm{g})\) \(\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})\) The temperature of the calorimeter, which contained 775 g of water, increased from \(25.00^{\circ} \mathrm{C}\) to \(27.38^{\circ} \mathrm{C}\) The heat capacity of the bomb is \(893 \mathrm{J} / \mathrm{K}\). Calculate \(\Delta U\) per mole of carbon.

Suppose you burned \(1.500 \mathrm{g}\) of benzoic acid, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H},\) in a constant volume calorimeter and found that the temperature increased from \(22.50^{\circ} \mathrm{C}\) to \(31.69^{\circ} \mathrm{C} .\) The calorimeter contained \(775 \mathrm{g}\) of water, and the bomb had a heat capacity of \(893 \mathrm{J} / \mathrm{K}\). Calculate \(\Delta U\) per mole of benzoic acid. (IMAGE CAN'T COPY)

A 0.692 -g sample of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) was burned in a constant volume calorimeter. The temperature rose from \(21.70^{\circ} \mathrm{C}\) to \(25.22^{\circ} \mathrm{C} .\) The calorimeter contained 575 g of water, and the bomb had a heat capacity of \(650 \mathrm{J} / \mathrm{K} .\) What is \(\Delta U\) 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 energy transferred from the metal to the ice can be determined from the amount of ice melted. Suppose you heated a 50.0 -g piece of silver to \(99.8^{\circ} \mathrm{C}\) and then dropped it onto ice. When the metal's temperature had dropped to \(0.0^{\circ} \mathrm{C},\) it is found that \(3.54 \mathrm{g}\) of ice had melted. What is the specific heat capacity of silver?

You wish to know the enthalpy change for the formation of liquid \(\mathrm{PCl}_{3}\) from the elements. $$ \mathrm{P}_{4}(\mathrm{s})+6 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{PCl}_{3}(\ell) \quad \Delta_{\mathrm{r}} H^{\circ}=? $$ 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 \(\mathrm{PCl}_{5}(\mathrm{s}):\) \(\begin{aligned} \mathrm{P}_{4}(\mathrm{s})+10 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{PCl}_{5}(\mathrm{s}) & \\ \Delta_{r} H^{\circ} &=-1774.0 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} \\\ \mathrm{PCl}_{3}(\ell)+\mathrm{Cl}_{2}(\mathrm{g}) \rightarrow \mathrm{PCl}_{5}(\mathrm{s}) & \\ \Delta_{\mathrm{r}} H^{\circ} &=-123.8 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} \end{aligned}\) Use these data to calculate the enthalpy change for the formation of 1.00 mol of \(\mathrm{PCl}_{3}(\ell)\) from phosphorus and chlorine.

Write a balanced chemical equation for the formation of \(\mathrm{CH}_{3} \mathrm{OH}(\ell)\) from the elements in their standard states. Find the value for \(\Delta_{f} H^{\circ}\) for \(\mathrm{CH}_{3} \mathrm{OH}(\ell)\) in Appendix L.

The standard enthalpy of formation of solid barium oxide, \(\mathrm{BaO},\) is \(-553.5 \mathrm{kJ} / \mathrm{mol},\) and the standard 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? \(2 \mathrm{BaO}_{2}(\mathrm{s}) \rightarrow 2 \mathrm{BaO}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g})\) (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 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) \(\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) (b) \(2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (c) \(\mathrm{H}_{2} \mathrm{O}\left(\ell, 25^{\circ} \mathrm{C}\right) \rightarrow \mathrm{H}_{2} \mathrm{O}\left(\ell, 15^{\circ} \mathrm{C}\right)\) (d) \(\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\)

For each of the following, define a system and its surroundings, and give the direction of energy transfer between system and surroundings. (a) Methane burns in a gas furnace in your home. (b) Water drops, sitting on your skin after a swim, 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 energy is evolved as heat.

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

You have a large balloon containing 1.0 mol of gaseous water vapor at \(80^{\circ} \mathrm{C} .\) How will each step affect the internal energy of the system? (a) The temperature of the system is raised to \(90^{\circ} \mathrm{C}\) (b) The vapor is condensed to a liquid, at \(40^{\circ} \mathrm{C}\)

Determine whether energy as heat is evolved or required, and whether work was done on the system or whether the system does work on the surroundings, in the following processes at constant pressure: (a) Liquid water at \(100^{\circ} \mathrm{C}\) is converted to steam at \(100^{\circ} \mathrm{C}\) (b) Dry ice, \(\mathrm{CO}_{2}(\mathrm{s}),\) sublimes to give \(\mathrm{CO}_{2}(\mathrm{g})\)

Determine whether energy as heat is evolved or required, and whether work was done on the system or whether the system does work on the surroundings, in the following processes at constant pressure: (a) Ozone, \(\mathrm{O}_{3},\) decomposes to form \(\mathrm{O}_{2}\) (b) Methane burns: \(\mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\ell)\)

You determine that 187 J of energy as heat is required to raise the temperature of \(93.45 \mathrm{g}\) of silver from \(18.5^{\circ} \mathrm{C}\) to \(27.0^{\circ} \mathrm{C} .\) What is the specific heat capacity of silver?

Calculate the quantity of energy required to convert \(60.1 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) at \(0.0^{\circ} \mathrm{C}\) to \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) at \(100.0^{\circ} \mathrm{C} .\) The enthalpy of fusion of ice at \(0^{\circ} \mathrm{C}\) is \(333 \mathrm{J} / \mathrm{g}\); the enthalpy of vaporization of liquid water at \(100^{\circ} \mathrm{C}\) is \(2256 \mathrm{J} / \mathrm{g}.\)

You add \(100.0 \mathrm{g}\) of water at \(60.0^{\circ} \mathrm{C}\) to \(100.0 \mathrm{g}\) of ice at \(0.00^{\circ} \mathrm{C} .\) Some of the ice melts and cools the water to \(0.00^{\circ} \mathrm{C} .\) When the ice and water mixture reaches thermal equilibrium at \(0^{\circ} \mathrm{C},\) how much ice has melted?

Three 45 -g ice cubes at \(0^{\circ} \mathrm{C}\) are dropped into \(5.00 \times 10^{2} \mathrm{mL}\) of tea to make iced tea. The tea was initially at \(20.0^{\circ} \mathrm{C} ;\) when thermal equilibrium was reached, the final temperature was \(0^{\circ} \mathrm{C} .\) How much of the ice melted, and how much remained floating in the beverage? Assume the specific heat capacity of tea is the same as that of pure water.

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.

A 192 -g piece of copper is heated to \(100.0^{\circ} \mathrm{C}\) in a boiling water bath and then dropped into a beaker containing \(751 \mathrm{g}\) of water (density \(=1.00 \mathrm{g} / \mathrm{cm}^{3}\) ) at \(4.0^{\circ} \mathrm{C} .\) What was the final temperature of the copper and water after thermal equilibrium was reached? \(\left(C_{\mathrm{Cu}}=0.385 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\right)\)

Insoluble \(\mathrm{AgCl}(\mathrm{s})\) precipitates when solutions of \(\mathrm{AgNO}_{3}(\mathrm{aq})\) and \(\mathrm{NaCl}(\mathrm{aq})\) are mixed. \(\mathrm{AgNO}_{3}(\mathrm{aq})+\mathrm{NaCl}(\mathrm{aq}) \rightarrow \mathrm{AgCl}(\mathrm{s})+\mathrm{NaNO}_{3}(\mathrm{aq})\) $$ \Delta_{\mathrm{r}} H^{\circ}=? $$ To measure the energy evolved in this reaction, \(250 . \mathrm{mL}\) of \(0.16 \mathrm{M} \mathrm{AgNO}_{3}(\mathrm{aq})\) and \(125 \mathrm{mL}\) of \(0.32 \mathrm{M} \mathrm{NaCl}(\mathrm{aq})\) are mixed in a coffee-cup calorimeter. The temperature of the mixture rises from \(21.15^{\circ} \mathrm{C}\) to \(22.90^{\circ} \mathrm{C} .\) Calculate the enthalpy change for the precipitation of AgCl(s), in kJ/mol. (Assume the density of the solution is \(1.0 \mathrm{g} / \mathrm{mL}\) and its specific heat capacity is \(4.2 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\) )