Draw an energy-level diagram that shows the relationship between the energy quantities involved in this problem.

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 by the amount of ice melted. Suppose you heated a $50.0-\mathrm{g}$ 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?

A $0.692-\mathrm{g}$ sample of glucose, $\mathrm{C}_0 \mathrm{H}_{12} \mathrm{O}_6$, 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 $575 \mathrm{~g}$ of water, and the bomb had a heat capacity of $650 \mathrm{~J} / \mathrm{K}$. What is $\Delta U$ per mole of glucose?

If the decomposition of $\mathrm{1.00~g}$ nitroglycerin releases $\mathrm{6.23 kJ/g}$ of energy in the form of heat, what is the standard molar enthalpy of the formation of nitroglycerin?

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.

heating $\mathrm{CaCO}_3$ (s) to form $\mathrm{CaO}$ (s) and $\mathrm{CO}_2$ (g)

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 $775 \mathrm{~g}$ 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.

raising the temperature of water from $25^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$

Sulfur ( $2.56 \mathrm{~g}$ ) was burned in a constant volume calorimeter with excess $\mathrm{O}_2(\mathrm{~g})$. The temperature increased 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 contained $815 \mathrm{~g}$ of water. Calculate $\Delta U$ per mole of $\mathrm{SO}_2$ formed for the reaction

$$\mathrm{S}_{\mathrm{B}}(\mathrm{s})+8 \mathrm{O}_2(\mathrm{~g}) \rightarrow 8 \mathrm{SO}_2(\mathrm{~g})$$

Sulfur burns in oxygen with a bright blue flame to give $\mathrm{SO}_2(\mathrm{~g})$.

melting of ice

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 $135 \mathrm{~g}$ 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 $\mathrm{kJ} / \mathrm{mol}$.

For the purposes of this analysis, let us use octane $({C}_8 {H}_{18})$ as a substitute for the complex mixture of hydrocarbons in gasoline. Data you will need for this question are:

$$\begin{gathered} \Delta_f H^{\circ}\left[{C}_8 {H}_{18}(\ell)\right]=-250.1 {~kJ} / {mol} \\ \text { Density of ethanol }=0.785 {~g} / {mL} \\ \text { Density of octane }=0.699 {~g} / {mL} \end{gathered}$$

Now contrast the fuels on an energy-equivalent basis. What volume of ethanol would have to be burned to get the same energy as 1.00 L of octane? When you burn enough ethanol to have the same energy as a liter of octane, which fuel produces more ${CO}_2$?

Identify whether the following processes are exothermic or endothermic.
combustion of methane

Adding $5.44 \mathrm{~g}$ of $\mathrm{NH}_4 \mathrm{NO}_5(\mathrm{~s})$ 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 $\mathrm{NH}_4 \mathrm{NO}_9(\mathrm{~s})$ in water, in $\mathrm{kJ} /$ 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.)
A cold pack uses the endothermic enthalpy of a solution of ammonium nitrate.