Chapter 5

Under constant-volume conditions, the heat of combustion of naphthalene $\left({\mathrm{C}}_{10}{\mathrm{H}}_8\right)$ is $40.18\mathrm{kJ}/\mathrm{g}$. A 2.50 -g sample of naphthalene is burned in a bomb calorimeter. The temperature of the calorimeter increases from 21.50 to ${28.83}^{\circ }\mathrm{C}$. (a) What is the total heat capacity of the calorimeter? (b) A 1.50-g sample of a new organic substance is combusted in the same calorimeter. The temperature of the calorimeter increases from 21.14 to ${25.08}^{\circ }\mathrm{C}$. What is the heat of combustion per gram of the new substance? (c) Suppose that in changing samples, a portion of the water in the calorimeter were lost. In what way, if any, would this change the heat capacity of the calorimeter?

Can you use an approach similar to Hess's law to calculate the change in internal energy, $\mathrm{\Delta }E,$ for an overall reaction by summing the $\mathrm{\Delta }E$ values of individual reactions that add up to give the desired overall reaction?

Consider the following hypothetical reactions: $$\begin{array}{l}\mathrm{A}⟶\mathrm{B}\mathrm{\Delta }{H}_I=+60\mathrm{kJ}\\ \mathrm{B}⟶\mathrm{C}\mathrm{\Delta }{H}_{II}=-90\mathrm{kJ}\end{array}$$ (a) Use Hess's law to calculate the enthalpy change for the reaction $\mathrm{A}⟶\mathrm{C}$. (b) Construct an enthalpy diagram for substances A, B, and C, and show how Hess's law applies.

Calculate the enthalpy change for the reaction $${\mathrm{P}}_4{\mathrm{O}}_6(s)+2{\mathrm{O}}_2(g)⟶{\mathrm{P}}_4{\mathrm{O}}_{10}(s)$$ given the following enthalpies of reaction: $$\begin{array}{ll}{\mathrm{P}}_4(s)+3{\mathrm{O}}_2(g)⟶{\mathrm{P}}_4{\mathrm{O}}_6(s)& \mathrm{\Delta }H=-1640.1\mathrm{kJ}\\ {\mathrm{P}}_4(s)+5{\mathrm{O}}_2(g)⟶{\mathrm{P}}_4{\mathrm{O}}_{10}(s)& \mathrm{\Delta }H=-2940.1\mathrm{kJ}\end{array}$$

From the enthalpies of reaction $$\begin{array}{rlr}2\mathrm{C}(s)+{\mathrm{O}}_2(g)& ⟶2\mathrm{CO}(g)& \mathrm{\Delta }H=-221.0\mathrm{kJ}\\ 2\mathrm{C}(s)+{\mathrm{O}}_2(g)+4{\mathrm{H}}_2(g)& ⟶& 2{\mathrm{CH}}_3\mathrm{OH}(g)& \mathrm{\Delta }H=-402.4\mathrm{kJ}\end{array}$$ calculate $\mathrm{\Delta }H$ for the reaction $$\mathrm{CO}(g)+2{\mathrm{H}}_2(g)⟶{\mathrm{CH}}_3\mathrm{OH}(g)$$

From the enthalpies of reaction $$\begin{array}{rlrl}{\mathrm{H}}_2(g)+{\mathrm{F}}_2(g)& ⟶2\mathrm{HF}(g)& & \mathrm{\Delta }H=-537\mathrm{kJ}\\ \mathrm{C}(s)+2{\mathrm{F}}_2(g)& ⟶{\mathrm{CF}}_4(g)& & \mathrm{\Delta }H=-680\mathrm{kJ}\\ 2\mathrm{C}(s)+2{\mathrm{H}}_2(g)& ⟶{\mathrm{C}}_2{\mathrm{H}}_4(g)& & \mathrm{\Delta }H=+52.3\mathrm{kJ}\end{array}$$ calculate $\mathrm{\Delta }H$ for the reaction of ethylene with ${\mathrm{F}}_2$ : $${\mathrm{C}}_2{\mathrm{H}}_4(g)+6{\mathrm{F}}_2(g)⟶2{\mathrm{CF}}_4(g)+4\mathrm{HF}(g)$$

(a) What is meant by the term standard conditions with reference to enthalpy changes? (b) What is meant by the term enthalpy of formation? (c) What is meant by the term standard enthalpy of formation?

(a) Why does the standard enthalpy of formation of both the very reactive fluorine $\left({\mathrm{F}}_2\right)$ and the almost inert gas nitrogen $\left({\mathrm{N}}_2\right)$ both read zero? (b) Write the chemical equation for the reaction whose enthalpy change is the standard enthalpy of formation of naphthalene $\left({\mathrm{C}}_{10}{\mathrm{H}}_8\right)$.

For each of the following compounds, write a balanced thermochemical equation depicting the formation of one mole of the compound from its elements in their standard states and then look up $\mathrm{\Delta }{H}^{\circ }{}_f$ for each substance in Appendix $\mathrm{C}$. (a) ${\mathrm{NO}}_2(g),$ (b) ${\mathrm{SO}}_3(g),$ (c) $\mathrm{NaBr}(s),$ (d) $\mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2(s).$

Write balanced equations that describe the formation of the following compounds from elements in their standard states, and then look up the standard enthalpy of formation for each substance in Appendix C: (a) ${\mathrm{CH}}_3\mathrm{OH}(l),$ (b) ${\mathrm{CaSO}}_4(s),$ (d) ${\mathrm{P}}_4{\mathrm{O}}_6(s),$ (c) $\mathrm{NO}(g)$.