Question

The bomb calorimeter in Exercise 97 is filled with 987 g of water. The initial temperature of the calorimeter contents is 23.32^oC. A 1.056-g sample of benzoic acid( =-26.42 kJ/g) is combusted in the calorimeter. What is the final temperature of the calorimeter contents?

Short answer

The final temperature of the calorimeter content is 27.48^oC.

Step-by-step solution

Determination of heat capacity of benzoic acid

The heat capacity of benzoic acid is,

$\begin{array}{rcl}\mathit{H}\mathit{e}\mathit{a}\mathit{t}\mathbf{ }\mathit{c}\mathit{a}\mathit{p}\mathit{a}\mathit{c}\mathit{i}\mathit{t}\mathit{y}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }{\mathit{C}}_{\mathbf{6}}{\mathit{H}}_{\mathbf{5}}\mathit{C}\mathit{O}\mathit{O}\mathit{H}& \mathbf{=}& \mathit{T}\mathit{o}\mathit{t}\mathit{a}\mathit{l}\mathbf{ }\mathit{h}\mathit{e}\mathit{a}\mathit{t}\mathbf{ }\mathit{c}\mathit{a}\mathit{p}\mathit{a}\mathit{c}\mathit{i}\mathit{t}\mathit{y}\mathbf{-}\mathit{h}\mathit{e}\mathit{a}\mathit{t}\mathbf{ }\mathit{c}\mathit{a}\mathit{p}\mathit{a}\mathit{c}\mathit{i}\mathit{t}\mathit{y}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{w}\mathit{a}\mathit{t}\mathit{e}\mathit{r}\\ & \mathbf{=}& \mathbf{10}\mathbf{.}\mathbf{84}\mathbf{-}\mathbf{4}\mathbf{.}\mathbf{12}\\ & \mathbf{=}& \mathbf{6}\mathbf{.}\mathbf{72}\mathit{k}\mathit{J}\mathbf{/}{}^{\mathbf{o}}\mathit{C}\\ & & \end{array}$

Determination of final temperature 

The final temperature of the calorimeter content is,

$\begin{array}{rcl}Heat capacity& =& \frac{ enthalpy change}{change in temperature}\\ 6.72kJ/{}^{o}C& =& \frac{26.42kJ/g\times 1.056g}{T_2-23.32{}^{o}C}\\ T_2& =& 27.48{}^{o}C\\ & & \end{array}$

Thus, the final temperature of the calorimeter content is 27.48^oC.