Question 4.3: When 0.972 g of cyclohexane undergoes complete combustion in...
When 0.972 g of cyclohexane undergoes complete combustion in a bomb calorimeter,\Delta T of the inner water bath is 2.98°C. For cyclohexane, \Delta U_{combustion} is –3913 kJ mol^{-1}. Given this result, what is the value for \Delta U_{combustion} for the combustion of benzene if \Delta T is 2.36°C when 0.857 g of benzene undergoes complete combustion in the same calorimeter? The mass of the water in the inner bath is 1.812 × 10^{3}g, and the C_{P,m } of water is 75.3 J K^{-1} mol^{-1}.
To calculate the calorimeter constant through the combustion of cyclohexane, we write
Equation (4.21) in the following form:
\Delta U=\frac{m_{s}}{M_{s}}\Delta U_{combustion}+\frac{m_{H_{2}O}}{M_{H_{2}O}}× C_{P,m}\left( H_{2} O\right)× \Delta T + C_{calorimeter} × \Delta T=0 (4.21)
C_{calorimeter}=\frac{-\frac{m_{s}}{M_{s}}\Delta U_{combustion}-\frac{m_{H_{2}O}}{M_{H_{2}O}}C_{P,m}\left( H_{2}O \right)\Delta T}{\Delta T}
=\frac{\frac{0.972 g}{84.16 g mol^{-1}}× 3913 × 10^{3} J mol^{-1}-\frac{1.812 × 10^{3}g}{18.02 g mol^{-1}}× 75.3 J mol^{-1}K^{-1}× 2.98°C}{2.98°C}
=7.59 × 10^{3}J \left(°C \right)^{-1}
In calculating \Delta U_{combustion} for benzene, we use the value for C_{calorimeter}:
\Delta U_{combustion}=-\frac{M_{s}}{m_{s}}\left( \frac{m_{_{H_{2}O}}}{M_{H_{2}O}}C_{P,m }\left( H_{2}o\right)\Delta T + C_{calorimeter}\Delta T \right)=-\frac{78.12 g mol^{-1}}{0.857 g} × \left( ^{\frac{1.812 ×10^{3} g}{18.02 g mol^{-1}}× 75.3 J mol^{-1}K^{-1}× 2.36°C}_{+7.59 × 10^{3} J \left( °C \right)^{-1}× 2.36°C} \right)
=-3.26 × 10^{6} J mol^{-1}