Question

Heat of combustion of benzoic acid $\left(C_6{H}_{5}COOH\right)$ at constant volume at ${25}^0$ is 3233KJ/mole. When 0.5g of benzoic acid is burnt in bomb calorimeter, the temperature of calorimeter increased by ${0.53}^{0}C$. Now in the same bomb calorimeter 1g of $C_2{H}_6$ burnt then temperature increased by ${2.04}^{0}C$. $△H$ for combustion of $C_2{H}_6$ is?

Answer 1

Given,

For Benzoic acid,

$△H=-3233kJ/mol$

$T=298K$

Molar Mass = $M=122g$

Burned mass of Benzoic acid = $w=0.5g$

We know that,

$△H=△U_1+△nRT$

$\Rightarrow -3233=△U_1+(-3)\times 8.314\times 298\times {10}^{-3}$

$△U_1=7.43-3233=-3225.56kJ$

Also we know that, $U_1=Z\times \theta \times \frac{M_1}{w_1}$

For Benzoic acid:

$Z=\frac{△U_1\times w_1}{{\theta }_1\times M_1}$..........(i)

For Ethane:

$Z=\frac{△U_2\times w_2}{{\theta }_2\times M_2}$..........(ii)

From (i) and (ii) we have,

$\frac{△U_1\times w_1}{{\theta }_1\times M_1}=\frac{△U_2\times w_2}{{\theta }_2\times M_2}$

$△U_2=\frac{-3225.56\times 0.5}{0.53\times 122}\times \frac{2.04\times 30}{1}$

$△H_2=△U_2+△nRT$

$=-1536.2kJ$.