Question

$0.3\, g$ of ethane undergoes combustion at $27^{\circ} C$ in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by $0.5^{\circ} C$. The heat evolved during combustion of ethane at constant pressure is ___$kJ \, mol ^{-1}$.
(Nearest integer)
[Given : The heat capacity of the calorimeter system is $20 \, kJ\, K ^{-1}, R =8.3 \, JK ^{-1}\, mol ^{-1}$.
Assume ideal gas behaviour.
Atomic mass of $C$ and $H$ are 12 and $1\, g\, mol ^{-1}$ respectively]

Answer 1

(Bomb calorimeter $\rightarrow$ const volume
Heat released
By combustion of 1 mole
$C _2 H _6(\Delta U )=-\frac{20 \times 0.5}{0.3} \times 30=-1000\, kJ$
$C _2 H _6( g )+7 / 2 O _2( g ) \rightarrow 2 CO _2( g )+3 H _2 O (l)$
$\Delta ng =2-(2+7 / 2)=-(7 / 2)$
$\Delta H =\Delta U +\Delta nRT$
$=-1000-7 / 2 \times 8.3 \times 300\, k J$
$=-1000-6.225$
$=-1006 \,kJ$
So heat released $=1006\, kJ \,mol ^{-1}$