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  4. 0.3 g of ethane undergoes combustion at 27° C in a bomb calorimeter. The temperature of calorimeter system (including the water) is found to rise by 0.5° 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]

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Q. $0.3\, g$ 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]

JEE MainJEE Main 2023Thermodynamics

Solution:

(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 $=1006\, kJ \,mol ^{-1}$