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 $20 kJ K^{- 1}, R = 8.3 J K^{- 1} {mol}^{- 1}$
Assume ideal gas behavior.
Atomic mass of C and H are 12 g mol^-1 and 1 g mol^-1 respectively]

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answer is 1006.

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Detailed Solution

$\begin{array}{l} Q = C_{V} \times ΔT \times \frac{m . wt}{wt of organic compound} \\ = 20 \times 0.5 \times \frac{30}{0.3} = 1000 kJ {mol}^{- 1} \end{array}$
Heat of combustion at constant volume, $ΔU = - 1000 kJ {mol}^{- 1}$

$\begin{array}{l} C_{2} H_{6_{(g)}} + \frac{7}{2} O_{2_{(g)}} \to 2 {CO}_{2_{(g)}} + 3 H_{2} O_{(l)} \\ {Δn}_{(g)} = (2 - 4.5) = - 2.5 \\ ΔH = ΔU + {Δn}_{g} RT \\ = - 1000 + (- 2.5) \times 8.314 \times 10^{- 3} \times 300 \\ = - 1000 - 6.2 \\ ≅ - 1006 kJ {mol}^{- 1} \end{array}$