Question

Chemical reaction is invariably associated with the transfer of energy either in the form of heat or light. In the laboratory, heat changes in physical and chemical processes are measured with an instrument called Calorimeter. Heat change in the process is calculated as :

$q=ms\Delta T$ ........ $s=specificheat$
$=c\Delta T$ ....... $c=heatcapacity$
Heat of reaction at constant volume is measured using bomb Calorimeter.
$q_V=\Delta U=$internal energy change
Heat of reaction at constant pressure is measured using bomb Calorimeter.
$q_P=\Delta H$
$q_P=q_V+P\Delta V$
$\Delta H=\Delta U+\Delta nRT$

The heat capacity of a bomb calorimeter is $500J{K}^{-1}$. When $0.1g$ of Methane was burnt in this calorimeter, the temperature rose by $2^{\circ }C$. The value of $\Delta U$ per mole will be :

• A. $-160kJ$
• B. $+260kJ$
• C. $-2kJ$
• D. $+2kJ$

Answer 1

The correct option is A $-160kJ$

Internal energy of the system can be defined as :

$\Delta E=n{C}_v\Delta T$

$n=\frac{m}{M}=\frac{0.1}{16}=6.25\times {10}^{-3}mol$

Specific heat of methane is $C_v=500KJ{mol}^{-1}$

$T_1=273K{T}_2=273+2=275K$

$\Delta E=n{C}_v\Delta T$

$\Delta E=6.25\times {10}^{-3}\times 500\times (275-273)=-160KJ/mol$

Therefore, internal energy per mole will be -160KJ/mol.