Question

For a reaction, $\Delta C_p=2.0+0.2Tca{l}^{\circ }C$ and enthalpy of reaction at 10 K is -14.2 kcal. The enthalpy of this reaction at 100 K in kcal is:

• A. $-13.03$
• B. $-16.02$
• C. $-15.3$
• D. $7.08$

Answer 1

The correct option is A $-13.03$

For a reaction, $\Delta C_p=2.0+0.2Tca{l}^{\circ }C$ and enthalpy of reaction at 10 K is -14.2 kcal. The enthalpy of this reaction at 100 K will be -13.03 kcal.
The calculations are shown below.
$\Delta H_2=\Delta H_1+\stackrel{100}{\underset{10}{\int }}\Delta C_p.dT=-14.2+\stackrel{100}{\underset{10}{\int }}[2.0+0.2T].dT$
$\Delta H_2=-14.2\times {10}^3+[20\times [100-10]+0.2[\frac{{100}^2}{2}-\frac{{10}^2}{2}]]$
$\Delta H_2=-14.2\times {10}^3+[180+1000-10]$
$\Delta H_2=-14.2\times {10}^3+1170=-13.03kcal$