Question

The heat of formaiton of $HCl$ at 348 K from the given data will be :
$\frac{1}{2}{H}_2\left(g\right)+\frac{1}{2}C{l}_2\left(g\right)\to HCl\left(g\right)△H_{298}^o=-22060calmo{l}^{-1}$
The mean heat capacities over this temperature range are,
$H_2\left(g\right),C_P=6.82calmo{l}^{-1}{K}^{-1};$
$C{l}_2\left(g\right),C_P=7.71calmo{l}^{-1}{K}^{-1};$
$HCl\left(g\right),C_P=6.81calmo{l}^{-1}{K}^{-1}.$

• A. $20095cal$
• B. $-32758cal$
• C. $37725cal$
• D. $-22083cal$

Answer 1

The correct option is D $-22083cal$

Balanced chemical reaction
$\frac{1}{2}{H}_2\left(g\right)+\frac{1}{2}C{l}_2\left(g\right)\to HCl\left(g\right)$
So, here
$△C_P=C_{P\left(Product\right)}-C_{P\left(Reactant\right)}$
$△C_P=C_P\left(HCl\right)-\frac{1}{2}{C}_P\left(H_2\right)-\frac{1}{2}{C}_P\left(C{l}_2\right)$
putting the values,
$=6.81-\frac{1}{2}\times 6.82-\frac{1}{2}\times 7.71$
$=6.81-3.41-3.855=-0.45calmo{l}^{-1}{K}^{-1}$

According to kirchoff equation :
$△H_{348}=△H_{298}+\left(△C_P\right)\left(△T\right)$
putting the values,
$=-22060+(-0.45)\times (348-298)$
$=-22060+(-0.45)\times 50$
$=-22082.5calmo{l}^{-1}$


Theory:

Kirchoff’s Equation:
Kirchhoff's Law describes the enthalpy of a reaction's variation with temperature changes. The overall enthalpy of the reaction will change if the increase in the enthalpy of products and reactants is different.

Kirchoff’s equation can be written as:
${\Delta }_r{H}_2={\Delta }_r{H}_1+{\Delta }_r{C}_{p,m}\left[\Delta T_2-T_1\right]$

If $C_{p,m}$ is given as a function of temperature,

${\Delta }_r{H}_2={\Delta }_r{H}_1$+ ${\int }_{T_1}^{T_2}{\Delta }_r{C}_{p,m}dT$

Where $T_1$ and $T_2$ are in Kelvin $\left(K\right)$