Question

Find ${\Delta }_f{U}^{}$ for the reaction $4HCl\left(g\right)+O_2\left(g\right)\rightleftharpoons 2{Cl}_2\left(g\right)+2H_{2}O\left(g\right)$ at 300 K. Assume all gases are ideal.
Given:
$H_2\left(g\right)+{Cl}_2\left(g\right)⟶2HCl\left(g\right){\Delta }_f{H}_{300}^{{}^{}}=-184.5kJ/mole$
$H_2\left(g\right)+O_2\left(g\right)⟶{2H}_{2}O\left(g\right){\Delta }_f{H}_{300}^{{}^{}}=-483kJ/mole(UseR=8.3J/mole)$

• A. $111.5kJ/mole$
• B. $-109.01kJ/mole$
• C. $-111.5kJ/mole$
• D. None of these

Answer 1

The correct option is C $-111.5kJ/mole$

$\left(H_2\right(g)+C{l}_2(g)⟶2HCl(g)$ ${\Delta }_{f}H=-184.5)\times 2$

$2H_2\left(g\right)+2C{l}_2\left(g\right)⟶4HCl\left(g\right)$ ${\Delta }_{f}H=-369.0kJ/mole⟶\left(1\right)$

$2H_2\left(g\right)+O_2\left(g\right)⟶2H_{2}O\left(g\right)$ ${\Delta }_{f}H=-483kJ/mole⟶\left(2\right)$

Reversing (1)

$4HCl⟶2H_2\left(g\right)+2C{l}_2\left(g\right)$ ${\Delta }_{f}H=+369.0⟶\left(3\right)$

$\left(3\right)+\left(2\right)⟶$

$4HCl\left(g\right)+O_2\left(g\right)\rightleftharpoons 2C{l}_2\left(g\right)+2H_{2}O$ ${\Delta }_f{H}_{300}=-114kJ/mole$

$\therefore {\Delta }_{f}U={\Delta }_{f}H-p\Delta V$

$={\Delta }_{f}H-\Delta n_{g}RT$ $\Delta ng=-1$

$=-114-(-1)(8.3\times {10}^{-3}\times 300)$

$=-114+2.49$

$=-111.5kJ/mol$