Question

Be sure to answer all parts. Be sure to report your answer to the correct number of significant figures. Calculate ΔG o and KP for the following processes at 25°C: (a) H2(g) + Br2(l) ⇌ 2HBr(g) ΔG o = kJ/mol KP = × 10 (Enter your answer in scientific notation.) (b) 1 2 H2(g) + 1 2 Br2(l) ⇌ HBr(g) ΔG o = kJ/mol KP = × 10 (Enter your answer in scientific notation.)

Answer 1

Answer: (a) The value of $K_{p}$ is $4 \times 10^{18}$ and value of $\Delta G^{o}$ is -106.4 kJ/mol.

(b) The value of $K_{p}$ is $2 \times 10^{9}$ and value of $\Delta G^{o}$ is -53.2 kJ/mol.

Explanation:

(a)   As the given reaction equation is as follows.

   $H_{2}(g) + Br_{2}(l) \rightleftharpoons 2HBr(g)$

Firs, we will calculate the value of $\Delta G^{o}$ as follows.

  $\Delta G^{o} = 2\Delta G^{o}_{F(HBr)} - \Delta G^{o}_{F(Br_{2})}$

               = $2 \times -53.2 kJ/mol - (1) \times (0) - (1) \times (0)$

               = -106.4 kJ/mol

      $ln K_{p} = \frac{-\Delta G^{o}}{RT}$

                      = $\frac{106.4 \times 10^{3} J/mol}{8.314 J/mol K \times 298 K}$

          $ln K_{p}$ = 42.9

          $K_{p} = 4 \times 10^{18}$

Therefore, the value of $K_{p}$ is $4 \times 10^{18}$ and value of $\Delta G^{o}$ is -106.4 kJ/mol.

(b)   As the given reaction equation is as follows.

     $\frac{1}{2}H_{2}(g) + \frac{1}{2}Br_{2}(l) \rightleftharpoons HBr(g)$

So,  $\Delta G^{o} = \Delta G^{o}_{F(HBr)} - \frac{1}{2}\Delta G^{o}_{F(Br_{2})}$

              = $(1)(-53.2 kJ/mol) - (\frac{1}{2})(0) - (\frac{1}{2})(0)$

              = -53.2 kJ/mol

As,     $ln K_{p} = \frac{-\Delta G^{o}}{RT}$

                     = $\frac{53.2 \times 10^{3} J/mol}{8.314 J/mol K \times 298 K}$

                     = 21.5

             $K_{p} = 2 \times 10^{9}$

Therefore, the value of $K_{p}$ is $2 \times 10^{9}$ and value of $\Delta G^{o}$ is -53.2 kJ/mol.