In methane combustion, the following reaction pair is important: At 1500 K, the equilibrium constant Kp has a value of 0.003691 based on a reference-state pressure of 1 atm (101,325 Pa). Derive an algebraic ex- pression for the forward rate coefficient kf . Evaluate your expression for a temperature of 1500 K. Give units.

Answer :

Explanation:

Let us assume that the value of [tex]K_{r}[/tex] = [tex]2.82 \times 10^{5} \times e^({\frac{-9835}{T}}) m^{6}/mol^{2}s[/tex]

Also at 1500 K, [tex]K_{r}[/tex] = [tex]2.82 \times 10^{5} \times e^({\frac{-9835}{1500}}) m^{6}/mol^{2}s[/tex]

                     [tex]K_{r} = 400.613 m^{6}/mol^{2}s[/tex]

Relation between [tex]K_{p}[/tex] and [tex]K_{c}[/tex] is as follows.

                  [tex]K_{p} = K_{c}RT[/tex]

Putting the given values into the above formula as follows.

                  [tex]K_{p} = K_{c}RT[/tex]

         [tex]0.003691 = K_{c} \times 8.314 \times 1500[/tex]

                [tex]K_{c} = 2.9 \times 10^{-7}[/tex]

Also,     [tex]K_{c} = \frac{K_{f}}{K_{r}}[/tex]

or,                [tex]K_{f} = K_{c} \times K_{r}[/tex]

                               = [tex]2.9 \times 10^{-7} \times 400.613[/tex]

                               = [tex]1.1617 \times 10^{-4} m^{6}/mol^{2}s[/tex]

Thus, we can conclude that the value of [tex]K_{f}[/tex] is [tex]1.1617 \times 10^{-4} m^{6}/mol^{2}s[/tex].

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