Question

hydrogen is manufactured on an industrial scale by this sequence of reactions:

$$\\mathrm { ch } _ { 4 } ( g ) + \\mathrm { h } _ { 2 } \\mathrm { o } ( g ) \ ightleftharpoons \\mathrm { co } ( g ) + 3 \\mathrm { h } _ { 2 } ( g )$$

$$\\mathrm { co } ( g ) + \\mathrm { h } _ { 2 } \\mathrm { o } ( g ) \ ightleftharpoons \\mathrm { co } _ { 2 } ( g ) + \\mathrm { h } _ { 2 } ( g )$$

the net reaction is:

$$\\mathrm { ch } _ { 4 } ( g ) + 2 \\mathrm { h } _ { 2 } \\mathrm { o } ( g ) \ ightleftharpoons \\mathrm { co } _ { 2 } ( g ) + 4 \\mathrm { h } _ { 2 } ( g )$$

write an equation that gives the overall equilibrium constant ( k ) in terms of the equilibrium constants ( k _ { 1 } ) and ( k _ { 2 } ). if you need to include any physical constants,
be sure you use their standard symbols, which youll find in the aleks calculator.

$$k = \square$$

Explanation:

Step1: Write the expression for \(K_1\)

For the reaction \(CH_4(g)+H_2O(g)
ightleftharpoons CO(g)+3H_2(g)\), the equilibrium constant \(K_1=\frac{[CO][H_2]^3}{[CH_4][H_2O]}\)

Step2: Write the expression for \(K_2\)

For the reaction \(CO(g)+H_2O(g)
ightleftharpoons CO_2(g)+H_2(g)\), the equilibrium constant \(K_2=\frac{[CO_2][H_2]}{[CO][H_2O]}\)

Step3: Write the expression for \(K\)

For the net reaction \(CH_4(g)+2H_2O(g)
ightleftharpoons CO_2(g)+4H_2(g)\), the equilibrium constant \(K = \frac{[CO_2][H_2]^4}{[CH_4][H_2O]^2}\)

Step4: Multiply \(K_1\) and \(K_2\)

\(K_1\times K_2=\frac{[CO][H_2]^3}{[CH_4][H_2O]}\times\frac{[CO_2][H_2]}{[CO][H_2O]}=\frac{[CO_2][H_2]^4}{[CH_4][H_2O]^2}\)

Answer:

\(K = K_1\times K_2\)