Question

A mixture of gaseous CO and H2, called synthesis gas, is used commercially to prepare methanol (CH3OH), a compound considered an alternative fuel to gasoline. Under equilibrium conditions at 550.3 K, [H2] = 0.07710 mol/L, [CO] = 0.02722 mol/L, and [CH3OH] = 0.0401 mol/L. What is the value of Kc for this reaction at 550.3 K?

Answer 1

Answer: The value of $K_c$ for the reaction at 550.3 K is 247.83

Explanation:

Equilibrium constant in terms of concentration is defined as the ratio of concentration of products to the concentration of reactants each raised to the power their stoichiometric ratios. It is expressed as $K_{c}$

For a general chemical reaction:

$aA+bB\rightarrow cC+dD$

The expression for $K_{c}$ is written as:

$K_{c}=\frac{[C]^c[D]^d}{[A]^a[B]^b}$

The chemical equation for the production of methanol follows:

$CO+2H_2\rightleftharpoons CH_3OH$

The expression of $K_c$ for above equation follows:

$K_c=\frac{[CH_3OH]}{[CO][H_2]^2}$

We are given:

$[CH_3OH]=0.0401mol/L$

$[CO]=0.02722mol/L$

$[H_2]=0.07710mol/L$

Putting values in above equation, we get:

$K_c=\frac{0.0401}{0.02722\times (0.07710)^2}\\\\K_c=247.83$

Hence, the value of $K_c$ for the reaction at 550.3 K is 247.83