# Considering the following reaction: CO(g) + 2 H2(g) --> CH3OH(g) Suppose that the initial concentrations of the reactants are [CO] = 0.500 M and [H2] = 1.00 M. Assuming that there is no product at the beginning of the reaction and that at equilibrium [CO] = 0.15 M, what is the equilibrium constant at this new temperature?

Sep 14, 2014

The equilibrium constant is 26.

First, write the balanced chemical equation with an ICE table.

CO(g) + 2H₂(g) ⇌ CH₃OH(g)

I/mol·L⁻¹: 0.500; 0.100; 0
C/mol·L⁻¹: -$x$; -2$x$; +$x$
E/mol·L⁻¹: 0.500 - $x$; 0.100 - 2$x$; $x$

At equilibrium, [CO] = 0.15 mol/L = (0.500 - $x$) mol/L

So $x$ = 0.500 – 0.15 = 0.35

Then $\left[{\text{H}}_{2}\right]$ = (0.100 - 2$x$) mol/L = (0.100 – 2×0.35) mol/L = 0.30 mol/L

and

$\left[\text{CH"_3"OH}\right]$ = $x$ mol/L = 0.35 mol/L

K_"eq" = (["CH"_3"OH"])/(["CO"] ["H"_2]^2) = 0.35/(0.15 × 0.30^2) = 26