I cannot figure out how to solve this problem! Help! Thanks! The water gas shift

Question

I cannot figure out how to solve this problem! Help! Thanks!

The water gas shift reaction plays a central role in the chemical methods for obtaining cleaner fuels from coal: CO (g) + H_2 O(g) doubleheadarrow CO_2 + H_2(g) A study was made in which equilibrium Has reached with [CO] = [H_2O] = [H_2] = 0.100 M and [CO_2] = 0.400 M. After 1.30 mol of H_2 is added to the 2.00 L container and equilibrium is reestablished, what are the new concentrations of all the components? [CO]_eq 0.222 M H_2 O_eq 0.222 M [CO_2]_eq 0.222 M H_2_eq 0.222 M

Explanation / Answer

K = 0.4 x 0.1 / 0.1 x 0.1 = 4

Conc. of H2 added = 1.30 / 2 = 0.65 M

CO + H2O -----> CO2 + H2

0.1+X, 0.1+X......0.4-X,..0.1 + 0.65-X

K = (0.75-X) x (0.4-X) / (0.1+X)^2 = 4

This equation simplifies down to,

3X^2 + 1.95X - 0.26 = 0

=> X = 0.1135 M

[CO] = [H2O] = 0.1 + X = 0.1 + 0.1135 = 0.21 M

[CO2] = 0.4 - X = 0.29 M

[H2] = 0.75 - X = 0.64 M

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