How Do You Calculate the Equilibrium Constant for This Reaction?

[Malgrif]

Homework Statement

Consider the system

CO2(g) + H2(g) <====> CO(g) + H2O(g)

Initially, 0.25 mol of water vapour and 0.2 mol of carbon monoxide are placed in a 1.00 L reaction vessel. At equilibrium, spectroscopic evidence shows that 0.1 mol of carbon dioxide is present. Calculate K for the reaction.

Homework Equations

equilibrium law

The Attempt at a Solution

So writing down the equilibrium law we get.
Kc = [CO][H2O]/[CO2]

Now we need to find the unknowns. We know 3/4 of the reaction's concentrations but how do you find the forth? An ice table won't work since we don't have a Kc value and without a given H2 value we can't calculate Kc. Stoichometry sounds useless since the system is in equilibrium so what the heck. How do you solve this problem?

 

[Borek]

You were already answered somewhere else, but let me repeat: stoichiometry is a key.

Think this way: you start with 25 molecules of water and 20 molecules of carbon monoxide. At equlibrium you find there are 10 molecules of carbon dixode. There were 20 atoms of carbon in the system - if 10 are in the form of dioxide, other 10 must be still in the form of monoxide. That means that 10 molecules of monoxide reacted with water molecules - stoichiometry of the reaction tells you how many molecules of water reacted and how many molecules of hydrogen were produced.