Lets assume that we start with 2 moles of steam:
We are told that 20% of the steam dissociates. This means that 20% of 2 moles dissociate which = 2 x 0.2 = 0.4 moles.
This means that the number of moles of steam left @ equilibrium = (2 - 0.4) = 1.6 mol
From the equation we can see that if 0.4 mol steam dissociate then 0.4 mol of hydrogen must form as well as 0.2 mol oxygen.
So equilibrium moles
So the total moles @equilibrium
We can now work out the mole fraction of each gas since
We can then find the partial pressure of each gas since for a gas
Lets do a check here and see if they add up to the total pressure of
!! LONG ANSWER !!
Here's how you should approach this problem.
You know that at a total pressure of 1 atm and at very high temperatures, water dissociates to form hydrogen gas,
The equilibrium reaction that describes that dissociation looks like this
Notice that 2 moles of water produce 2 moles of hydrogen gas and 1 mole of oxygen.
You also know that only 20% of the molecules dissociate. If you have
Out of the molecules that do dissociate, you know that each pair produces a pair of hydrogen molecules and 1 oxygen molecule. This means that you have
So, at equilibrium, your vessel will contain
The total number of molecules will be
You can write the partial pressure of each gas by using the mole fraction they hold in the mixture and the total pressure of the mixture by using Dalton's Law of Partial Pressures.
The mole fraction is defined as the number of moles of a gas divided by the total number of moles of gas present in a mixture. In your case, you have
The partial pressures of the three gases will be
The equilibrium constant,