Equilibrium constant expression

1. Apr 22, 2014

Dassinia

Hello
I'm solving previous exams and there is this exercise that appears in almost every exam :
1. The problem statement, all variables and given/known data

Suppose v moles of a gas H2O are enclosed in a constant volume V at a low temperature so the gas is in aN undissociated state. At highest temperatureS, H2O molecules are dissociated
2H2O-> 2H2 + O2

If "f" is the fraction of H2O molecules that are dissociated at a known temperature T, and p the total pressure of the gas at that temperature, show that Kp(T) at this pressure is :
Kp(T)= p f^3/ (( 1-f)^2(2+f) )

2. Relevant equations

3. The attempt at a solution
Kp(T)=[ (P02)*PH2² ]/(PH20

We have Pi=xi*p
Kp(T)= [ x02*p*(xH2*p)² ]/(xH20*p)²
Kp(T)= [ p*x02*xH2² ]/xH20²

xi=ni/ntot

Kp(T)= [ p*n02*nH2² ]/(nH20²*ntot)

nH20²=(1-f)²
but I don't get why ntot=2+f and n02=nH2=f

Last edited: Apr 22, 2014
2. Apr 22, 2014

Staff: Mentor

If you have v moles of H2O to start with, and fv moles H2O dissociated to H2 and O2, how many moles of H2O are left, and how many moles of O2 and H2 are formed (in terms of v and f)? What is the total number of moles of H2O remaining (in terms of v and f)? What is the total number of moles in the container after fv moles of H2O has dissociated? What is the mole fractions of H2O, H2, and O2? What are the partial pressures of these species?

Chet

3. Apr 22, 2014

Dassinia

For H2O we have (v-vf) remaining
If we have fv moles of H2O are dissociated we will have fv moles of H2 and fv moles of O2 ?

4. Apr 22, 2014

Staff: Mentor

From the stoichiometry, you will have fv/2 moles of water, correct?

Chet

5. Apr 22, 2014

Dassinia

My chemistry courses are so far away :uhh:
Why fv/2 moles of H2O and not (v-vf)moles ?

6. Apr 22, 2014

Staff: Mentor

Oops. Sorry. I meant fv/2 moles of oxygen.

Chet

7. Apr 22, 2014

Dassinia

Oh so it is fv/2 of O2 and fv of H2

So we have ntot=fv/2+fv-fv+v=v/2(f+2)
nO2=fv/2
nH2=fv
nH2O=v(1-f)

Thank you thank you ! now it is really clear in my head !

Last edited: Apr 22, 2014
8. Apr 22, 2014

Staff: Mentor

Good. Nice job.

Chet