Equilibrium constant expression

[Dassinia]

Hello
I'm solving previous exams and there is this exercise that appears in almost every exam :

Homework Statement

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) )

Homework Equations

The Attempt at a Solution

Kp(T)=[ (P₀₂)*P_H2² ]/(P_H20)²

We have Pi=xi*p
Kp(T)= [ x₀₂*p*(x_H2*p)² ]/(x_H20*p)²
Kp(T)= [ p*x₀₂*x_H2² ]/x_H20²

xi=ni/ntot

Kp(T)= [ p*n₀₂*n_H2² ]/(n_H20²*n_tot)

n_H20²=(1-f)²
but I don't get why n_tot=2+f and n₀₂=n_H2=f

 

[Chestermiller]

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

 

[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 ?

 

[Chestermiller]

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 ?

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

Chet

 

[Dassinia]

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

 

[Chestermiller]

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

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

Chet

 

[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 !

 

[Chestermiller]

Good. Nice job.

Chet