How is Kp(T) Derived for Dissociation of H2O at High Temperatures?

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Discussion Overview

The discussion revolves around deriving the expression for Kp(T) for the dissociation of H2O at high temperatures, specifically focusing on the stoichiometry and mole fractions involved in the reaction 2H2O -> 2H2 + O2. Participants explore the relationships between the amounts of reactants and products, as well as the implications for calculating Kp(T).

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a homework problem involving the dissociation of H2O and asks for the derivation of Kp(T) based on the fraction of dissociated molecules.
  • Another participant questions how to calculate the remaining moles of H2O and the moles of H2 and O2 formed in terms of the initial moles and the fraction dissociated.
  • There is a clarification that if fv moles of H2O are dissociated, then fv moles of H2 and fv/2 moles of O2 are produced.
  • Participants discuss the total number of moles remaining and the mole fractions of each species, leading to a formula for the total number of moles in the container.
  • One participant expresses confusion about the stoichiometric relationships and corrects their earlier misunderstanding regarding the amounts of products formed.
  • Another participant confirms the calculations and expresses satisfaction with the clarity of the discussion.

Areas of Agreement / Disagreement

Participants generally agree on the stoichiometric relationships and the calculations involved, but there are moments of confusion and clarification regarding the specific amounts of products formed from the dissociation of H2O.

Contextual Notes

Some assumptions about the initial conditions and definitions of variables are not fully articulated, which may affect the clarity of the derivation process.

Dassinia
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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)*PH2² ]/(PH20)²

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

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

Chet
 
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:
Good. Nice job.

Chet
 

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