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I've been assigned the following problem at school:

Given the following reaction:

$$\ce{C (s) + CO2 (g) <=> 2 CO (g)}$$

Find the mole fraction of $\ce{CO2}$ provided that, in equilibrium, $K_\mathrm{p} = 14.1$.

Our teacher's solution is $x(\ce{CO2}) = 0.324$ (mole fraction).

I suspect that the problem as is provides insufficient information to arrive at the solution above. Assuming that the total pressure of the system is $\pu{10 atm}$, the resulting mole fraction is indeed $0.324$.

Is the problem truly incomplete or can it be solved without knowing the total pressure?

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Grego
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    You seem to be comfortable enough working out the answer when you're given a pressure. Why not try working it out without explicitly choosing a pressure? Use $p$ as a symbol instead of putting in something like 10 atm, and if you find that all the $p$'s cancel out in your answer, then it follows that you don't actually need to know the pressure. – orthocresol Jan 11 '19 at 20:42
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    I have attempted this. The final expression is: 14.1x = (1-x)^2*PT. The total pressure does not seem to cancel out. Here, x is the mole fraction. X seems to be a function of PT. The value of X changes with other values of PT. – Grego Jan 11 '19 at 20:44
  • Took me a while to understand what that equation meant, but yeah, you are correct! So, the question is indeed incomplete. [More common notation would be something like $p_\text{tot}$; PT suggests some pressure multiplied by temperature...] – orthocresol Jan 11 '19 at 20:48
  • You can format mathematical and chemical expressions on Chemistry.SE using MathJax; this post contains further details. – orthocresol Jan 11 '19 at 20:50
  • Ok! Thanks for the quick reply! My bad. I'll keep this in mind for the next question. – Grego Jan 11 '19 at 20:51
  • Does you teacher at least give you the units of Kp? – Chet Miller Jan 12 '19 at 01:43
  • @ChesterMiller $K_\mathrm{p}$ is supposed to be dimensionless, isn't it? – andselisk Jan 12 '19 at 05:35
  • @andselisk Actually, it is expressed in terms of the ratio of the partial pressure of each substance to the pressure of each substance in its pure reference state. If the reference state happens to be 1 bar, and all the partial pressures are in bars, then the units cancel. If the units of the reference state are other than 1 bar, the pressure of the reference state must be included in the expression for Kp in order for it to be dimensionless. Otherwise, Kp will have units, and the partial pressures must be expressed in these units (assuming moles products and reactants don't match exactly). – Chet Miller Jan 12 '19 at 12:52
  • @ChesterMiller I'm not sure I follow, but what prevents the conversion of pressure units into bars with subsequent cancellation as the reference state is included by definition in $K_\mathrm{p}$?Of course, it's not always denoted as such, but it's always there, just as we speak of $K_\mathrm{c}$ in terms of concentrations keeping in mind they are multiplied by activity coefficients. Besides, I've never seen a respectable source showing $K_\mathrm{p}$ with any units (maybe I haven't seen everything in my life yet:) ). – andselisk Jan 12 '19 at 13:00
  • @andselisk That's because all the partial pressures are assumed to be in bars and the reference pressure is in bars. Try solving the same problem with the partial pressures expressed in mm Hg instead. You'll get a different answer (unless, fortuitously, the moles of reactants in the formula equal the mole of products). – Chet Miller Jan 12 '19 at 13:34
  • @ChesterMiller Why would I want to use mmHg scale in this case? It make as much sense as converting a temperature difference in degrees Celsius into degrees Kelvin by adding 273.15 to it:) – andselisk Jan 12 '19 at 13:40
  • @andselisk Well, suppose the total pressure were measured in mm Hg or psi. In that case, you would calculate partial pressures as mole fraction times total pressure, and you would have to convert back to bars. I feel like this is leading down a rabbit hole. – Chet Miller Jan 12 '19 at 14:39
  • @ChesterMiller I think you right both about the rabbit hole and unit conversion, in a sense. The thing is that there are too many textbooks and results published with $K_\mathrm{p}$ taken too liberally and it brings up a lot of confusion. I might also be totally wrong since you have more experience with physical chemistry in general than I do (judging from your answers:) ). – andselisk Jan 12 '19 at 15:10
  • @ChesterMiller My teacher did not provide the units of $Kp$ – Grego Jan 12 '19 at 21:10
  • Then, in that case, the partial pressures must be expressed in bars. – Chet Miller Jan 13 '19 at 02:55
  • In this case, total pressure "P" must be given to solve for "XA" (equilibrium molar fraction of CO2); however, that's because this reaction has Δn=1≠0. If a different reaction was given where Δn=0, the problem could be solved without knowing "P". – Sam202 Oct 06 '22 at 01:09

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