TBR Gen Chem Equilibrium

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leathersofa

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My question is on the answer explanation. i have provided the question and the chemical reaction for reference. For the answer explanation (i have colored in pink the confusing part), how do we estimate the magnitude of x and how do we know that more than half units need to shift over?? Why is it more than half and not more than a quarter, what is the relation between this and Keq? Thank you.

PCl3(g) + Cl2(g) <---> PCl5(g)

17. If a flask were filled with PCI3 and CI2 to a total
pressure of 1.50 atm. such that the mole fraction of PCI3 is twice that of CI2, then what is the total pressure of the system once at equilibrium?
A . Less than 1.00 atm.
B . Between 1.00 atm. and 1.25 atm.
C . Between 1.25 atm. and 1.50 atm.
D . Greater than 1.50 atm.

Answer: B, To solve this question, use the formula X Pj = Ptotal- ln this case the following holds true:
Ptotal = PPCI3 + PC12 + pPCl5 = (1 " x) + (0-5 - x) + x = 1.5 - x.
If everything reacted to the limiting reagent capacity, then x is 0.5. But the reaction does not go to completion, so the value of x falls between 0 and 0.5. To solve this question, you must estimate the magnitude of x. The value of x is greater than 0.25, because over half shifts to products to reach an equilibrium constant of 1.95. This makes choice B the best answer.

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You know that you start with 1.00 atm of PCl3 and 0.5 atm Cl2. Eliminate choice D immediately since you know total pressure will decrease as PCl5 is formed.

Total pressure at equilibrium = pressure of PCl3 + pressure of Cl2 + pressure PCl5 = (1-x) + (.5-x) + (0+x) = 1.5 - x

Note that x can't be greater than 0.5, since that means that Cl2 would have a negative partial pressure at equilibrium

So now you know that total pressure at equilibrium MUST be greater than 1.0 (since 1.5 - 0.5 = 1.0). Eliminate A.

How do you decide between choices B and C? I'm assuming you are given that Keq = 1.95
Look at the case where x = .25. In that case, Q for the reaction will be (.25)/(.25)(.75) which is only 1.33. Since Q < K the reaction will keep shifting right. The answer must be B.
 
You know that you start with 1.00 atm of PCl3 and 0.5 atm Cl2. Eliminate choice D immediately since you know total pressure will decrease as PCl5 is formed.

Total pressure at equilibrium = pressure of PCl3 + pressure of Cl2 + pressure PCl5 = (1-x) + (.5-x) + (0+x) = 1.5 - x

Note that x can't be greater than 0.5, since that means that Cl2 would have a negative partial pressure at equilibrium

So now you know that total pressure at equilibrium MUST be greater than 1.0 (since 1.5 - 0.5 = 1.0). Eliminate A.

How do you decide between choices B and C? I'm assuming you are given that Keq = 1.95
Look at the case where x = .25. In that case, Q for the reaction will be (.25)/(.25)(.75) which is only 1.33. Since Q < K the reaction will keep shifting right. The answer must be B.

how do you know that pressure decreases as PCl5 is formed? Is it because it goes from 2 moles of reactants to 1 mole of products?

thanks!
 
how do you know that pressure decreases as PCl5 is formed? Is it because it goes from 2 moles of reactants to 1 mole of products?

thanks!
Yes. As the reactants combine to form products, the total # of moles decreases, so the total pressure in the system must also decrease.
 
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Thank you jetsfan, that makes sense. rather than intuitively trying to do it as the TBR method suggested by using the "half shifts" method, I guess its better to do it using your mathematical method.
 
How do you decide between choices B and C? I'm assuming you are given that Keq = 1.95
Look at the case where x = .25. In that case, Q for the reaction will be (.25)/(.25)(.75) which is only 1.33. Since Q < K the reaction will keep shifting right. The answer must be B.

Could you reiterate this part please. I follow you up until this point but I'm still a bit confused on how to determine between the 2 values.
 
Since Q < K, that means that the reaction needs to shift to the right. Since the reaction has to shift to the right, more product has to be made. For more product to be made, the x value has to increase and be bigger than 0.25. An increase in the x-value will decrease the expression "1.5 - x". This is why the answer is B between 1 to 1.25 atm.
For example, since x has to increase, let's say it is 0.34
When plugged in "1.5 - x", the pressure is 1.16 atm, which is between 1 and 1.25 atm
 
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