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### Course: AP®︎/College Chemistry>Unit 7

Lesson 7: Le Châtelier's principle

# Worked example: Calculating the equilibrium total pressure after a change in volume

How does the total pressure change when the volume of a gaseous equilibrium system is reduced? In this video, we'll explore the answer to this question using both qualitative and quantitative approaches. Created by Jay.

## Want to join the conversation?

• Why do we choose the 0.33 value and ignore the other root of the quadratic, 2.97?
• Mathematically it makes sense that we get two solutions to the quadratic equation which are equally valid, but in a chemistry context only the 0.33 is valid. This is because x represents the change in the pressure changes for the chemicals and we use this x value to calculate the equilibrium pressures of the chemicals. For PCl3 and Cl2 these equilibrium pressures are determined by the equation: 1.40 - x. If x = 2.97 then the equation would look like 1.40 - 2.97 = - 1.57. So both PCl3 and Cl2 would have negative pressures which doesn't exactly make sense. This is why only the 0.33 value is valid because it produces positive pressures for all the chemicals.

Hope that helps.
• I'm still confused on how we could know that the reaction is not going to move MUCH to the left? Especially in the qualitative analysis.
• Since the Kp for this reaction is close to 1 (0.500), the equilibrium pressures for the chemicals will be approximately close to each other. When the volume is initially decreased, the initial pressures are already close to each other. We’ll still see a shift left to relieve the pressure increase, but the pressures will not change much from the initial pressures since they’re already close in value and equilibrium wants to keep them close in value.

Hope that helps.
• At
Resolving the quadratic equation I obtained x=0.77 How do you resolve de equation? It give me a different answer.
• (1) 0.500 = ((1.40 – x)(1.40 – x))/(1.96 + x) Given equation.
(2) (0.500)(1.96 + x) = (1.40 – x)(1.40 – x) Multiply both sides of equation by 1.96 + x.
(3) 0.98 + 0.500x = (1.40 – x)(1.40 – x) Distribute 0.500.
(4) 0.98 + 0.500x = 1.96 – 2.80x + x^(2) Multiply out terms on right side of equation.
(5) 0 = 0.98 - 3.30x + x^(2) Subtract 0.98 from both sides of equation. Subtract 0.500x from both sides.
(6) x = 0.329962 & x = 2.97004 Solve quadratic equation by any method. I used quadratic formula.
You should get two possible answers from the quadratic formula, but only one is correct. Only the 0.329962 answer is valid for this problem because the 2.97004 answer would make the PCl3 and Cl2 concentrations negative.

Hope that helps.
• I might just be blanking, but what's the reason for not using the total pressure equation? I know it doesn't work, but why?
(1 vote)
• We can’t use Dalton’s Law of partial pressures for the final equilibrium state because we don’t know the total pressure. The amount the partial pressures change, x, would still be a variable, and we wouldn’t know the total pressure which would be a second variable. We would have too many variables and not enough equations. Using the equilibrium expression limits the amount of variable to one, x, which is something we can solve for.

Hope that helps.