Matthieu Z.

asked • 07/17/22

How to break down the math for solving problems concerning equilibrium and partial pressure

2.76=(x)(x)/(0.04-2x)2 , the answer found was 0.0292, how was this found step by step?

Matthieu Z.

solved for x
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07/17/22

Michael L.

tutor
Hi Matthieu: just want to clarify what you need first. Do you need to know how the equation was set up? Or do you just need to know how to solve the equation for x now that it's set up?
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07/18/22

Matthieu Z.

How to solve the equation for x now that it is set up
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07/18/22

Ryan C.

Hi Michael! I'm assuming your equation is 2.76 = x^2/(0.04-2x)^2. There are a couple approaches for solving this equation: one way is long and the other way is short. For the long way, you can rewrite the equation as 2.76*(0.04-2x)^2 = x^2, 2.76*(0.04 - 2x)^2 - x^2 = 0, 2.76*(0.0016 - 0.16*x + 4*x^2) - x^2 = 0, 10.04 x^2 - 0.4416 x + 0.004416 = 0, and then use the quadratic formula to solve for x. For the short way, notice that the original equation can be written as 2.76 = (x/(0.04-2x))^2, so we can take a square root on both sides to get +/- sqrt(2.76) = x/(0.04 -2x). Then, you can solve for x of this linear equation. Whichever you decide to do, x ~ 0.0286 or x ~ 0.0153. The correct solution depends on the context of the problem.
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07/19/22

1 Expert Answer

By:

JACQUES D. answered • 07/19/22

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This equation, if it is correct, can be expressed as a quadratic:

Multiply both sides by denominator

2.76(.04-2x)2 = x2

Multiply out and distribute constant term:

.004416 - .4416x + 11.04x2 -x2 = 0


.10.04x2 - .4416x +.004416 = 0


Use quadratic formula: x = .0286 or .0154 (The second answer would be chosen)

The answer quoted doesn't make sense with respect to the K expression as this would mean that the extent of reaction was more than the initial amount of reactant.

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