# Pressure equilibrium -- I am getting my math wrong somewhere

• maylandchastity
In summary, the equilibrium constant Kp for the reaction COCl2(g) CO(g) + Cl2(g) is 0.636 at 600 K. When COCl2(g) is introduced into an evacuated flask at a pressure of 1.73 atm at 600 K, the equilibrium partial pressures of all species are calculated using the ICE method. The resulting equilibrium partial pressures are PCOCl2 = 0.689 atm, PCO = 1.041 atm, and PCl2 = 1.041 atm.
maylandchastity

## Homework Statement

The equilibrium constant, Kp, for the following reaction is 0.636 at 600 K:

COCl2(g) CO(g) + Cl2(g)

Calculate the equilibrium partial pressures of all species when COCl2(g) is introduced into an evacuated flask at a pressure of 1.73 atm at 600 K.

Included below

## The Attempt at a Solution

The equilibrium constant, Kp, for the following reaction is 0.636 at 600 K:

COCl2(g) CO(g) + Cl2(g)

Calculate the equilibrium partial pressures of all species when COCl2(g) is introduced into an evacuated flask at a pressure of 1.73 atm at 600 K.

PCOCl2=
PCO=
PCl2=

setting up ICE, I know that Kp=x/(1.73-x)=.636

(.636)[1.73-x]^2=x
(.636)[1.73^2-2(1.73)x + x^2]=x
(.636)x^2-[2(1.73)(.636)+1]x + (.636)(1.73)^2

x^2-[2(1.73)+1/(.636)]x + 1.73^2= 0

a=1
b= -[2(1.73)+1/(.636)]= -5.032
c= (1.73)^2= 2.993

[(-5.032)^2-4(2.993)]^1/2 = [13.349]^1/2= 3.654

x=(-(-5.032)+-3.654)/2
x=4.343 or .689

Go with .689 since the other value of x is greater than the initial pressure of 1.73.
PCO=PCL2=(1.73-x)=(1.73-.689)=1.041
PCOCL2=x=.689

maylandchastity said:
setting up ICE, I know that Kp=x/(1.73-x)=.636

Already doesn't look correct to me.

## 1. What is pressure equilibrium?

Pressure equilibrium is a state in which the pressure on both sides of a barrier or partition is equal. This means that the forces exerted by the gas or liquid particles on the barrier are the same on both sides, resulting in no net movement of the particles.

## 2. How is pressure equilibrium related to math?

Pressure equilibrium involves the use of mathematical equations, such as the ideal gas law, to calculate the pressure on each side of the barrier and ensure that they are equal. This allows us to determine the conditions for pressure equilibrium to occur.

## 3. What are some common mistakes made when solving for pressure equilibrium?

One common mistake is not properly converting units of measurement, such as using different units for pressure on each side of the barrier. Another mistake is not including all relevant factors, such as temperature and volume, in the calculations.

## 4. How can I check if my math is correct when solving for pressure equilibrium?

You can check your math by plugging your calculated values into the ideal gas law equation and ensuring that they result in equal pressures on both sides of the barrier. It can also be helpful to double-check your unit conversions and make sure you have included all relevant factors in your calculations.

## 5. What are some real-life examples of pressure equilibrium?

Some examples of pressure equilibrium include the pressure inside a balloon, the pressure inside a sealed water bottle, and the pressure inside a scuba diving tank. In all of these cases, the pressure on both sides of the barrier (the balloon, bottle, or tank) is equal, resulting in a stable system.

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