# Pressure and concentration equilibria

• vipertongn
In summary, the equilibrium concentrations of the three gases in a 5.0L reaction vessel with 1.0 atm of phosgene (COCl2) at 100oC are [COCl2]eq = 0.033M and [CO]eq = [Cl2]eq = 2.69 x 10-10M. The calculation for the equilibrium concentrations requires a complete solution, taking into account the initial and change in amounts of each gas. The assumption that the 'x' value can be ignored in the numerator is not valid when calculating the precise concentrations of the products.
vipertongn
1. COCl2(g) D CO(g) + Cl2(g) Kp = 6.8 x 10-9 at 100oC

What will be the equilibrium concentrations of all 3 gases if 1.0 atm of phosgene (COCl2) is placed into 5.0L reaction vessel?

[COCl2]eq = 0.033M
[CO]eq = [Cl2]eq = 2.69 x 10-10M

I don't get how the second one is solved. I used this method

I found out it's going towards the products because the reactant is decomposing and there is no products yet to be in equilibrium

Finding initial 1 -> 0 + 0
Finding the amount taken out -x +x +x

I can use the assumption method to assume that since Kp is sooo small x can be ignored for 1-x so...

Kp= x^2/1

Also since it can be ignored i assumed that the equilibrium pressure for phosgene is 1 and then i used C=P/RT to get 0.033.

However! for the concentrations of the products I can't seem to get them at all!

I tried converting Kp to Kc --> Kc=Kp(RT)^-delta (n)

delta(n)=2-1=1 so its Kc= Kp/RT which equals 2.27e-10.

So I tried doing products/reactants=Kc

but (2.69 x 10-10)^2/0.033 does NOT equal 2.27e-10 so I'm lost to where I went wrong with this equation...

So, in the denominator you think that the 'x' (1-x in your analysis) is small enough to be ignored but you want to assume it is there in the numerator. I'm afraid you are going to have to do a complete solution. 'Complete' means that 1-x is not equal to 1.

You can make that assumption (x=0) when you are only using two significant figures to denote the phoshene concentration but you can't if you ever want to actually calculate 'x'.

I can understand your confusion and I would like to help clarify your understanding of pressure and concentration equilibria. First, it is important to note that the equilibrium constant, Kp, is a measure of the equilibrium concentrations of gases based on their partial pressures. This means that Kp is not directly related to the actual concentrations of the gases, but rather the ratio of their partial pressures at equilibrium.

Now, let's look at the given reaction: COCl2(g) ⇌ CO(g) + Cl2(g). The equilibrium constant, Kp, is given as 6.8 x 10^-9 at 100°C. This means that at equilibrium, the ratio of the partial pressures of CO and Cl2 to the partial pressure of COCl2 is 6.8 x 10^-9. In other words, the equilibrium concentration of CO and Cl2 will be very small compared to the concentration of COCl2.

Now, let's look at how to solve for the equilibrium concentrations of all three gases. We are given that 1.0 atm of phosgene (COCl2) is placed into a 5.0L reaction vessel. This means that the initial partial pressure of COCl2 is 1.0 atm. Using the ideal gas law, we can calculate the initial concentration of COCl2 as 1.0 atm / (0.0821 L atm/mol K * 373 K) = 0.033 M.

To solve for the equilibrium concentrations of CO and Cl2, we can use the equilibrium constant expression: Kp = (PCO * PCl2) / (PCOCl2). Since we know that the initial partial pressure of COCl2 is 1.0 atm and the equilibrium constant, Kp, is 6.8 x 10^-9, we can set up the following equation:

6.8 x 10^-9 = (PCO * PCl2) / 1.0

We also know that at equilibrium, the partial pressures of CO and Cl2 will be equal, so we can substitute P for both gases with the same variable, x. This gives us:

6.8 x 10^-9 = (x * x) / 1.0

Solving for x, we get x = 2.6 x 10^-5. Since the partial pressure is equal to the concentration in moles

## What is pressure and concentration equilibrium?

Pressure and concentration equilibrium is a state in which the rate of a forward chemical reaction is equal to the rate of the reverse reaction. This means that the concentration of reactants and products remain constant over time, and the system is at a stable balance.

## How is pressure and concentration equilibrium affected by temperature?

The equilibrium constant of a reaction, which is a measure of the stability of the equilibrium, is affected by temperature. Increasing the temperature will shift the equilibrium towards the endothermic reaction, and decreasing the temperature will shift it towards the exothermic reaction.

## What factors determine the direction of a pressure and concentration equilibrium?

The direction of a pressure and concentration equilibrium is determined by Le Chatelier's principle. This principle states that if a stress is applied to a system at equilibrium, the system will respond in a way to counteract the stress. For example, if the concentration of a reactant is increased, the equilibrium will shift towards the products to balance out the concentration.

## How can pressure and concentration equilibria be manipulated?

Pressure and concentration equilibria can be manipulated by changing the conditions of the reaction, such as temperature, pressure, or concentration of reactants and products. This can be done to shift the equilibrium in a desired direction, and is often used in industrial processes to increase the yield of a desired product.

## How is the equilibrium constant related to pressure and concentration equilibria?

The equilibrium constant, represented by K, is a measure of the ratio of the concentrations of products to reactants at equilibrium. It is used to calculate the direction and stability of a pressure and concentration equilibrium, and can be affected by changes in pressure, temperature, and concentration.

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