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#### regd293

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##### Question about methods for solving equilibrium problems involving pressure
« on: January 19, 2014, 05:10:01 PM »

0.0487 mol of nitrosyl chloride was injected into an otherwise empty 1.00-L reaction vessel at 500 K. The nitrosyl chloride decomposed into nitrogen monoxide and chlorine:
2 NOCl(g) 2 NO(g) + Cl2(g)
When the system reached equilibrium at 500 K, the total pressure within the reaction vessel was found to be 2.63 atm. What is Kp for the above reaction at 500 K?

First, I converted moles of nitrosyl chloride into pressure. Using the ideal gas law PV=nRT and solving for P using 0.08206 L·atm·mol-1·K-1 as the gas constant, I obtained 2.00 atm as the initial pressure of NOCl.

Setting up the ICE table:

Usually in other problems I've seen you would be given partial pressure values for one or more of the compounds that appear in the balanced equation, making it a simple task to solve for x. In this case, the total pressure is given. So Dalton's law of partial pressure should be applicable, as the "E" terms in the ICE table are the equilibrium partial pressures of each gas, and the sum of the partial pressures at equilibrium should be equal to the total pressure of the system at equilibrium, as per Dalton's law.

Hence
(2.00 atm - 2x) + 2x + x = 2.63 atm
and x = 0.63 atm.

Substituting in the newly found equilibrium partial pressure values into the expression for Kp, I obtain

1.83 as the Kp (sorry for using Microsoft Word; I will make an effort to learn LaTeX in the future).

Here is the issue:
I was told that an alternative way to solve this problem is to observe that the stoichiometric coefficients represent the fraction that each compound in the chemical equation contributes to the total pressure at equilibrium.

So the partial pressure of NOCl should be 2/5 of the total pressure, which is
(2/5)2.63 atm = 1.052 atm
Similarly, the partial pressure at equilibrium of NO should be 2/5 of the total pressure, and that of chlorine gas is 1/5 of the total pressure, or 0.526 atm.

This means that the expression for Kp is

and the Kp would be 0.526.

Clearly one of these methods is incorrect as they result in different answers. So which of these methods is correct? Or are they both wrong and there is yet another way to solve this problem? Also, for the incorrect method, can you please explain which particular step(s) and/or assumption(s) used is flawed?
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#### Borek

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##### Re: Question about methods for solving equilibrium problems involving pressure
« Reply #1 on: January 19, 2014, 09:22:47 PM »

2nd approach is wrong, period.
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#### regd293

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##### Re: Question about methods for solving equilibrium problems involving pressure
« Reply #2 on: January 26, 2014, 11:10:17 AM »

Thank you for your response. Can you (or someone else) explain what in particular is wrong about the second approach and why?
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#### Borek

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##### Re: Question about methods for solving equilibrium problems involving pressure
« Reply #3 on: January 26, 2014, 11:24:57 AM »

Calculate the pressures and see if they follow the "observation" the second method is based on.
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