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With no change in the amount of material in the flask, the volume of the container in question is increased to 5.000 times the original. Assuming constant temperature, calculate the (new) total pressure, at equilibrium

Jan 29th, 2015

Assuming ideal gas behavior, the partial pressures and the amount of substance is proportional by the same factor: 
p(x)∙V = n(x)∙R∙T 
=> 
p(x) = n(x)∙R∙T/V 

That means equal amount lead to equal partial pressures irrespective of the type of gaseous component. Therefore you can solve by setting up ICE table in terms of partial pressures 

......... p(N₂O₄)......... p(NO₂) 
I............. p₀................ 0 
C........... -x............... +2∙x 
E......... p₀-x............... 2∙x 
where p₀ = 4.0atm 

Hence, 
Kp = p(NO₂)² / p(N₂O₄) 
<=> 
Kp = 4∙x² / (p₀ - x) 
<=> 
x² + (Kp/4)∙x - (Kp∙p₀/4) 
=> 
x = - (Kp/8) + √( (Kp/8)² + (Kp∙p₀/4)) 
= (Kp/8)∙[√( 1 + 16∙p₀/Kp) - 1] 
= (0.490/8)∙[√( 1 + 16∙4/0.49) - 1] 
= 0.641 atm 

The total pressure in equilibrium equals the sum of the equilibrium partial pressures: 
P = p(N₂O₄) + p(NO₂) 
= p₀ - x + 2∙x 
= p₀ + x 
= 4 atm + 0.641 atm 
= 4.641 atm 


Because p(x)∙V = constant for an ideal gas under isothermal conditions, quadrupling volume quarters the partial pressures. To solve the part you could adjust the equilibrium partial pressures from previous part and then set up a new ICE table and find the new x. I would solve in different way. 
For the final equilibrium it makes no difference if you let equilibrium establish, change the volume and let reestablish equilibrium volume or if change initial volume thus initial pressure and let establish equilibrium. 

So all you need to repeat calculation above with an initial pressure of: 
p₀ = 4atm / 4 = 1atm 
=> 
x = (Kp/8)∙[√( 1 + 16∙p₀/Kp) - 1] 
= (0.490/8)∙[√( 1 + 16∙1/0.49) - 1] 
= 0.294 atm 
=> 
P = p₀ + x 
= 1 atm + 0.294 atm 
= 1.294 atm


best me please

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Jan 29th, 2015

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