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Question

Consider the following equilibrium in a closed container:

N2O4 (g) 2NO2 (g)

At a fixed temperature, the volume of the reaction container is halved. For this change, which of the following statements holds true regarding the equilibrium constant Kp and degree of dissociation α?


A

neither Kp nor α changes

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B

both Kp and α changes

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C

Kpchanges, but α does not change

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D

Kp does not change, but α changes

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Solution

The correct option is D

Kp does not change, but α changes


The Equilibrium is established at a particular temperature T, for which the equilibrium constant is Kp

Let us assume there were initially n moles of N2O4 (g) and there were no products.

N2O4(g)NO2(g)t=0n0t=eqn(1α)2α

At Equilibrium, total number of moles = n(1+α)

Partial pressure of NO2 (g) = mole fraction of 2NO2(g) × Total Pressure P

Partial pressure of N2O4 (g) = mole fraction of N2O4 (g) × Total Pressure P

Using ideal gas equation, PV=n(1+α)RT. Can we use boyle's law here??

Boyle's law cannot be used here because there are three variables P, V and α. As a special case, boyle's law can be used under one exceptional condition. When Δn = 0 { Δn = sum of stoichiometric coefficients of gaseous products - sum of stoichiometric coefficients of gaseous reactants}

In this case, Δn=1>0; For a homogeneous equilibrium which has the Δn = 0, the number of moles in the system is constant at all times, even when equilibrium is not reached. In such cases, Kp=Kc

For a given temperature, the value of Kp does not change. In the above ideal gas equation, P, V and α are all variables while n R and T are all constants. Can we say that the value nRT is constant? Definitely!

The product on the right hand side is constant since Kp is a constant ( T =constant). So if V is halved would be doubled (increased). As α (which is less than 1) increases, (1α) decreased. So its reciprocal increases.

Consequently, increases as α increases. So definitely α changes. If V decreases, α also decreases. Similarly if V increases, α also follows a similar pattern. This could be generally extended to systems which follow Δn> 0. What can you comment about systems which have Δn>0?


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