Chemical Equilibrium Questions and Answers

Given,
(i) H2 (g) + 1/2 S2 (g) = H2S (g), KP1 
(ii) 2H2 (g) + S2 (g) = 2H2S (g), KP2 
Show that, KP2 = (KP1)2
For the first reaction, ΔG10 = - RT lnKP1
For the second reaction, ΔG20 = - RT lnKP2
Since, ΔG20 = 2ΔG10, therefore, it follows that,
- RT lnKP2 = - 2RT lnKP1 
KP2 = (KP1)2
Chemical Equilibrium Questions and Answers
Equilibrium Constant
Use Gibbs - Helmholtz equation to derive the Vant Hoff reaction isochore. Under What condition do you expect a linear relationship between logk and 1/T ?
The Gibbs - Helmholtz equation is,
ΔG0 = ΔH0 + T[d(ΔG0)/dT]P 
Zero superscript is indicating the stranded values.
or, - (ΔH0/T2 ) = -(ΔG0/T2 ) + 1/T[d(ΔG0)/dT]P
or, - (ΔH0/T2 ) = [d/dT(ΔG0/T)]P
Again Vant Hoff isotherm is,
- RT lnKP = ΔG0
or, - R lnKP = ΔG0/T
Differentiating with respect to T at constant P,
- R [dlnKP/dT]P = [d/dT(ΔG0/T)]P
Comparing the above two equation we have,
dlnKP/dT = (ΔH0/T2
This is the Van't Hoff Equation isochore.
Greater the value of ΔH0, the faster the equilibrium constant(KP)changes with temperature(T), ΔH0 should remains constant for the linear plot of logKP vs 1/T.
How does the equilibrium constant for a reaction, 2A + 3B 4C + Heat, Change when (i) pressure is increases (ii) Temperature is decreases (iii) a catalyst added?
  1. Equilibrium constant remains same when P is increases .
  2. The reaction is exothermic, hence ΔH = (-)ve so the equilibrium constant is increased with decreases of temperature.
  3. Equilibrium constant remains same though a catalyst is added.
  4. ΔG0 = - RT lnKa but ΔG0 is not changed due to addition of catalyst as the latter does not participate in the reaction. The initial state and the final state of a chemical reaction remains same weather the catalyst is added or not.
    Hence the equilibrium constant (Ka) remains unchanged.
For a reaction,2A + B 2C, ΔG0(500 K) = 2 KJ mol-1. Find the KP at 500 K for the reaction A + ½B C.
ΔG0 (500 K) for the reaction,
A + ½B C 
= (2 KJ mol-1)/2
= 1 KJ mol-1
The relation is, ΔG0 = - RT lnKP
or, 1 = - (8.31 × 10-3) × (500) lnKP
or, lnKP = 1/(8.31 × 0.5)
= 0.2406
KP = 1.27
Justify or criticize the following: "The Equilibrium yield of products can not change if the equilibrium constant is kept fixed."
This statement is not correct.
Equilibrium yield of the product is changed if pressure is changed (Δγ ≠ 0), if inert gas is added at constant P (Δγ ≠ 0), and any of the reacting component is added a depleted.
For example, N2 + 3 H2 2NH3
Equilibrium yield of NH3 is increased if P is increased though equilibrium constant kept fixed. 
Justify or criticize the following: Heat of reaction is the same weather a catalyst is used or not.
H is a state function hence ΔH (heat of a reaction) does no change if initial state and final state of a Process is same.
A catalyst can not change the initial and final state of a chemical reaction, hence ΔH remains same weather a catalyst is used or not.
Therefore the statement is correct.

Chemical Equilibrium Questions and Answers: Law of Mass Action and Van't Hoff Equation.

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