• Problem 1:
1. H2 (g) + 1/2 S2 (g) = H2S (g), KP1
2. 2H2 (g) + S2 (g) = 2H2S (g), KP2
Show that, KP2 = (KP1)2
For the first reaction,Î”G10 = - RT ln KP1
For the second reaction, Î”G20 = - RT ln KP2
Since, Î”G20 = 2Î”G10,
therefore, it follows that,
- RT ln KP2 = - 2RT ln KP1
 ∴ KP2 = (KP1)2
 Equilibrium Constant
• Problem 2:
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,
Î”G0 = Î”H0 + T[d(Î”G0)/dT]P
Zero superscript is indicating the stranded values.
or, - (Î”H0/T2 ) = -(Î”G0/T2 ) + 1/T[d(Î”G0)/dT]P
or, - (Î”H0/T2 ) = [d/dT(Î”G0/T)]P
Again Vant Hoff isotherm is,
- RT lnKP = Î”G0
or, - R lnKP = Î”G0/T
Differentiating with respect to T at constant P,
- R [dlnKP/dT]P = [d/dT(Î”G0/T)]P
Comparing the above two equation we have,
 dlnKP/dT = (Î”H0/T2
Greater the value of Î”H0, the faster the equilibrium constant(KP)changes with temperature(T), Î”H0 should remain constant for the linear plot of logKP vs 1/T.
• Problem 3
How does the equilibrium constant for a reaction, 2A + 3B 4C + Heat, Change when (i) pressure is increasing (ii) Temperature is decreasing (iii) a catalyst added?
1. Equilibrium constant remains the same when P is increased.
2. The reaction is exothermic, hence Î”H = (-) ve so the equilibrium constant is increased with decreases of temperature.
3. Equilibrium constant remains the same though a catalyst is added. Î”G0 = - RT lnKa but Î”G0 is not changed due to the addition of catalyst as the latter does not participate in the reaction. The initial state and the final state of a chemical reaction remains the same whether the catalyst is added or not. Hence the equilibrium constant (Ka) remains unchanged.
• Problem 4:
For a reaction,2A + B 2C, Î”G0(500 K) = 2 KJ mol-1. Find the KP at 500 K for the reaction A + ½B C.
Î”G0 (500 K) for the reaction,
A + ½B C
= (2 KJ mol-1)/2
= 1 KJ mol-1
The relation is, Î”G0 = - RT lnKP
or, 1 = - (8.31 × 10-3) × (500) lnKP
or, lnKP = 1/(8.31 × 0.5)
= 0.2406
KP = 1.27
• Problem 5:
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 (Î”Î³ ≠ 0), if an inert gas is added at constant P (Î”Î³ ≠ 0), and any of the reacting components are added a depleted.
For example, N2 + 3 H2 2NH3
Equilibrium yield of NH3 is increased if P is increased though equilibrium constant kept fixed.
• Problem 6:
Justify or criticize the following: Heat of reaction is the same whether a catalyst is used or not.
H is a state function hence Î”H (heat of a reaction) does not change if initial state and final state of a Process is same. A catalyst cannot change the initial and final state of a chemical reaction, hence Î”H remains the same whether 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.

## Inorganic Chemistry

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