
(a)
Interpretation:
The equilibrium constant at 25oC has to be determined for the given reaction.
CH4(g)+Cl2(g)⇌ CH3Cl(g)+HCl(g)
Concept Introduction:
The equilibrium constant of a reaction can be calculated using the given expression,
lnK= -ΔGroRT where,R=Gas constant (8.314 JK-1mol-1)ΔG°r = Standard Gibb's free energyT = TemperatureK= Equilibrium constant
(a)

Answer to Problem 5G.22E
The equilibrium constant of the given reaction is 2.0×10−1.
Explanation of Solution
Given reaction is
The synthesis of trichloromethane (chloroform) from natural gas (methane):
CH4(g)+Cl2(g)⇌ CH3Cl(g)+HCl(g)
Temperature of the reaction is 298 K,
The ΔG°f value of CH3Cl is 48.5 k J⋅mol-1
The ΔG°f value of HCl is −95.30 k J⋅mol-1
The ΔG°f value of Cl2 is 0
The ΔG°f value of CH4 is −50.72 k J⋅mol-1
R= 8.3145 J ⋅K-1⋅mol-1
T=298K
Here, ΔG°r is calculated using given formula,
ΔG°r =[ΔG°f CH3Cl(g)+ΔG°f HCl(g)]-[ΔG°f CH4(g)+ΔG°f Cl2(g)]=(48.5 ×103−95.30 ×103)−(−50.72 ×103−0)=4.0 ×103
Now, the equilibrium constant of the reaction is calculated as
lnK= -ΔGroRT =-4.0×103 J⋅mol-1(8.3145 J⋅K-1⋅mol-1)×(298 K)=−1.61
To calculate K value, inverse logarithm is taken for the above reaction.
K=e−1.61=2.0×10−1
Therefore, the K value of given reaction is 2.0×10−1.
(b)
Interpretation:
The equilibrium constant at 25oC has to be determined for the given reaction.
C2H2(g)+2H2(g)⇌ C2H6(g)
Concept introduction:
Refer to part (a).
(b)

Answer to Problem 5G.22E
The equilibrium constant of the given reaction is.
Explanation of Solution
Given reaction is
The hydrogenation of acetylene to ethane:
C2H2(g)+2H2(g)⇌ C2H6(g)
Temperature of the reaction is 298 K,
The ΔG°f value of C2H6 is −32.82 k J⋅mol-1
The ΔG°f value of C2H2 is +209.20 k J⋅mol-1
The ΔG°f value of H2 is 0
R= 8.3145 J ⋅K-1⋅mol-1
T=298K
Here, ΔG°r is calculated using given formula,
ΔG°r =ΔG°f (C2H6(g))-[ΔG°f (C2H2(g))+2ΔG°f (H2(g))]=(-32.82 ×103)−[209.20 ×103−0]=−2.42 ×105
Now, the equilibrium constant of the reaction is calculated as
lnK= -ΔGroRT =2.42 ×105 J⋅mol-1(8.3145 J⋅K-1⋅mol-1)×(298 K)=97.7
To calculate K value, inverse logarithm is taken for the above reaction.
K=e97.7=2.7×1042
Therefore, the K value of given reaction is 1×1090.
(c)
Interpretation:
The equilibrium constant at 25oC has to be determined for the given reaction.
3NO2(g)+H2O(l)⇌ 2HNO3(aq)+NO(g)
Concept introduction:
Refer to part (a).
(c)

Answer to Problem 5G.22E
The equilibrium constant of the given reaction is 1.8×109.
Explanation of Solution
Given reaction is
The final step in the industrial production of nitric acid:
3NO2(g)+H2O(l)⇌ 2HNO3(aq)+NO(g)
Temperature of the reaction is 298 K,
The ΔG°f value of HNO3 is −111.25 k J⋅mol-1
The ΔG°f value of NO is +86.55 k J⋅mol-1
The ΔG°f value of NO2 is +51.31
The ΔG°f value of H2O is −237.13 k J⋅mol-1
R= 8.3145 J ⋅K-1⋅mol-1
T=298K
Here, ΔG°r is calculated using given formula,
ΔG°r =[ΔG°f 2HNO3(aq)+ΔG°f NO(g)]-[3ΔG°f NO2(g)+ΔG°f H2O(aq)]=[2×(-111.25 ×103)+86.55×103]−[3×(51.31×103)−237.13×103]=−5.28 ×104
Now, the equilibrium constant of the reaction is calculated as
lnK= -ΔGroRT =5.28 ×104 J⋅mol-1(8.3145 J⋅K-1⋅mol-1)×(298 K)=21.31
To calculate K value, inverse logarithm is taken for the above reaction.
K=e21.31=1.8×109
Therefore, the K value of given reaction is 1.8×109.
(d)
Interpretation:
The equilibrium constant at 25oC has to be determined for the given reaction.
N2H4(l)+O2(g)⇌ N2(g)+2H2O(l)
Concept introduction:
Refer to part (a).
(d)

Answer to Problem 5G.22E
The equilibrium constant of the given reaction is 2.4×10109.
Explanation of Solution
Given reaction is
The reaction of hydrazine and oxygen in a rocket:
N2H4(l)+O2(g)⇌ N2(g)+2H2O(l)
The ΔG°f value of N2 is 0
The ΔG°f value of H2O is −237.13 k J⋅mol-1
The ΔG°f value of N2H4 is +149.34 k J⋅mol-1
The ΔG°f value of O2 is 0
Temperature of the reaction is 298 K
R= 8.3145 J ⋅K-1⋅mol-1
T=298K
Here, ΔG°r is calculated using given formula,
ΔG°r =[ΔG°f N2(g)+2ΔG°f H2O(l)]-[ΔG°f N2H4(l)+ΔG°f O2(g)]=[0+2×(−237.13×103)]−[149.34×103)−0]=−6.24 ×105
Now, the equilibrium constant of the reaction is calculated as
lnK= -ΔGroRT =6.24 ×105 J⋅mol-1(8.3145 J⋅K-1⋅mol-1)×(298 K)=251.84
To calculate K value, inverse logarithm is taken for the above reaction.
K=e251.84=2.4×10109
Therefore, the K value of given reaction is 2.4×10109.
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