Consider the following reaction:
CO(g)+2H2(g)⇌CH3OH(g)
Kp=2.26×104 at 25 ∘C. Calculate ΔGrxn for the reaction at 25 ∘C under each of the following conditions.
A) Standard Conditions
B) at equilibrium
C)PCH3OH= 1.3atm ; PCO=PH2= 1.2×10−2atm
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A) -24.8kJ
B)0
C) ?
To calculate ΔGrxn for the given reaction under each condition, we can use the equation:
ΔGrxn = ΔG°rxn + RTln(Q)
Where:
ΔGrxn = Standard Gibbs free energy change for the reaction
ΔG°rxn = Standard Gibbs free energy change for the reaction under standard conditions
R = Gas constant (8.314 J/mol∙K)
T = Temperature (in Kelvin)
Q = Reaction quotient
Let's calculate ΔGrxn under each condition:
A) Standard Conditions:
Under standard conditions, the reaction is at equilibrium, and the reaction quotient Q is equal to the equilibrium constant Kp. Therefore, Q = Kp.
ΔGrxn = ΔG°rxn + RTln(Kp)
B) At equilibrium:
At equilibrium, the reaction quotient Q is equal to the equilibrium constant Kp. Therefore, Q = Kp.
ΔGrxn = ΔG°rxn + RTln(Kp)
C) PCH3OH= 1.3 atm; PCO= PH2= 1.2×10−2 atm:
In this case, we need to calculate the reaction quotient Q using the given partial pressures.
Q = (PCH3OH) / (PCO * PH2^2)
ΔGrxn = ΔG°rxn + RTln(Q)
Now we can calculate ΔGrxn for each condition using the given values.
a) -24.8 kJ
b) 0
c) 9.4 kJ