In a one-litre flask, 6 moles of A undergoes the reaction A (g) ⇌ P (g). The progress of product formation at two temperatures (in Kelvin), T1 and T2, is shown in the figure:
If T1 = 2T2 and (∆G2Θ − ∆G1Θ) = RT2 ln x, then the value of x is ___ .
[∆G1Θ and ∆G2Θ are standard Gibb’s free energy change for the reaction at temperatures T1 and T2, respectively.]
If T1 = 2T2 and (∆G2Θ − ∆G1Θ) = RT2 ln x, then the value of x is ___ .
[∆G1Θ and ∆G2Θ are standard Gibb’s free energy change for the reaction at temperatures T1 and T2, respectively.]
Correct Answer: 8
Solution and Explanation
The answer is 8.
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Concepts Used:
Law of Chemical Equilibrium
Law of Chemical Equilibrium states that at a constant temperature, the rate of a chemical reaction is directly proportional to the product of the molar concentrations of the reactants each raised to a power equal to the corresponding stoichiometric coefficients as represented by the balanced chemical equation.
Let us consider a general reversible reaction;
A+B ↔ C+D
After some time, there is a reduction in reactants A and B and an accumulation of the products C and D. As a result, the rate of the forward reaction decreases and that of backward reaction increases.
Eventually, the two reactions occur at the same rate and a state of equilibrium is attained.
By applying the Law of Mass Action;
The rate of forward reaction;
Rf = Kf [A]a [B]b
The rate of backward reaction;
Rb = Kb [C]c [D]d
Where,
[A], [B], [C] and [D] are the concentrations of A, B, C and D at equilibrium respectively.
a, b, c, and d are the stoichiometric coefficients of A, B, C and D respectively.
Kf and Kb are the rate constants of forward and backward reactions.
However, at equilibrium,
Rate of forward reaction = Rate of backward reaction.
Kc is called the equilibrium constant expressed in terms of molar concentrations.
The above equation is known as the equation of Law of Chemical Equilibrium.