Answer:
K = 8.1 x 10⁻³
Explanation:
We are told here that these gas phase reactions are both elementary processes, thus the reactions forward and reverse are both first order:
A→B Rate(forward) = k(forward) x [A]
and for
B→A Rate(reverse) = k(reverse) x [B]
At equilibrium we know the rates of the forward and reverse reaction are equal, so
k(forward) x [A] = k(reverse) x [B] for A(g)⇌B(g)
⇒ k(forward) / k(reverse) = [B] / [A] = K
4.7 x 10⁻³ s⁻1 / 5.8 x 10⁻¹ s⁻¹ = 8.1 x 10⁻³ = K
Notice how this answer is logical : the rate of the reverse reaction is greater than the forward reaction ( a factor of approximately 120 times) , and will be expecting a number for the equilibrium constant, K, smaller than one where the reactant concentration, [A], will prevail.
It is worth to mention that this is only valid for reactions which are single, elementary processes and not true for other equilibria.
