At a given temperature, the elementary reaction A <=> B in the forward direction is first order in A with a rate constant of 2.60 x 10^-2 s^-1. The reverse reaction is first order in B and the rate constant is 8.50 x 10^-2 s^-1.

What is the value of the equilibrium constant for the reaction A <=> B at this temperature and
What is the value of the equilibrium constant for the reaction B <=> A at this temperature?

do you I take 2.60 x 10^-2 s^-1/8.50 x 10^-2 s^-1 for the first and 8.50 x 10^-2 s^-1/2.60 x 10^-2 s^-1 for the second..?

To calculate the equilibrium constant for a reaction, you need to use the rate constants for both the forward and reverse reactions. The equilibrium constant (K) is defined as the ratio of the rate constant for the forward reaction (k_f) to the rate constant for the reverse reaction (k_r).

For the reaction A <=> B, the equilibrium constant can be calculated using the formula:

K = k_f / k_r

Given:
k_f = 2.60 x 10^-2 s^-1 (forward rate constant)
k_r = 8.50 x 10^-2 s^-1 (reverse rate constant)

To find the equilibrium constant for the reaction A <=> B, substitute the given values into the formula:

K = (2.60 x 10^-2 s^-1) / (8.50 x 10^-2 s^-1)

Solving this equation will give you the equilibrium constant for the reaction A <=> B.

To find the equilibrium constant for the reverse reaction B <=> A, you just need to take the reciprocal of the equilibrium constant for the forward reaction:

K_rev = 1 / K

In this case, you would substitute the value of K (calculated above) into the formula to find the equilibrium constant for the reaction B <=> A.

To find the value of the equilibrium constant for the reaction A <=> B at a given temperature, you need to use the rate constants of the forward (k_f) and reverse (k_r) reactions.

The equilibrium constant, K, is defined as the ratio of the rate constants for the forward and reverse reactions:

K = k_f / k_r

In this case, the rate constant for the forward reaction (k_f) is given as 2.60 x 10^-2 s^-1, and the rate constant for the reverse reaction (k_r) is given as 8.50 x 10^-2 s^-1.

So, to calculate the value of the equilibrium constant for the first reaction A <=> B, you would do:

K1 = k_f / k_r
= (2.60 x 10^-2 s^-1) / (8.50 x 10^-2 s^-1)
= 0.3059

Therefore, the value of the equilibrium constant for the reaction A <=> B at this temperature is approximately 0.3059.

For the second reaction B <=> A, you would use the rate constants in the same way:

K2 = k_f / k_r
= (8.50 x 10^-2 s^-1) / (2.60 x 10^-2 s^-1)
= 3.2692

Therefore, the value of the equilibrium constant for the reaction B <=> A at this temperature is approximately 3.2692.

So, in summary, to find the equilibrium constant, K, for a reaction at a given temperature, you need to divide the rate constant of the forward reaction by the rate constant of the reverse reaction.

That's what I would do.