Question

The rate law for the reaction 2NO(g) + 2H2(g) -> N2(g) + 2H2O(g) is

rate = k[NO]^2[H2]. If the reaction is 2.63 x 10^-3 mol L^-1 s^-1 when the concentrations of NO and H2 are both 4.7 x 10^-6 mol L^-1, what is the value of the rate constant and what are the units for the rate constant?​

Answer 1

the value of the rate constant (k) is approximately 1.195 x 10^8 L^2 mol^-2 s^-1. The units for the rate constant are L^2 mol^-2 s^-1.

Step-by-step explanation:

To determine the rate constant (k) and its units, you can use the given rate law and the provided initial concentrations of NO and H2 to solve for k.

The rate law is given as:

Rate = k[NO]^2[H2]

You're given the following information:

- Rate (r) = 2.63 x 10^-3 mol L^-1 s^-1

- [NO] = 4.7 x 10^-6 mol L^-1

- [H2] = 4.7 x 10^-6 mol L^-1

Plug in these values into the rate law equation:

2.63 x 10^-3 mol L^-1 s^-1 = k * (4.7 x 10^-6 mol L^-1)^2 * (4.7 x 10^-6 mol L^-1)

Now, calculate k:

k = (2.63 x 10^-3 mol L^-1 s^-1) / [(4.7 x 10^-6 mol L^-1)^2 * (4.7 x 10^-6 mol L^-1)]

k ≈ 2.63 x 10^-3 mol L^-1 s^-1 / (2.199 x 10^-11 mol^3 L^-3)

k ≈ 1.195 x 10^8 L^2 mol^-2 s^-1

So, the value of the rate constant (k) is approximately 1.195 x 10^8 L^2 mol^-2 s^-1. The units for the rate constant are L^2 mol^-2 s^-1.