Question

It took 150 seconds for 50.0% of a substance to decompose. If the initial concentration was 0.080 M and the reaction is first order, what is the value of the rate constant with units?

a) 0.0029 s⁻¹
b) 0.0046 s⁻¹
c) 0.0091 s⁻¹
d) 0.0068 s⁻¹

Answer 1

To find the value of the rate constant for a first-order reaction, we can use the integrated rate law. By substituting the given values into the equation, we find that the rate constant is approximately 0.0046 s⁻¹.

Step-by-step explanation:

To solve this problem, we can use the integrated rate law for a first-order reaction:

ln([A]t / [A]0) = -kt

Given that 50.0% of the substance decomposes in 150 seconds, we can substitute the given values into the equation:

ln(0.500 / 1.000) = -k(150)

By solving for k, we get:

k = -ln(0.500) / 150

k ≈ 0.0046 s⁻¹

Therefore, the value of the rate constant with units is approximately 0.0046 s⁻¹.