If it takes 30 seconds for a reactant concentration to decrease from 1.0 M to 0.5 M in a first-order chemical reaction, then what is the rate constant for the reaction?
A. 43 s–1
B. 0.046 s–1
C. 0.023 s–1
D. 0.033 s–1
ln(No/N) = kt
It’s C
To find the rate constant for the first-order chemical reaction, we can use the equation:
ln(concentration final / concentration initial) = -k * time
Given:
- concentration initial = 1.0 M
- concentration final = 0.5 M
- time = 30 seconds
Plugging in the values into the equation, we get:
ln(0.5 / 1.0) = -k * 30
-ln(2) = -k * 30
k = -ln(2) / 30
Using a calculator, we can solve for k:
k ≈ -0.023 s^(-1)
Hence, the rate constant for the reaction is approximately 0.023 s^(-1).
Therefore, the correct answer is C. 0.023 s^(-1).
To determine the rate constant for a first-order reaction, we can use the integrated rate law for a first-order reaction, which is given by:
ln([A]/[A₀]) = -kt
Where [A] is the concentration of the reactant at time t, [A₀] is the initial concentration of the reactant, k is the rate constant, and t is the time.
In this case, the initial concentration [A₀] is 1.0 M and the concentration after 30 seconds [A] is 0.5 M.
ln(0.5/1.0) = -k * 30
Simplifying the equation, we get:
ln(0.5) = -k * 30
Now, we can solve for k by rearranging the equation:
k = -ln(0.5) / 30
Using a calculator, we can calculate the value of k:
k ≈ 0.023 s^(-1)
Therefore, the rate constant for the reaction is approximately 0.023 s^(-1).
Therefore, the correct option is C. 0.023 s^(-1).