Determine the rate constant for the following second-order reaction: A=C+2D given that the initial concentration of A is .3 M and that the concentration of C increase to .01 M in 200 seconds. Express the result in terms of the rate law for the loss of A.
To determine the rate constant for a second-order reaction, you need to use the integrated rate law for the reaction. In this case, the given reaction is A = C + 2D, and we want to express the result in terms of the rate law for the loss of A.
The integrated rate law for a second-order reaction is given by:
1/[A]t - 1/[A]0 = kt
where [A]t is the concentration of A at time t, [A]0 is the initial concentration of A, k is the rate constant, and t is time.
From the given information, we know that the initial concentration of A is 0.3 M and that the concentration of C increases to 0.01 M in 200 seconds. We can use this information to calculate the rate constant k.
Plugging in the values, we have:
1/0.01 - 1/0.3 = k * 200
Simplifying:
100 - 3.33 = 200k
96.67 = 200k
Dividing both sides by 200:
k = 96.67 / 200
k ≈ 0.4833
Therefore, the rate constant for the second-order reaction A = C + 2D, expressed in terms of the rate law for the loss of A, is approximately 0.4833.