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.
(1/A) - (1/Ao) = kt
Substitute and solve for k.
Second part.
rate = delta A/delta T = -0.01/200
To determine the rate constant for the given second-order reaction, we can use the rate expression for the loss of A.
The rate law for the loss of A can be written as:
rate = -k[A]^2
Here, [A] represents the concentration of A at any given time, and k is the rate constant we need to determine.
Given 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.
In order to use the given data to calculate the rate constant, we need to find the initial rate and the rate at a specific time.
To determine the initial rate, we'll need to use the initial concentration of A. Let's assume the initial rate is r0.
r0 = -k[A]0^2
r0 = -k(0.3)^2
r0 = -0.09k
Next, we'll determine the rate at a specific time, t, when [C] reaches 0.01 M. Let's assume this rate is rt.
rt = -k[A]t^2
rt = -k(0.3 - [C])^2
rt = -k(0.3 - 0.01)^2
rt = -k(0.29)^2
rt = -0.0841k
Using these expressions for the initial rate (r0) and the rate at a specific time (rt), we can now set up a ratio to calculate the rate constant:
rt / r0 = (-0.0841k) / (-0.09k)
rt / r0 = 0.0841 / 0.09
rt / r0 = 0.9344
Now we can solve for the rate constant (k):
0.9344 = rt / r0
0.9344 = -0.0841k / -0.09k
0.9344 = 0.9344
Therefore, the rate constant for the given second-order reaction is 0.9344.