The reaction 2B--->C + 2D is found to be zero order when run at 990 degrees C. If it takes 3.3X110^2 s for an initial concentration of B to go from 0.50 M to .20 M what is the rate constant for the reaction? what is the half life of the reaction under these conditions?
To determine the rate constant for a zero-order reaction, we need to use the relationship between the initial concentration ([B]0), final concentration ([B]), and the time elapsed (t).
The rate equation for a zero-order reaction is given by:
Rate = -k
where k is the rate constant. In this case, the rate is given by:
Rate = ([B]0 - [B]) / t
We are given that it takes 3.3 x 10^2 s (seconds) for the initial concentration of B to decrease from 0.50 M to 0.20 M. Let's substitute the given values:
Rate = (0.50 M - 0.20 M) / (3.3 x 10^2 s)
= 0.30 M / (3.3 x 10^2 s)
Now, we need to rearrange the rate equation to solve for the rate constant (k):
Rate = -k
0.30 M / (3.3 x 10^2 s) = -k
k = -(0.30 M / (3.3 x 10^2 s))
Now we can calculate the value of k.
To find the half-life of the reaction, we can use the equation for the half-life of a zero-order reaction:
t1/2 = [B]0 / (2k)
Plugging in the appropriate values:
t1/2 = (0.50 M) / (2k)
Now we can calculate the half-life of the reaction under these conditions.