Calculate the rate constant K.

Question

Consider the following data for first order reaction:

Z = Products

Time:                    [Z]:

0 s                          1.0000 M

900 s                      .5231 M

3000 s                    .1153 M

 

Calculate the rate constant K.

 

Answer 1

Don’t forget to include units. Since it’s first order, units should be 1/s, or s^-1 (reciprocal seconds). 

Answer 2

Let's recall the equation is [Z]= [Z]₀*e^-kt where [Z]₀ is the initial concentration and t is time.

 

To make it easier on ourselves, let's do some rearranging to isolate the k:

 

[Z]/[Z]₀= e^-kt

ln([Z]/[Z]₀)= -kt

- (ln([Z]/[Z]₀)/t= k

 

From here, we can just plug and chug:

 

- (ln (0.1153/1))/3000= k

 

7.201 x 10^-4= k

 

To double check, I like to plug the k back into the original ( [Z]= [Z]₀e^-kt) with the other data point:

 

[Z]= 1.000e^{-((7.201x10^-4)*900)}

[Z]= 1.000*(0.5231)

[Z]= 0.5231 which is what the data shows.

 

So the final answer is that the rate constant k= 7.201 x 10^-4