Using the data in the table, determine the rate constant of the reaction and select the appropriate units. A+2B-->C+D

Question

Trial [A] (M) [B] (M) Rate (M/s)

1 0.200 0.280 0.0240

2 0.200 0.560 0.0240

3 0.400 0.280 0.0960

k=

Units=

Answer 1

To answer this, realize that the rate equation takes the form

rate= k[A]ⁿ[B]^m eq (1)

n and m have no relationship to the coefficients of the reactants, A and B in the balanced equation. They must be experimentally determined. They are called the order of the reaction with respect to A and B, respectively. Looking at the data, you can clearly see that the reaction rate does not depend on [B] because it remains the same even if [B] doubles. Therefore, the reaction is zero order with respect to B. That is, m=0. To get the order with respect to a, use eqn 1 for trials 1 & 3. These two trials show you the variation of rate with respect to A.

rate₃/rate₁ = [A]₃/[A]₁ note that k is present in both numerator and denominator on the right side of this ratio and so will cancel out.

,0960/.0240 = (.4)ⁿ/(.2)ⁿ gives you the condition that 4 = 2ⁿ therefore n must be 2. The reaction is second order in A. So your rate equation is

rate = k[A]²

To get k, pick any trial (or if you are feeling industrious, do this process for all three trials and take the average k) and substitute the values for rate and [A] to get k.

Let's set up the equation for trial 1:

.0240 M/sec = k[0.200 M]² You should be able to solve for k from this equation. I will leave you to carry out the math.

Treat the units the same way you do the numbers. The units of k will be (M/sec)/ M² = 1/M-sec

To verify your answer for k, try doing another trial and see if you get the same k. You should.