(A) Calculate the values of the rate constant k assuming that the reaction is fi

Question

(A)Calculate the values of the rate constant k assuming that the reaction is first order.

What is the value of k at 5 s?  s-1
What is the value of k at 10 s?  s-1
What is the value of k at 15 s?  s-1
What is the value of k at 25 s?  s-1

(B)Calculate the value of k assuming that the reaction is second order.

What is the value of k at 5 s?  M-1s-1
What is the value of k at 10 s?  M-1s-1
What is the value of k at 15 s?  M-1s-1
What is the value of k at 25 s?  M-1s-1

(C)Use your results from parts A and B above to decide what the order of the reaction is for your data. (Enter 1 or 2)

(D)What is the concentration of [A] at time t=52 s?  M

Explanation / Answer

Use the first order expression which is:

ln A = ln Ao - kt

With this you can solve part A

For the second order expression you may use the following:

1/A = 1/Ao + kt

Use these two expressions and solve for k. I will solve A and B for t = 5 s and t = 10 s. Try to do yourself the other two times:

a) and b) Solving for k you have:

First order: ln A - lnAo / t = -k ----> k = lnAo - lnA / t

Second order: k = (1/A - 1/Ao) / t

For 5 s:

k1 = ln(30) - ln(18.40) / 5 = 0.0978 s-1

k2 = 1/18.4 - 1/30 / 5 = 4.203x10-3 s-1

for 10 s:

k1 = ln(30) - ln(13.27) / 10 = 0.0816 s-1

k2 = 1/13.27 - 1/30 / 10 = 8.405x10-3 s-1

c) For this part, you have to plot both equation with the order 1 and 2. The one with the r2  closer to 1, would be the one with the correct order:

For order 1: Equation: y = 3.25 - 0.05518x; a = y intercept = 3.25 ; b = slope = -0.05518 ; r2 = 0.951225788

For order 2: Equation: y = 0.033 + 0.00419x; a = y intercept = 0.033 ; b = slope = 0.00419 ; r2 = 0.99999999881

So, the reaction is order 2.

d) Now, we use the above equation and substitute for A at time 52 s:

1/A = 0.033 + 0.00419(52)

1/A = 0.251696 ---> A = 3.9730 M

Hope this helps

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