Question

Finding the reaction order from a table...?

So, I'm trying to find the reaction order with respect to the concntration of ClO- and then calculate the full rate law, but I'm a little lost. Here's the table:

Trial	[Dye] (M)	[ClO-] (M)	Initial Rate (M/s)
1	6.00*10^-6	0.152	0.0015618
2	6.00*10^-6	0.303	0.0028939
3	6.00*10^-6	0.455	0.003382
4	6.00*10^-6	0.606	0.0038187

I've gotten different answers depending on the rows I've used. So, using the first and second rows, I calculated that the reaction order is 1. But for the second and third rows, I got about 2. Are they supposed to be different?

Thank you in advance for any help!

Answer 1

The reaction is independent of the concentration of the dye.

Let the rate of the reaction be given as

Rate = k*[ClO^-]^a

where k = rate constant for the reaction and a = order of the reaction with respect to ClO^-.

Trail 1	[ClO-] (M)	Initial Rate (M/s)	Ratio of	Ratio of
1	0.152	0.0015618	-	-
2	0.303	0.0028939	R2/R1 = (0.0028939)/(0.0015618) = 1.8529 ≈ 2.0	(0.303)(0.152) = 1.9934 ≈ 2.0
3	0.455	0.0033820	R3/R1 = (0.0033820)/(0.0015618) = 2.1654 ≈ 2.0	(0.455)/(0.152) = 2.9934 ≈ 3.0
4	0.606	0.0038187	R4/R1 = (0.0038187)/(0.0015618) = 2.4451 ≈ 2.0	(0.606)/(0.152) = 3.9868 ≈ 4.0

From the first and second entries, the order of the reaction with respect to ClO^- is 1. The third and fourth entries give fractional orders. Check the data.

From practical experience, it seems that the order of the reaction with respect to ClO^- is 1.0. Put the value of the rate and [ClO^-] and a = 1 in the rate law to get k.

k = Rate/[ClO^-]^a = (0.0015618 M/s)/(0.152 M) = 0.010275 s^-1

The rate law for the reaction is

Rate = (0.010275 s^-1)*[ClO^-]