Question

For the reaction \[\ce{2x + y -> L}\] find the rate law from the following data.

[x] (M)	[y] (M)	rate (M s−1)
0.2	0.02	0.15
0.4	0.02	0.30
0.4	0.08	1.20

Answer 1

rate = k [x]ⁿ [y]^m

0.15 = k [0.2]ⁿ [0.02]^m ……………..(1)

0.30 = k [0.4]ⁿ [0.02]^m ………………(2)

1.20 = k [0.4]ⁿ [0.08]^m ………………(3)

`((3))/((2))`

`1.2/0.3 = ("k" [0.4]^"n" [0.08]^"m")/("k" [0.4]^"n" [0.02]^"m")`

4 = `(([0.08])/([0.02]))^"m"`

4 = (4)^m

∴ m = 1

`((2))/((1))`

`0.30/0.15 = ("k" [0.4]^"n" [0.02]^"m")/("k" [0.2]^"n" [0.02]^"m")`

2 = `(([0.4])/([0.2]))^"n"`

2 = (2)ⁿ

∴ n = 1

Rate = k [x]¹ [y]¹

0.15 = k [0.2]¹ [0.02]¹

`0.15/([0.2]^1 [0.02]^1)` = k

k = 37.5 mol⁻¹ Ls⁻¹