Answer to Question #171341 in General Chemistry for Boye Zephaniah

Question

Haw to prove the half life the third order reaction?

Answer 1

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In the Method of Initial Rates, two of the concentrations must be equal.

Let's assume your numbers and we get this table (ignoring units).

Expt_[A]__[B]___R

_1__0.40_0.30_3.99

_2__0.60_0.30_6.14

_3__0.80_0.60_32.2

R = k[A]^x[B]^y

Expts 1 and 2: R₂/R₁ = [k(0.60)^x (0.30)^y]/[k(0.40)^x (0.30)^y] = 6.14/3.99

(0.60/0.40)^x = 1.50^x = 1.54

xlog1.50 = log1.54

x = log1.54/log1.50 = 0.188/0.176= 1.07 ≈ 1

∴ 1st order in [A] and R = k[A][B]^y

Expts 2 and 3: R₃/R₂ = [k(0.80) 0.60^y]/[k(0.60) 0.30^y] = (0.80/0.60)(0.60/0.30)^y = 32.2/6.14

1.333×2.0^y = 5.24

2.0^y = 5.24/1.333 = 3.93

y = log3.93/log2.0 = 0.594/0.301 = 1.97 ≈ 2

∴ 2nd order in [B] and R = k[A][B]².