Here is a reaction: 2 NO (g) + O₂(g) → 2 NO₂(g)

We measure the initial rate of reaction of 3 experiments with different initial concentrations.

Determine the rate constant of the reaction.

Exp1: [NO] = 0.010 M; [O₂] = 0.015 M; rate = 0.032 M.s^-1

Exp2: [NO] = 0.020 M; [O₂] = 0.015 M; rate = 0.064 M.s^-1

Exp3: [NO] = 0.010 M; [O₂] = 0.030 M; rate = 0.128 M.s^-1

Question

Here is a reaction: 2 NO (g) + O₂(g) → 2 NO₂(g)

We measure the initial rate of reaction of 3 experiments with different initial concentrations.

Determine the rate constant of the reaction.

Exp1: [NO] = 0.010 M; [O₂] = 0.015 M; rate = 0.032 M.s^-1

Exp2: [NO] = 0.020 M; [O₂] = 0.015 M; rate = 0.064 M.s^-1

Exp3: [NO] = 0.010 M; [O₂] = 0.030 M; rate = 0.128 M.s^-1

| General Chemistry 2

Accepted Answer

Rate = k [NO]^α [O₂]^β

Let’s determine α:

[NO]_exp2 = 2 x [NO]_exp1; [O₂]_exp2 = [O₂]_exp1 and rate_exp2 = 2 x rate_exp1

rate_exp2 = 2 x rate_exp1

⇒ k [NO]_exp2^α [O₂]_exp2^β = 2 k [NO]_exp1^α [O₂]_exp1^β

⇒ k 2^α x [NO]_exp1^α [O₂]_exp1^β = 2 k [NO]_exp1^α [Cl₂]_exp1^β

⇒ 2^α = 2

⇒ α = 1

Let’s determine β:

[NO]_exp3 = [NO]_exp2; [O₂]_exp3 = 2 [O₂]_exp2 and rate_exp3 = 4 x rate_exp2

rate_exp3 = 4 x rate_exp2

⇒ k [NO]_exp3^α [O₂]_exp3^β = 4 k [NO]_exp2^α [O₂]_exp2^β

⇒ k [NO]_exp2^α 2^β [O₂]_exp2^β = 4 k [NO]_exp2^α [O₂]_exp2^β

⇒ 2^β = 4

⇒ β = 2

Rate = k [NO][O₂]²

Rate_exp1 = k [NO]_exp1 [O₂]_exp1²

⇒ k = $\frac{{Rate}_{\exp 1}}{{[NO]}_{\exp 1} [O}$ ₂]_exp12 = $\frac{0.032}{0.010 \times 0 . 015^{2}}$ = 1.4 x 10⁴ M ^-2.s^-1

Final - Question 3 | General Chemistry 2