Question

Some measurements of the initial rate of a certain reaction are given in the table below.
[N2]. [H2]. Initial rate of reaction
0.434 M 2.29 M 8.00 x 10^4M/s
0.434 M 3.23M 1.13 x 10^5M/s
0.630M 2.29 M 1.69x10^5M/s
Use this information to write
rate law for this reaction, and calculate the value of the rate constant k.
Rate =k
K=

Answer 1

The rate law for the reaction between nitrogen, N₂ and hydrogen, H₂ as given in the table of concentration of reactants and reaction rates below is: Rate = k [N₂]²[H₂]

The rate constant, K for the reaction between nitrogen, N₂ and hydrogen, H₂ as given in the table of concentration of reactants and reaction rates below is: K = 1.85 * 10⁵ M⁻²s⁻¹

The rate law for the reaction is given by:

• Rate = k [N₂]ᵃ[H₂]ᵇ

• where a and b are orders of reaction in N₂ and H₂ respectively.

Taking the ratio of the rates of experiment 3 and experiment 1 to find a:

1.69 * 10⁵/8.00 * 10⁴ = (0.63/0.434)ᵃ * (2.29 * 2.29)ᵇ

2.11 = (1.45)ᵃ

Take logarithm of both sides

log 2.11 = log (1.45)ᵃ

log 2.11 = a * log 1.45

a = log 2.11 / log 1.45

• a = 2

Taking the ratio of the rates of experiment 2 and experiment 1 to find b:

1.13 * 10⁵/8.00 * 10⁴ = (0.434/0.434)ᵃ * (3.23 * 2.29)ᵇ

1.41 = (1.41)ᵇ

b = 1

Therefore, the rate law is: Rate = k [N₂]²[H₂]

To determine the rate constant K, make K subject of formula in the rate law of the reaction:

Rate constant K = Rate / [N₂]²[H₂]

Using the values from experiment 1:

K = 8.00 * 10⁴ M/s / (0.434 M )² * (2.29 M)

K = 1.85 * 10⁵ M⁻²s⁻¹

Therefore, the rate constant K is 1.85 * 10⁵ M⁻²s⁻¹

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