Initial rates, a suspicious termolecular step, and temperature
A student studies the bromate-bromide reaction in acidic solution: BrO3- + 5Br- + 6H+ -> 3Br2 + 3H2O. The initial rate is measured colorimetrically at 25.0 degC by timing the first appearance of a fixed bromine concentration. Experiment 1 uses [BrO3-] = 0.0100 M, [Br-] = 0.0100 M and [H+] = 0.0100 M, and gives rate = 4.0 x 10^-5 M/s. Experiment 2 uses 0.0200 M BrO3-, 0.0100 M Br- and 0.0100 M H+, and gives 8.0 x 10^-5 M/s. Experiment 3 uses 0.0100 M BrO3-, 0.0200 M Br- and 0.0100 M H+, and gives 8.0 x 10^-5 M/s. Experiment 4 uses 0.0100 M BrO3-, 0.0100 M Br- and 0.0200 M H+, and gives 1.6 x 10^-4 M/s. A fifth run at 35.0 degC with the experiment-1 concentrations gives 1.2 x 10^-4 M/s. The student proposes a single elementary slow step: BrO3- + 2Br- + 3H+ -> products.
1. Deduce the order with respect to each reactant and calculate the rate constant at 25.0 degC, including its units.
Read the worked answer
Compare experiments 1 and 2: [BrO3-] doubles while the other concentrations are constant, and the rate doubles from 4.0 x 10^-5 to 8.0 x 10^-5 M/s. Thus the reaction is first order in BrO3-.
Compare experiments 1 and 3: [Br-] doubles and the rate doubles, so the reaction is first order in Br-.
Compare experiments 1 and 4: [H+] doubles and the rate increases from 4.0 x 10^-5 to 1.6 x 10^-4 M/s, a factor of four. Thus the reaction is second order in H+.
The rate law is rate = k[BrO3-][Br-][H+]^2. Using experiment 1:
k = (4.0 x 10^-5)/[(0.0100)(0.0100)(0.0100)^2]
k = 4.0 x 10^-5 / 1.00 x 10^-8 = 4.0 x 10^3 M^-3 s^-1.
The units follow from M/s divided by M^4, giving M^-3 s^-1.
2. Evaluate the proposed elementary slow step against the experimental rate law. Is it plausible? Justify your answer and suggest what kind of mechanism would be more consistent.
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For an elementary step, the rate law is written directly from its stoichiometry. The proposed step BrO3- + 2Br- + 3H+ -> products would give
rate = k[BrO3-][Br-]^2[H+]^3,
which does not match the experimental rate = k[BrO3-][Br-][H+]^2. The proposed step is therefore inconsistent with the data. It is also chemically implausible as a single elementary step because it requires six species to collide in one event, and a termolecular step involving three H+ ions is especially unlikely.
A more reasonable mechanism would involve fast pre-equilibria, such as protonation of BrO3- and Br-, followed by a slower bimolecular or trimolecular step whose composition reproduces the observed orders. The key judgement is that a mechanism must fit the rate law, not merely the overall balanced equation.
3. Use the 25.0 degC and 35.0 degC results at the same concentrations to estimate the activation energy. Comment on whether a 10 degC rise causing a threefold rate increase is reasonable.
Read the worked answer
For the same concentrations, the rate ratio equals the rate-constant ratio: k(35)/k(25) = 1.2 x 10^-4 / 4.0 x 10^-5 = 3.0.
Using the two-point Arrhenius equation:
ln(k2/k1) = (Ea/R)(1/T1 - 1/T2).
ln 3.0 = 1.099.
1/298.15 - 1/308.15 = 1.088 x 10^-4 K^-1.
Ea = (1.099)(8.314)/(1.088 x 10^-4) = 8.4 x 10^4 J/mol = 84 kJ/mol.
An activation energy of about 84 kJ/mol is typical for a reaction in solution. A threefold increase for a 10 degC rise is also reasonable: the Arrhenius factor exp[-Ea/R(1/T1 - 1/T2)] gives about 3 for this Ea, so the observation is consistent rather than anomalous.