2 ClO2(aq) + 2 OH –(aq) → ClO3– (aq) + ClO2–(aq) + H2O(l)
A series of experiments were conducted to study the above reaction. The initial concentrations and rates are
reported in the table below.
a.
i.
b.
c.
d.
Determine the order of the reaction with respect to each reactant. Make sure you explain
your reasoning.
ii.
Give the rate law for the reaction.
Determine the value of the rate constant, making sure the units are included.
Calculate the initial rate of disappearance of ClO2 in experiment 1.
The following has been proposed as a mechanism for this reaction.
Step 1: ClO2 + ClO2 → Cl2O4
Step 2: Cl2O4 + OH– → ClO3 – + HClO2
Step 3: HClO2 + OH– → ClO2 – + H2O
Which step is the rate–determining step? Show that this mechanism is consistent with both the rate
law for the reaction and with the overall stoichiometry.
Answers and Explanations
a.
This part of the problem begins with a generic rate equation: Rate = k[ClO2]m[OH –]n. The
values of the exponents, the orders, must be determined. It does not matter which is done
first. If you want to begin with ClO2, you must pick two experiments from the table
where its concentration changes but the OH – concentration does not change. These are
experiments 1 and 3. Experiment 3 has twice the concentration of ClO 2 as experiment 1.
This doubling of the ClO2 concentration has quadrupled the rate. The relationship
between the concentration (× 2) and the rate (× 4 = × 2 2) indicates that the order for ClO2
is 2 (= m). Using experiments 1 and 2 (only the OH – concentration changes), we see that
doubling the concentration simply doubles the rate. Thus, the order for OH – is 1 (= n).
Give yourself 1 point for each order you got correct.
ii.
Inserting the orders into the generic rate law gives: Rate = k[ClO2]2 [OH –]1,which is
usually simplified to: Rate = k[ClO2]2[OH –]. Give yourself 1 point if you got this correct.
Any one of the three experiments may be used to calculate the rate constant. If the problem asked
for an average rate constant, you would need to calculate a value for each of the experiments and
then average the values.
i.
b.
The rate law should be rearranged to: k = Rate/[ClO2]2[OH –]. Then the appropriate values are
entered into the equation. Using experiment 1 as an example:
k = (0.166 mol/L min)/[(0.020 M)2(0.030 M)]
= 1.3833 × 104 M/M3 min = 1.4 × 104/M2 min
The answer could also be reported as 1.4 × 10 4 L2/mol2 min. You should not forget that M =
mol/L.
Give yourself 1 point for the correct numerical value. Give yourself 1 point for the correct units.
c.
The coefficients from the equation say that for every mole of ClO 3– that forms, 2 mol of ClO2
reacted. Thus, the rate of ClO2 is twice the rate of ClO3–. Do not forget that since ClO3– is forming,
it has a positive rate, and since ClO2 is reacting it has a negative rate. This gives:
Rearranging and inserting the rate from experiment 1 gives:
Δ[ClO]/Δt = –2(0.166 mol/L min)] =–8.332 mol/L min
Give yourself 2 points if you got the entire answer correct. You get only 1 point if the sign or units
are missing.
d.
The rate–determining step must match the rate law. One approach is to determine the rate law for
each step in the mechanism. This gives:
Step 1: Rate = k[ClO2]2
Step 2: Rate = k[Cl2O4][OH –] = k[Cl2O]2[OH –]
Step 3: Rate = k[HClO2][OH –] = k[ClO2][OH –]2
For steps 2 and 3, the intermediates must be replaced with reactants. Step 2 gives a rate law matching the
one derived in part a. Give yourself 1 point if you picked step 2, or if you picked a step with a rate law that
matches a wrong answer for part a. Give yourself 1 more point if you explained the substitution of reactants
for intermediates.
To see if the stoichiometry is correct, simply add the three steps together and cancel the intermediates
(materials that appear on both sides of the reaction arrow).
Step 1: ClO2 + ClO2 → Cl2O4
Step 2: Cl2O4 + OH – → ClO3– + HClO2
Step 3: HClO2 + OH – → ClO2– + H2O
Total: 2 ClO2 + Cl2O4 + 2 OH – + HClO2 → Cl2O4 + ClO3– + HClO2 + ClO2– + H2O
After removing the intermediates (Cl2O4 and HClO2):
2 ClO2 + 2 OH –→ ClO3–, + ClO2– + H2O
As this matches the original reaction equation, the mechanism fulfills the overall stoichiometry
requirement. Give yourself 1 point if you have done this.
The total is 10 points for this question. Subtract one point if any answer has an incorrect number of
significant figures.