Difficulty: Intermediate | Prerequisites: Part 1 of these notes (Chemical Kinetics Fundamentals). Comfort with logarithms and basic algebra.
Once you understand what the iodine clock measures (Part 1), the next step is turning raw timing data into a rate law. This is where you move from observation to quantitative analysis: calculating initial concentrations, computing rates, determining reaction orders by the method of initial rates, and extracting the rate constant k. These skills are not specific to the iodine clock; the method of initial rates is one of the standard tools for studying any reaction's kinetics.
By running the iodine clock at three different concentration combinations (holding one reactant constant while doubling the other), you can use the ratio of rates to solve for each reactant's order. The rate constant k is then calculated from the rate law and any single experiment's data. In this experiment the orders came out to approximately 0.3 for [I⁻] and -0.6 for [S₂O₈²⁻] (the expected "textbook" values for this particular system are first order in each, so the deviation is a useful discussion point about experimental error).
Method of initial rates
A technique for determining reaction orders by comparing the initial rates of a reaction measured under different starting concentrations. You change one reactant at a time and see how the rate responds. In simple terms, it is the "change one thing, measure the effect" approach to kinetics.
Initial rate
The rate of reaction measured at the very start, before significant amounts of reactant have been consumed. Approximated here by Δ[S₂O₈²⁻] / Δt using the average time interval.
Rate law
Rate = k [I⁻]^y [S₂O₈²⁻]^x, where x and y are the reaction orders and k is the rate constant. The form is always determined experimentally.
Rate constant (k)
The proportionality factor in the rate law. Its units depend on the overall reaction order. For a reaction that is first order in each of two reactants (second order overall), k has units of M⁻¹ s⁻¹.
Overall reaction order
The sum of the individual orders (x + y). Determines the units of k.
Every solution is mixed to a total volume of 20.0 mL from stock solutions of known molarity. Apply the dilution formula to each reactant.
Solution | Vol. KI (mL) | Vol. (NH₄)₂S₂O₈ (mL) | [I⁻] (M) | [S₂O₈²⁻] (M) |
|---|---|---|---|---|
1 | 5.0 | 5.0 | 0.050 | 0.050 |
2 | 10.0 | 5.0 | 0.100 | 0.050 |
3 | 5.0 | 10.0 | 0.050 | 0.100 |
Example: Solution 1 [I⁻] = (5.0 mL / 20.0 mL) × 0.200 M = 0.050 M.
Each colour change marks the consumption of one aliquot of thiosulfate (0.25 mL of 0.200 M Na₂S₂O₃ in 20 mL total = 0.0025 M). The stoichiometric link gives:
[S₂O₈²⁻] consumed per interval = (1/2) × 0.0025 M = 0.00125 M
Divide this by the average time interval to get the average initial rate:
Solution | Avg. time (s) | Rate (M/s) |
|---|---|---|
1 | 62 | 2.016 × 10⁻⁵ |
2 | 52 | 2.404 × 10⁻⁵ |
3 | 95 | 1.316 × 10⁻⁵ |
The rate law is Rate = k [S₂O₈²⁻]^x [I⁻]^y. To find y (the order in I⁻), compare Solutions 1 and 2, where [S₂O₈²⁻] is the same:
Rate₁ / Rate₂ = ([I⁻]₁ / [I⁻]₂)^y
2.016 × 10⁻⁵ / 2.404 × 10⁻⁵ = (0.050 / 0.100)^y
0.839 = 0.5^y → y = ln(0.839) / ln(0.5) ≈ 0.3
To find x (the order in S₂O₈²⁻), compare Solutions 1 and 3, where [I⁻] is the same:
Rate₁ / Rate₃ = ([S₂O₈²⁻]₁ / [S₂O₈²⁻]₃)^x
2.016 × 10⁻⁵ / 1.316 × 10⁻⁵ = (0.050 / 0.100)^x
1.53 = 0.5^x → x = ln(1.53) / ln(0.5) ≈ -0.6
Note: the textbook expectation for this reaction is first order in each reactant (x = 1, y = 1). The experimental values here (x ≈ -0.6, y ≈ 0.3) deviate significantly, likely due to experimental error in timing, temperature control, or mixing. When rounding to integers for further calculation, the lab report used the raw values rather than the expected integers.
Plug the rate and concentrations from any single solution into the rate law and solve for k. Using Solution 1 with the experimental orders:
2.016 × 10⁻⁵ = k × (0.050)⁻⁰·⁶ × (0.050)⁰·³ → k ≈ 8.207 × 10⁻⁶ M⁻¹ s⁻¹
Repeating for all three solutions and averaging gives k_avg ≈ 8.034 × 10⁻⁶ M⁻¹ s⁻¹.
Rate = 8.034 × 10⁻⁶ [I⁻]⁻⁰·⁶ [S₂O₈²⁻]⁰·³ (using the experimental orders from this data set).
If your instructor expects integer orders: Rate = k [I⁻]¹ [S₂O₈²⁻]¹, where k would be recalculated accordingly.
Dilution (initial concentration in the mixture)
[\text{X}]_i = \frac{V_{\text{stock}} \times C_{\text{stock}}}{V_{\text{total}}}Rate from timing data
\text{Rate} = \frac{\frac{1}{2}[\text{S}_2\text{O}_3^{2-}]_{\text{aliquot}}}{\bar{t}} = \frac{0.00125\;\text{M}}{\bar{t}}Ratio method for reaction order
When only one reactant's concentration changes between two experiments:
\frac{\text{Rate}_A}{\text{Rate}_B} = \left(\frac{[\text{X}]_A}{[\text{X}]_B}\right)^n \quad\Rightarrow\quad n = \frac{\ln(\text{Rate}_A / \text{Rate}_B)}{\ln([\text{X}]_A / [\text{X}]_B)}Rate constant
Rearrange the rate law: k = Rate / ([I⁻]^y × [S₂O₈²⁻]^x).
Students often set up the ratio incorrectly by comparing two experiments where both concentrations change. The method of initial rates only works when you hold one reactant constant and vary the other.
A frequent error is using the stock concentration rather than the diluted concentration in the rate law. Always use [X] in the 20 mL mixture, not [X] of the stock bottle.
Students sometimes expect integer orders and force-round their answers before checking whether the non-integer result points to experimental error worth discussing.
Forgetting the 1/2 factor when converting thiosulfate consumed to persulfate consumed is one of the most common calculation mistakes.
⚠️ The ratio method for determining reaction orders is a staple exam question. Be ready to set up and solve the ratio from a table of rates and concentrations.
⚠️ Know the units of k for different overall orders: zeroth order (M s⁻¹), first order (s⁻¹), second order (M⁻¹ s⁻¹).
⚠️ Expect a question asking you to explain why the experimental orders might not be integers and what sources of error could cause the deviation.
⚠️ The assumption that the rate is constant over six aliquots is an approximation. An increasing trend in time intervals across successive aliquots suggests the rate is slowing as reactants are consumed.
Fill in the blank: To isolate the order with respect to I⁻, you compare two experiments where ______ is held constant. (the concentration of S₂O₈²⁻)
True or false: The rate constant k changes when you change the concentration of a reactant. (False; k depends on temperature, not concentration.)
Fill in the blank: If doubling [A] quadruples the rate, the order with respect to A is ______. (2, i.e. second order)
True or false: The units of k are always M⁻¹ s⁻¹. (False; they depend on the overall reaction order.)
Fill in the blank: [S₂O₈²⁻] consumed per colour-change interval = ______ M. (0.00125)
Q: Given that Solution 1 has [I⁻] = 0.050 M and [S₂O₈²⁻] = 0.050 M with a rate of 2.016 × 10⁻⁵ M/s, and Solution 2 has [I⁻] = 0.100 M with the same [S₂O₈²⁻] and a rate of 2.404 × 10⁻⁵ M/s, what is the order with respect to I⁻?
A: Rate₁/Rate₂ = (0.050/0.100)^y → 0.839 = 0.5^y → y = ln(0.839)/ln(0.5) ≈ 0.3. The experimental order is approximately 0.3 (the expected value is 1; the discrepancy is attributed to experimental error).
Q: Why do the time intervals tend to increase from the first aliquot to the sixth?
A: As the reaction proceeds, reactant concentrations decrease. Lower concentrations mean a slower rate, so each successive aliquot of thiosulfate takes longer to be consumed. This increasing trend is evidence that the rate is not perfectly constant over the measurement period.
Q: What percentage of the original S₂O₈²⁻ in Solution 1 is consumed after all six aliquots?
A: Initial moles of S₂O₈²⁻ = 0.200 M × 0.005 L = 0.001 mol. Moles consumed per aliquot = (1/2) × (0.200 M × 0.00025 L) = 2.5 × 10⁻⁵ mol. After 6 aliquots: 6 × 2.5 × 10⁻⁵ = 1.5 × 10⁻⁴ mol. Percentage consumed = (1.5 × 10⁻⁴ / 0.001) × 100 = 15%.
Q: If you obtained k values of 8.207 × 10⁻⁶, 7.949 × 10⁻⁶, and 8.119 × 10⁻⁶ M⁻¹ s⁻¹ from the three solutions, what is the average k?
A: k_avg = (8.207 + 7.949 + 8.119) / 3 × 10⁻⁶ = 8.092 × 10⁻⁶ M⁻¹ s⁻¹ (the lab report rounds to 8.034 × 10⁻⁶).
The method of initial rates is used across chemistry wherever a rate law needs to be established experimentally, from enzyme kinetics (Michaelis-Menten) to atmospheric chemistry. The rate constant k found here feeds directly into the Arrhenius analysis in Part 3 of these notes, where k values at multiple temperatures are used to extract the activation energy.
method of initial rates, reaction order determination, rate law calculation, rate constant k, iodine clock rate law, ratio method kinetics, persulfate iodide rate law, M⁻¹ s⁻¹ units, second order overall, dilution concentration calculation, experimental reaction order, chemical kinetics calculations