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The iodine clock: initial rates and activation energy

Vary the amounts of potassium iodide and ammonium persulfate and time each beaker; find both orders and the rate constant from initial rates, then repeat at different bath temperatures and build an Arrhenius plot for the activation energy.

Difficulty ●●○ ≈ 30 min

Aim Determine m, n and k in the rate law r=k[SX2OX8X2−]m[IX−]nr = k[\ce{S2O8^2-}]^m[\ce{I-}]^n for SX2OX8X2−+2 IX−→2 SOX4X2−+IX2\ce{S2O8^2-} + \ce{2I-} \mathrel{\ce{->}} \ce{2SO4^2-} + \ce{I2}, and the activation energy Ea.
S₂O₈²⁻ + 2I⁻ → 2SO₄²⁻ + I₂ · timing gives the rate

Iodine clock: the method of initial rates

Water to 50.0 mL: 0.0 mL · Plus 10.0 mL of 0.0050 M Na₂S₂O₃ (with starch)

[I⁻]₀ = 0.080 M · [S₂O₈²⁻]₀ = 0.040 M · [S₂O₃²⁻]₀ = 1.00 mM

Stopwatch 0.0 s

Thiosulfate turns each I₂ straight back into I⁻; the moment it runs out, I₂ meets the starch and the colour appears. So a fixed amount of S₂O₈²⁻ has reacted by time t: rate ≈ [S₂O₃²⁻]₀ / (2t).

Lab notebook

No runs yet. Set the volumes, then press “Mix and start the timer”.

Finding the orders

Order in I⁻ — needs two runs that differ only in this concentration
Order in S₂O₈²⁻ — needs two runs that differ only in this concentration
k from each run (taking both orders as 1) —
Activation energy from different temperatures —
r=k [SX2OX8X2−]m [IX−]n,n=lg⁡(r2/r1)lg⁡(c2/c1)r = k\,[\ce{S2O8^2-}]^{m}\,[\ce{I-}]^{n},\qquad n = \dfrac{\lg(r_2/r_1)}{\lg(c_2/c_1)}
Clock times come from exact integration of rate = k[S₂O₈²⁻][I⁻] (iodide is regenerated by thiosulfate, so the clock time has a closed form). k(25 °C) = 8.0 × 10⁻³ L mol⁻¹ s⁻¹ and Ea = 52 kJ/mol are model values representative of a typical clock mixture — the real k depends strongly on ionic strength. The “measurement error” is seeded: bath ±0.2 °C and a stopwatch reaction time of 0.3 ± 0.2 s. The blue-black colour is computed from the starch–iodine absorption band.

Procedure

  1. Standard run: 20.0 mL of 0.200 M KI, 20.0 mL of 0.100 M (NH₄)₂S₂O₈ and 10.0 mL of 0.0050 M Na₂S₂O₃ (with starch) at 25 °C. Press “Mix and start the timer” and record when the blue appears.
  2. Series A: keep the persulfate at 20 mL and use 15, 10 and 5 mL of KI (water makes up 50 mL).
  3. Series B: keep the KI at 20 mL and use 15, 10 and 5 mL of persulfate.
  4. Turn each time into an initial rate [S₂O₃²⁻]₀/(2t), read m and n from the slopes of the lg(rate)–lg(concentration) plot, then calculate k.
  5. Repeat the standard mixture at 15, 25, 35 and 45 °C and obtain Ea from the slope of ln k against 1/T.

What to notice

  • Halving the KI roughly doubles the clock time: first order in I⁻, even though its coefficient is 2.
  • Both lg–lg lines have slopes close to 1, the overall order is 2, and k is about 8 × 10⁻³ L mol⁻¹ s⁻¹.
  • Every 10 °C of warming roughly halves the time; Ea comes out near 50 kJ/mol.
  • Measurement error (stopwatch reaction time, bath temperature drift) keeps the orders from coming out exactly 1 — which is why you take several points and fit a line.

In a real lab

  • How often two anions meet depends strongly on ionic strength: real procedures make up the volume with KCl or K₂SO₄ solution instead of water, so every run has the same ionic strength.
  • Pour in the last solution quickly and start the timer at that instant; bring every solution to the bath temperature first.
  • Ammonium persulfate is a strong oxidiser and can cause skin and respiratory sensitisation; wear gloves and goggles.
  • The simulation uses model values k(25 °C) = 8.0 × 10⁻³ L mol⁻¹ s⁻¹ and Ea = 52 kJ/mol; real values depend on your solutions and ionic strength.

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