Chemical Kinetics · Lesson 1 of 10
Measuring Reaction Rates
“Measure chemical change over time and distinguish species disappearance, product appearance and normalised reaction rates.”
• Distinguish reaction feasibility, equilibrium extent and reaction speed. • Calculate average and instantaneous species rates from concentration–time data. • Relate species rates using balanced stoichiometric coefficients. • Convert rate units and state constant-volume and pressure assumptions.
A possible reaction need not be a fast reaction
Silver chloride can precipitate almost immediately when suitable silver-ion and chloride-ion solutions are mixed, while visible rusting of iron develops much more slowly in moist air. Sugar hydrolysis can occur on an intermediate timescale under suitable conditions. The difference is kinetic: it concerns how rapidly chemical change takes place. A reaction can be thermodynamically favourable yet proceed so slowly that little change is noticed.
The study of reaction rates, their dependence on experimental conditions and the sequences of molecular events that can account for them.
Thermodynamics asks whether a specified change is favourable under stated conditions; chemical equilibrium describes the composition approached; kinetics asks how quickly the system moves toward that state. Diamond converting to graphite under ordinary conditions illustrates the distinction: favourability alone does not remove the kinetic barrier. Food storage, curing materials and fuel combustion all require control of speed as well as knowledge of possible products.
The net ionic precipitation equation Ag⁺(aq) + Cl⁻(aq) → AgCl(s) conserves silver, chlorine and charge. Its speed is not determined simply by how short the equation looks. Conditions such as concentration, temperature, solvent, gas pressure and available catalytic surface can change the observed timescale.
Average rate over a measured interval
Square brackets mean concentration, commonly mol L⁻¹. Subtract the earlier concentration from the later one and divide by the elapsed time. The reactant change is negative during consumption, so a minus sign gives a positive disappearance rate. Product appearance uses a plus sign. These sign choices describe forward progress; a net reverse process requires signs interpreted consistently rather than forcing every derivative to be positive.
| Time / s | Butyl chloride concentration / mol L⁻¹ |
|---|---|
| 0 | 0.1000 |
| 50 | 0.0905 |
| 100 | 0.0820 |
| 150 | 0.0741 |
| 200 | 0.0671 |
| 300 | 0.0549 |
| 400 | 0.0439 |
| 500 | 0.0335 |
| 700 | 0.0210 |
| 800 | 0.0170 |
Problem
For C₄H₉Cl + H₂O → C₄H₉OH + HCl, calculate butyl chloride disappearance over 0–50 s, 100–150 s and 400–700 s from the table.
- 1.For 0–50 s, concentration falls by 0.0095 mol L⁻¹. Divide by 50 s: v=1.90×10⁻⁴ mol L⁻¹ s⁻¹.
- 2.For 100–150 s, v=(0.0820−0.0741)/50=1.58×10⁻⁴ mol L⁻¹ s⁻¹.
- 3.For 400–700 s, v=(0.0439−0.0210)/300=7.6333×10⁻⁵ mol L⁻¹ s⁻¹.
- 4.Each is an interval average, not a measurement of the exact rate at every time inside the interval. The declining averages show that this dataset’s disappearance slows as the reactant is consumed.
| Interval / s | Average disappearance rate / mol L⁻¹ s⁻¹ |
|---|---|
| 0–50 | 1.90×10⁻⁴ |
| 50–100 | 1.70×10⁻⁴ |
| 100–150 | 1.58×10⁻⁴ |
| 150–200 | 1.40×10⁻⁴ |
| 200–300 | 1.22×10⁻⁴ |
| 300–400 | 1.10×10⁻⁴ |
| 400–500 | 1.04×10⁻⁴ |
| 500–700 | 6.25×10⁻⁵ |
| 400–700 | 7.63×10⁻⁵ |
| 700–800 | 4.00×10⁻⁵ |
Instantaneous rate is a tangent slope
A line joining two concentration measurements is a secant and gives the average rate across that interval. A tangent touches the smooth concentration curve at a chosen time and gives the instantaneous rate there. On a decreasing reactant curve the tangent slope is negative, while the disappearance rate is its negative. A tangent constructed from a plotted experimental curve is an estimate whose accuracy depends on data density and drawing precision.
Problem
A tangent near 600 s passes through convenient construction points (400 s, 0.037 mol L⁻¹) and (800 s, 0.017 mol L⁻¹). Estimate disappearance rate.
- 1.Use the two construction points on the tangent, which need not both be measured points on the concentration curve.
- 2.Slope=(0.017−0.037)/(800−400)=−5.00×10⁻⁵ mol L⁻¹ s⁻¹.
- 3.Disappearance rate is the negative of the slope: about 5.00×10⁻⁵ mol L⁻¹ s⁻¹.
- 4.The estimate should not acquire extra precision from reading a small printed graph. A fitted kinetic model can give another estimate, but introduces model assumptions.
Different species change at different stoichiometric rates
For 2HI(g) → H₂(g) + I₂(g), every two moles of HI consumed yield one mole of each product. Therefore HI disappears twice as fast as either product appears. A single reaction rate is defined by dividing each species concentration derivative by its stoichiometric coefficient. This removes an arbitrary dependence on which species was monitored, provided the balanced overall conversion applies without substantial intermediate accumulation or side reactions.
Problem
For 2N₂O₅ → 4NO₂ + O₂ in a monitored solution, [N₂O₅] falls from 2.33 to 2.08 mol L⁻¹ in 184 min. Find the average normalised rate and NO₂ appearance rate.
- 1.N₂O₅ disappearance rate=(2.33−2.08)/184=0.0013587 mol L⁻¹ min⁻¹. Divide by coefficient 2: r=0.000679348 mol L⁻¹ min⁻¹.
- 2.Convert time units: r=0.0407609 mol L⁻¹ h⁻¹ = 1.13225e-05 mol L⁻¹ s⁻¹. A per-minute value is multiplied by 60 to express the amount per hour.
- 3.NO₂ appearance rate is 4r=0.00271739 mol L⁻¹ min⁻¹; oxygen appearance rate is r.
- 4.The stoichiometric equation describes the conversion; phase labels must match the actual experimental medium rather than implying that a dissolved concentration was measured as a free gas.
Another balanced example is 5Br⁻ + BrO₃⁻ + 6H⁺ → 3Br₂ + 3H₂O. Bromide disappearance is 5r, bromate disappearance r and bromine appearance 3r. The heterogeneous conversion Hg(l)+Cl₂(g)→HgCl₂(s) illustrates another caution: a pure solid or liquid has essentially constant activity even while its amount changes, so one must not infer a solid-consumption rate from the derivative of an unchanged pure-phase concentration. Amount changes per time, or amounts per fixed reference volume, are suitable for heterogeneous stoichiometric bookkeeping.
Every reported rate needs a species or a normalised-reaction definition. In aA→products, −d[A]/dt and r differ by a. A numerical rate constant can absorb this factor, so do not switch conventions midway through a calculation.
Quick Quiz
Quiz
Which quantity answers how rapidly a reaction proceeds?
Explanation: Kinetics concerns speed; thermodynamic favourability and equilibrium extent answer different questions.
For 2A→P, A falls from 0.50 to 0.40 M in 10 min. What is the normalised average reaction rate?
Explanation: Disappearance is 0.10/10=0.010 M min⁻¹; divide by coefficient two to obtain r=0.0050 M min⁻¹.
The instantaneous disappearance rate of a reactant equals:
Explanation: The derivative gives the tangent slope; taking its negative gives a positive forward disappearance rate.
If r=2.0×10⁻⁴ M s⁻¹ for 2HI→H₂+I₂, how fast does HI disappear?
Explanation: HI has coefficient two, so its disappearance rate is 2r.
Which assumption allows concentration changes to directly track species amount changes without a dilution correction?
Explanation: Changing volume can alter concentration even without reaction. Constant volume avoids that contribution.
Practice Problems
- For R→P, concentration falls from 0.030 to 0.020 M in 25 min. Calculate average rate in M min⁻¹ and M s⁻¹.
- For 2A→products, concentration falls from 0.50 to 0.40 M in 10 min. Report both disappearance rate and normalised rate.
- In 5Br⁻+BrO₃⁻+6H⁺→3Br₂+3H₂O, bromate disappears at 2.0×10⁻⁵ M s⁻¹. Find bromide disappearance and bromine appearance.
- For the table, calculate average butyl chloride disappearance between 300 and 400 s and explain why it is not necessarily the exact rate at 350 s.
- A gas partial pressure decreases at 0.0100 bar s⁻¹ at 300 K. Find the concentration disappearance rate using R=0.08314 L bar mol⁻¹ K⁻¹.
- A pseudo-first-order dataset has [A]=0.55,0.31,0.17,0.085 M at 0,30,60,90 s. Find the average disappearance rate between 30 and 60 s.
Divide the positive disappearance 0.010 M by 25 min: v=0.0004 M min⁻¹. Divide again by 60 to obtain 6.66667e-06 M s⁻¹. The coefficient of R is one, so species disappearance equals the normalised rate.
Key Takeaways
• Kinetics measures speed; thermodynamics and equilibrium answer different questions. • Average rate uses a finite concentration change divided by elapsed time. • Instantaneous rate is a concentration–time tangent slope with the appropriate sign. • Species disappearance and appearance rates follow balanced stoichiometric ratios. • A normalised rate divides each species derivative by its coefficient. • Concentration-rate formulas require attention to volume changes and pure phases. • Gas pressure rates convert to concentration rates through the ideal-gas relationship when applicable.
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Rate Laws, Reaction Order and Rate Constants