Part 2: Measuring rates and interpreting curves

Choose a measurable change, control the comparison and use a tangent for the rate at a particular instant.

Choose a signal linked to reaction progress

Choose a method that measures a useful change

A gas syringe gives repeated volume readings during a gas-producing reaction. It should be gas-tight yet permit the plunger to move freely. Choose capacity above the expected final volume, start timing consistently and record temperature and pressure when converting volume to amount.

Mass loss works when gas escapes from a vessel on a balance. A cotton-wool plug can reduce spray loss without sealing the outlet. Hydrogen may give too little mass loss for the available balance even when its volume is readily measurable. A gas-producing reaction is not automatically equally suitable for both methods.

For a coloured species, a calibrated colorimeter can follow a changing signal. For a disappearing cross, use the same viewing geometry and final liquid depth. Taking aliquots for later analysis requires a justified way to stop or sufficiently slow further reaction; otherwise the sample changes while you measure it. Use supplied method information for unfamiliar contexts.

Rate is a gradient, not the total product

Mean rate = change in measured quantity/change in time. Instantaneous rate is the gradient of a tangent. For concentration, units may be mol dm⁻³ s⁻¹; gas-volume rate may be cm³ s⁻¹. A reactant concentration falls, so its gradient is negative; quote a positive rate of disappearance with the sign convention stated.

Illustrative gas volumes are 0, 24 and 36 cm³ at 0, 20 and 40 s. Mean rate over 0–20 s = 1.20 cm³ s⁻¹; over 20–40 s = 0.60 cm³ s⁻¹. A tangent is needed for the rate at exactly 20 s. A graph’s greater height does not mean a greater rate.

For a fixed amount of precipitate needed to obscure a cross, 1/time is a comparative rate measure, not automatically a concentration rate. It is valid only if the same extent of reaction defines each end point.

Use two points on the tangent, not two points on the curve

The illustrative curve shows V = 80(1 − e^(−t/40)) cm³ as a constructed model, not measured data or a required AS rate-law derivation. At 40 s the volume is about 50.6 cm³. A tangent through that point passes approximately through (20 s, 35.9 cm³) and (60 s, 65.3 cm³).

Gradient = (65.3 − 35.9)/(60 − 20) = 0.735 cm³ s⁻¹, or about 0.74 from the plotted line. By contrast V(40)/40 = 1.26 cm³ s⁻¹ is a mean rate from time zero. It is not the instantaneous rate at 40 s. The tangent’s endpoint coordinates need not be measured data points.

Use a large triangle so reading uncertainty has less relative effect. Include both axis units when stating the rate. If the plotted variable is concentration rather than gas volume, the units change accordingly.

Swipe horizontally to view the whole diagram.

Compare rate and final amount separately

To vary acid concentration, dilute a stock solution with water while keeping total liquid volume constant. Keep temperature and carbonate mass/surface area constant. Repeat to estimate scatter. For a temperature investigation, equilibrate reactants in a thermostatic bath before mixing.

A faster curve can reach the same final volume sooner if the same limiting moles are present. Adding more limiting reactant can instead increase the final volume. Separate statements about initial gradient from statements about the plateau.

A reaction slows as a dissolved reactant is depleted and collision frequency falls. It stops when a limiting reactant is used up, even if another remains in excess. These are PAG 9 rate-measurement skills.

Predict the slope and plateau independently

For a fixed amount of carbonate with acid in excess, a higher acid concentration can steepen the initial gas-volume curve while leaving the final plateau unchanged. If acid is limiting instead, increasing its amount can raise the plateau as well. Always determine the limiting amount before sketching the final height.

A catalyst or higher temperature can reach the same final product amount sooner in a simple effectively complete reaction with unchanged limiting amount. To compare gas-volume plateaus, measure or correct volumes to the same temperature and pressure: a hotter gas occupies more volume even when its amount is unchanged. Do not apply the unchanged-product prediction automatically to a reversible equilibrium, because temperature may alter equilibrium composition as well as rate.

For hydrogen peroxide decomposition, 2H₂O₂ → 2H₂O + O₂, an illustrative 72.0 cm³ final oxygen at RTP corresponds to 0.00300 mol O₂ and therefore 0.00600 mol H₂O₂. If the starting solution volume was 40.0 cm³, its concentration was 0.150 mol dm⁻³. Gas volume and solution volume play different roles.

Quick checks

Original Finesse questions. Reveal the indicative worked solutions after attempting each question; these are not official OCR A mark allocations.

Sources