What you will learn

Interpret concentration–time curves, distinguish concentration from rate, and calculate mean and instantaneous rates from gradients. Connect the shape to changing collision frequency and use balanced-equation ratios to compare species. This lesson covers Pearson AAQ Unit 2 D1.2.3.

1. Read the axes before describing the reaction

Time is on the horizontal axis; concentration is on the vertical axis, usually in mol dm⁻³. Square brackets mean concentration: [A] is the concentration of species A. A point tells you a concentration at one time. The gradient tells you how quickly that concentration changes. A high point on a curve does not necessarily mean a high rate.

For a simple reaction in a closed system at constant volume, a reactant concentration falls as it is used up and a product concentration rises as it forms. Product concentration need not start at zero if product was already present. A species label, the equation and the experimental conditions are needed to interpret a curve reliably.

At 40 s, [A] = 0.36 mol dm⁻³ and [B] = 0.64 mol dm⁻³. For this 1:1 conversion with no initial B, the fall in [A] equals the rise in [B]. The curves cross when their concentrations are equal; that crossing does not prove equilibrium or completion.

2. Curve shape and changing rate

A steep gradient means a large concentration change per unit time. As a reactant curve becomes less steep, the magnitude of its gradient decreases: its rate of disappearance becomes smaller. A product curve that rises steeply and then flattens shows a decreasing rate of formation. Compare gradients at the time requested, using the axis scales.

In many simple batch reactions, reactant concentrations decrease during the run. Fewer reactant particles per unit volume usually means fewer productive encounters per unit time, so the reaction slows. This is a useful explanation, not a universal curve shape: temperature changes, catalysts, changing surface area, mechanisms and other conditions can alter the behaviour.

A straight sloping segment represents a constant rate of concentration change over that interval. A horizontal segment represents no measurable net concentration change. Do not confuse a flat nonzero product concentration with the product disappearing, and do not describe a downward reactant curve as a negative amount of substance.

3. Mean rate: use two points on the curve

Mean rate describes a whole time interval. Read the concentrations at its start and end, subtract using one consistent order, and divide by elapsed time. The line joining two points is a secant or chord; its gradient gives the mean concentration-change rate.

Mean gradient = (final concentration − initial concentration) ÷ (final time − initial time)
Mean reactant disappearance rate = −Δ[A]/Δt
Mean product formation rate = +Δ[B]/Δt

A reactant gradient is normally negative because its concentration decreases. When asked for the rate of disappearance, report the positive magnitude and identify the species. With concentration in mol dm⁻³ and time in s, the rate unit is mol dm⁻³ s⁻¹. For a time axis in minutes, the direct unit is mol dm⁻³ min⁻¹.

4. Instantaneous rate: draw a tangent

An instantaneous rate is the rate at one specified time. Draw a straight tangent that matches the local direction of the curve at that time. Extend it and choose two well-separated readable points on the tangent. These points need not lie on the curve. Use a large gradient triangle to reduce the effect of reading uncertainty.

The initial rate is the tangent gradient at the start of the reaction, commonly t = 0. In this teaching model the initial disappearance rate is 0.0200 mol dm⁻³ s⁻¹. The mean rate over the first 40 s is smaller because the curve becomes less steep during that interval. A chord from the start to a later point is not generally an initial tangent.

5. Product gradients and equation ratios

Equal species rates are not a rule for every equation. For aA → bB at constant volume, the equation-normalised reaction rate is r = −(1/a)Δ[A]/Δt = +(1/b)Δ[B]/Δt for an interval, or the corresponding tangent gradients at one time. Always distinguish a named species rate from this normalised reaction rate.

6. Plateaux, completion and fair comparisons

A plateau tells you that the measured concentration is no longer changing detectably. In a simple irreversible closed batch reaction this may mean the limiting reactant has been used up. An excess reactant can remain at a nonzero final concentration. Products usually remain at their final concentration rather than falling to zero.

A plateau alone does not prove every reactant has gone or that all molecular reaction events have stopped. A reversible system can have constant concentrations at dynamic equilibrium, where forward and reverse reactions continue at equal rates. Cooling, inhibition or the resolution of measurements can also make a curve appear flat. Use the context; do not claim equilibrium from a plateau alone.

To compare experiments, use the same species, matching concentration and time units, and the same specified time or a clearly defined initial rate. A faster reaction can reach the same final product concentration sooner when starting amounts, volume, stoichiometry and final conversion are the same. A steeper initial gradient does not by itself mean more final product.

Concentration is amount divided by volume. The simple link between concentration change and amount reacted assumes constant volume and no addition, removal or dilution. If the volume changes, concentration may change without that amount of chemical conversion. Check how the experiment was performed.

7. Units and a reliable calculation method

• Read the species, time interval and axis units.
• Choose a chord for a mean rate or a tangent for a rate at one time.
• Record two coordinates and calculate Δconcentration and Δtime.
• Divide, show units, and interpret the sign.
• Use the balanced equation only if converting between species rates.
• Keep extra digits during working and round sensibly to the precision of the graph.

A tangent fitted to experimental points is an estimate. Use a smooth best-fit curve where appropriate rather than joining noisy points and treating every short segment as exact. The plotted teaching values here allow exact arithmetic checks; real readings generally carry greater uncertainty.

Common misconceptions

• A high concentration means a high rate. Use the gradient, not the height.
• The rate equals concentration divided by time. Use a change in concentration over an interval or a tangent gradient.
• A negative gradient means a negative disappearance rate. The negative gradient shows consumption; disappearance is normally reported positively.
• Any two points on a curve give the rate at its middle. A tangent gives an instantaneous rate; a chord gives a mean.
• A flat graph means zero concentration or no molecular reactions. It means no detectable net concentration change.
• Reactant and product gradients always have equal magnitudes. Check equation coefficients and constant volume.
• Crossing curves prove equilibrium. They show equal plotted concentrations at that time.

Exam tips

• Label both axes with quantities and units.
• For a tangent calculation, clearly draw the tangent and a large triangle on that line.
• Quote the time or interval when describing a rate.
• Compare steepness quantitatively after checking the scales.
• Distinguish a negative reactant gradient from a positive consumption rate.
• Support explanations of slowing with falling reactant concentration and fewer productive encounters when the context permits.
• Do not infer a reaction order from a curve shape alone. Rate equations and detailed energy distributions are separate topics.

Check your understanding

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