Calculating reaction rates and gradients

The rate and extent of chemical change • Rate of reaction

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How to calculate the gradient of a tangent

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Select two widely spaced points on the tangent and compute (change in quantity) ÷ (change in time).

Key concepts

What you'll likely be quizzed about

Mean rate from reactant used or product formed

Mean rate equals the change in quantity (amount, mass, volume or concentration) divided by the time taken. The formula appears as mean rate = change in quantity / time. If the quantity refers to a reactant, the change is the decrease in that reactant; if the quantity refers to a product, the change is the increase in that product. Units depend on the measured quantity, for example g s-1, cm3 s-1 or mol s-1. The calculation uses the magnitude of the change divided by the elapsed time between two measured points. Example: if 12 cm3 of gas forms in 30 s, the mean rate = 12 ÷ 30 = 0.40 cm3 s-1. Consistent units and careful reading of time intervals ensure correct results.

Practical measurement methods and limiting factors

Mass loss on a balance measures the loss of reactant or gain of gas and produces rates in g s-1. Gas syringes or displacement measure gas volume produced and give rates in cm3 s-1. Titration or colorimetry measures concentration changes and gives rates in mol dm-3 s-1. Each method produces data with different precision and time resolution. Measurement frequency and experimental control affect the reliability of calculated rates. Faster sampling or continuous recording produces more accurate mean rates for short intervals. Temperature, concentration, surface area, and catalysts change the true reaction rate; calculations record the observed rate under the experimental conditions.

(HT only) Instantaneous rate via gradient of a tangent

Instantaneous rate at a specific time equals the gradient (slope) of the curve at that time on a plot of quantity versus time. The tangent line represents the best straight-line approximation to the curve at the selected time. The gradient equals rise/run found by selecting two points on the tangent and calculating (change in quantity) ÷ (change in time). Sign conventions indicate direction of change: a decreasing reactant gives a negative gradient; a forming product gives a positive gradient. The instantaneous rate often requires precise drawing of a tangent and careful selection of widely spaced points on the tangent to reduce measurement error. Units remain the measured quantity per unit time.

Key notes

Important points to keep in mind

Mean rate = change in quantity ÷ time; use magnitude of change and consistent units.

Choose measurement method that matches the species being tracked (mass, volume, concentration).

Express units clearly: include quantity unit and s-1 (for example cm3 s-1 or g s-1).

For instantaneous rate, draw a clear tangent and use widely spaced points on the tangent to calculate gradient.

State whether the calculated rate refers to reactant disappearance or product formation; note sign convention.

Higher temperature, concentration, surface area or presence of a catalyst increases observed reaction rate.

Report numerical answers to an appropriate number of significant figures based on raw data precision.