Arrhenius equation & plots

Calculate with the Arrhenius equation, turn experimental data into a straight-line plot, and practise the graph and unit checks that these questions require.

Two-temperature practice: the derived relationship is supplied in core questions. Deriving or recalling it unaided is Stretch & challenge, not assumed recall.

Choose the Arrhenius form from the data you have

k = Ae−Ea/RT  ·  ln k = −Ea/R(1/T) + ln A

One temperature

With k, A and T given, use the exponential equation directly. Put Ea into joules when R is in J K−1 mol−1.

Several temperatures

Plot ln k against 1/T. The gradient is −Ea/R, so a steeper negative line means a larger activation energy.

AQA gives the required Arrhenius equations when needed; OCR A includes them on the Data Sheet.

OCR A intercept

The y-intercept is ln A and lies at 1/T = 0. Extrapolate the straight line to that point when the plotted axis starts above zero.

Before you accept an Arrhenius answer

J and kJ

R is in joules. Convert Ea to J mol−1 before it goes into the exponential, then convert the final Ea back to kJ mol−1 if required.

Kelvin

T means absolute temperature. A temperature quoted in °C must be converted before substitution.

Natural logarithms

The straight-line equation uses ln k. Using log10 changes the gradient and gives the wrong Ea.

What temperature changes

Higher temperature increases k. Ea belongs to the reaction pathway; a catalyst provides a pathway with a lower Ea.

Try next

Boltzmann questions & simulator

Temperature, Ea and catalysts

Practise