Determination of rate equation (A-level only) — AQA A-Level Chemistry
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Determination of rate equation (A-level only) explained
The rate equation cannot be written from the balanced equation; it has to be measured.
Read the full explanation
The stoichiometric equation counts what is consumed overall, whereas the rate equation reflects only the species involved up to and including the slowest step. The acid catalysed iodination of a ketone makes the point sharply: iodine is a reactant in the overall equation, yet the measured rate equation is rate = k[CH₃CH₂COCH₃][H⁺], so iodine is zero order and its concentration has no effect on the rate. Meanwhile H⁺ appears in the rate equation although, as a catalyst, it does not appear in the overall equation at all. Only experiments that vary one concentration at a time can establish these orders.
The orders with respect to reactants can provide information about the mechanism of a reaction.
A multi step reaction goes no faster than its slowest step, the rate determining step, so only the species taking part in that step, or in steps before it, can influence the rate. That makes the rate equation a window into the mechanism. A species that appears to the first power contributes one molecule to the rate determining step, one to the second power contributes two, and a zero order species is involved only in a fast step after the rate determining one. Hydrolysis of halogenoalkanes is the standard illustration: a tertiary halogenoalkane gives rate = k[RBr], showing the slow step is the breaking of the carbon to halogen bond alone, while a primary one gives rate = k[RBr][OH⁻], with both species in the slow step.
Students should be able to: use concentration–time graphs to deduce the rate of a reaction use initial concentration–time data to deduce the initial rate of a reaction use rate–concentration data or graphs to deduce the order (0, 1 or 2) with respect to a reactant derive the rate equation for a reaction from the orders with respect to each of the reactants use the orders with respect to reactants to provide information about the rate determining/limiting step of a reaction.
Two graph types do the work. On a concentration against time graph, the rate at any moment is the gradient of the tangent, and the initial rate is the gradient at time zero; a constant half life on such a curve signals first order. On a rate against concentration graph the shapes separate the orders directly: zero order gives a horizontal line, because rate does not change with concentration; first order gives a straight line through the origin, so doubling the concentration doubles the rate; second order gives an upward curve, with doubling the concentration quadrupling the rate. Combine the orders found for each reactant to write the rate equation, then substitute one set of data to find k and its units.
Required practical 7 Measuring the rate of reaction: by an initial rate method by a continuous monitoring method.
Required practical 7 covers the two standard ways of measuring a rate. The initial rate method times how long a fixed small amount of product takes to appear, as in an iodine clock where a limited amount of thiosulfate consumes the iodine until it runs out and the starch suddenly turns blue black; because the same tiny extent of reaction occurs each time, the initial rate is proportional to 1/t. The continuous monitoring method follows one mixture throughout, by collecting gas in a syringe, recording mass loss on a balance, or tracking colour with a colorimeter, then plotting the measurement against time and taking gradients. Repeat runs vary one concentration at a time, keeping the total volume and the temperature constant.
Your focus
- Deduce the order with respect to each reactant from a table of initial rates by comparing experiments that differ in one concentration.
- Explain why the rate equation cannot be predicted from the stoichiometric equation, using a zero order reactant as evidence.
- Explain how a catalyst can appear in the rate equation of a reaction in which it does not appear in the overall equation.
Show all 16 objectives
- Describe an experimental procedure that isolates the effect of one reactant on the rate.
- Deduce which species are involved in the rate determining step from a given rate equation.
- Suggest a two step mechanism consistent with a stated rate equation and with the overall balanced equation.
- Explain what the zero order of a reactant reveals about where it is consumed in the mechanism.
- Justify why rate data can support a proposed mechanism without proving it.
- Determine the initial rate of a reaction from the tangent at the start of a concentration against time graph.
- Deduce the order with respect to a reactant from the shape of a rate against concentration graph and state the graphical evidence.
- Derive the full rate equation from the individual orders and calculate the rate constant with its units.
- Use the deduced orders to identify which species appear in the rate determining step.
- Describe an initial rate experiment in which a fixed small extent of reaction is timed, and justify why rate is proportional to 1/t.
- Select a continuous monitoring technique appropriate to a given reaction and justify the choice.
- Determine the initial rate from a continuous monitoring graph by drawing a tangent at time zero.
- Explain why the total volume of the reaction mixture is kept constant when one concentration is varied.
Determination of rate equation (A-level only) exam tips
Marking Points
- one mark for stating that orders are determined experimentally and cannot be deduced from the equation
- one mark for identifying a species as zero order because changing its concentration leaves the rate unchanged
- one mark for recognising that a catalyst can appear in the rate equation while being absent from the overall equation
- one mark for describing a procedure in which one concentration is varied while the others are held constant
- one mark for stating that the rate determining step is the slowest step in the mechanism
- one mark for identifying the species present in the rate determining step from those in the rate equation
- one mark for matching the order with respect to a species to the number of its molecules in that step
- one mark for deducing that a zero order species takes part only after the rate determining step
- one mark for determining a rate as the gradient of a tangent drawn to a concentration against time curve
- one mark for stating the order together with the graphical evidence, such as first order shown by a straight line through the origin
- one mark for combining the individual orders into the rate equation
- one mark for the value of k with units, from substituting one consistent set of rate and concentration data
- one mark for using the orders to comment on the species present in the rate determining step
- one mark for stating that the initial rate is proportional to 1/t when a fixed small extent of reaction is timed
- one mark for naming an appropriate continuous measurement, such as gas volume, mass loss or colorimetry, matched to the reaction
- one mark for keeping the total volume and the temperature constant while one concentration is varied
- one mark for determining a rate from the gradient of the plotted curve at the required time
Examiner Tips
- 💡Compare pairs of experiments in which only one concentration differs; that comparison is the whole method.
- 💡If doubling a concentration leaves the rate unchanged, state that the order is zero and say so explicitly.
- 💡Never justify an order by pointing at the stoichiometry, however well the numbers seem to fit.
- 💡Check that your proposed steps add to give the overall equation before you commit to a mechanism.
- 💡Say consistent with rather than proves when using a rate equation to support a mechanism.
- 💡Use the orders to count molecules in the slow step: order one means one molecule, order two means two.
- 💡Label which graph you are reading before you answer; the same order has different shapes on the two axes.
- 💡Say straight line through the origin, or constant gradient through the origin, for first order.
- 💡When a question says state how the graph shows this, the evidence sentence carries its own mark.
- 💡Match the monitoring method to an observable change: colour for a coloured species, gas volume for a gaseous product.
- 💡Say why the total volume is kept constant, since it is what fixes all the other concentrations.
- 💡Draw tangents with a ruler across a wide span and show the triangle you used to find the gradient.
Common Mistakes
- reading the orders off the balancing numbers of the chemical equation
- assuming every reactant must appear in the rate equation
- assuming a species absent from the overall equation cannot appear in the rate equation
- varying two concentrations between experiments and then attributing the rate change to one of them
- describing a zero order reactant as one that is not consumed during the reaction
- claiming a zero order species plays no part in the reaction at all
- assuming the rate determining step is the first step of every mechanism
- proposing a mechanism whose steps do not add up to the overall balanced equation
- ignoring the order when counting molecules, so a second order species is shown once in the slow step
- treating the rate equation as proof of a single unique mechanism rather than as evidence consistent with one
- stating an order without saying what the graph shows, which loses the explanation mark
- describing a first order rate against concentration line as straight without adding that it passes through the origin
- reading a rate from a concentration against time graph as a chord between two distant points rather than a tangent
- mixing data from two different experiments when calculating k
- confusing the shapes of the concentration against time and the rate against concentration graphs for the same order
- varying a concentration by adding more reagent without topping up with water, so the total volume changes
- taking the gradient of a chord across a curved section and calling it the initial rate
- choosing mass loss to follow a reaction whose only gaseous product is hydrogen, where the change is too small to measure reliably
- starting the clock after mixing is complete, so the earliest and fastest part of the reaction is missed
- leaving the reaction mixture out of a water bath, so the temperature drifts between runs