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Rate and energy graph interpreter

A graph can look familiar and still leave you unsure whether the answer is a slope, a height or an area.

On this page
  1. How do I use it?
  2. Example walk-through
  3. How do I read the result?
  4. What are the limits?
  5. Which lessons explain the output?

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This tool gives you five original, labelled datasets: three rate graphs (gas volume, reactant concentration and flask mass) and two energy profiles. For a rate graph you choose two points and it computes the average gradient with units. For an energy profile it finds the activation energy and the energy change.

Every graph comes with a data table and a short reason for the reading, so the tool teaches the meaning of the graph as well as the number.

How do I use it?

  1. Pick a dataset. The graph and the exact data table appear below the controls.
  2. For a rate graph, choose a From point and a To point. They must be different points, or the change in x is zero and the tool asks you to choose again.
  3. Press Interpret. The result shows the working (change in y divided by change in x), the units, and whether the gradient is rising, falling or flat.
  4. Read the Why this reading line and the table of average rates for every interval.
  5. For an energy profile, there is nothing to choose: the result shows the activation energy, the energy change and whether the reaction is exothermic or endothermic. Reset returns to the start.

Example walk-through

The tool opens on the gas-volume curve with points 6 and 8 chosen, which are 50 s and 70 s. The volume is 63 cm3 at both, so the change in y is 0 and the gradient is 0. The result explains that a flat curve means no further net change in product, not that particles have vanished.

Now choose points 1 and 2 (0 s and 10 s). The volume goes from 0 to 24 cm3, so the gradient is 24 / 10 = 2.4 cm3 per second.

The interval table shows the rate falling: 2.4, 1.8, 1.2, 0.6, 0.3, then 0 and 0. The curve is steepest at the start because the reactant is most concentrated.

Switch to the exothermic profile. Reactants are at 50 kJ/mol, the peak is 130 and products are 20.

Activation energy is 130 - 50 = 80 kJ/mol, and the energy change is 20 - 50 = -30 kJ/mol, so energy is released. The endothermic profile (20, 100, 60) gives 80 and +40.

How do I read the result?

  • Gradient with units: the units are the y unit per x unit, such as cm3/s. Always copy them into your answer.
  • Sign: a falling quantity gives a negative gradient, and the rate is the size of it.
  • Average rates table: shows how the rate changes across the experiment, so you can describe a slowing reaction.
  • Energy values: the reverse activation energy is also shown, as peak minus product energy.

What are the limits?

The datasets are original teaching data, not measurements from a real experiment. The gradient here is always a chord between two plotted points, so it is an average, and the tool does not draw tangents.

It never assumes direct proportionality. You still need to decide which graph meaning applies to your question, and check your own syllabus on the Cambridge subject page for what is required.

Which lessons explain the output?

Begin with extracting a rate from a supplied graph, then see interpreting an energy profile and activation energy on a diagram. For motion graphs, finding acceleration from a gradient uses the same idea.

If slope and area get mixed up, read the clinic page on gradient and area, and keep the graph-reading checklist beside you. Browse other aids on the tools page.

When you can get the number but not the explanation, our team can work on your wording with you. See online one-to-one Chemistry tuition for how that works.

Questions people ask

Why does a flat curve not mean the reaction has no particles left?

A flat product-time curve means there is no further net change in the amount of product. The limiting reactant may have been used up, or in a reversible reaction the forward and backward changes may balance. The particles are still there, so describe the change, not the absence.

Why is the gradient called an average rate?

The tool joins two points with a straight line, and its gradient is the change over that whole interval. On a curve the steepness differs from point to point, so the chord only gives the average. Never assume the rate is constant or proportional to time.

Why is a negative gradient still a rate?

A falling reactant concentration gives a negative gradient because the amount is decreasing. The rate of reaction is the size of that gradient, quoted as a positive number with units such as mol/dm3 per minute.

How is the activation energy read from an energy profile?

Activation energy is the peak energy minus the reactant energy. The energy change is product energy minus reactant energy, so a negative value is exothermic and a positive value is endothermic.

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