Reading Graphs and Data in Chemistry Questions
A graph question is usually easier than the equivalent numerical, provided you read the axes before looking at the curve.
The order to read a graph in
- Both axis labels and their units. Not the shape — the axes. Much of the answer is usually there.
- What the slope would mean physically, given those axes.
- What the intercept would mean, if it is on the graph.
- Only then the shape — linear, curved, plateauing.
The standard linear plots
A large fraction of graph questions test whether you know which plot is straight for a given law. Each linearity is diagnostic.
| Plot | Linear for | Slope gives |
|---|---|---|
| ln[A] against t | First-order reaction | −k |
| 1/[A] against t | Second-order reaction | k |
| [A] against t | Zero-order reaction | −k |
| ln k against 1/T | Arrhenius behaviour | −Ea/R |
| P against 1/V | Boyle's law | Proportional to nRT |
| V against T in kelvin | Charles's law | Proportional to nR/P |
| log(x/m) against log p | Freundlich isotherm | 1/n |
| p/x against p | Langmuir isotherm | 1/xm |
The first three rows are the most commonly asked. Given concentration-time data, the way to determine order is to test which plot is straight — and saying that explicitly is the expected method, rather than guessing from the shape of the raw data.
What curvature tells you
A plot that should be linear but is not is informative rather than faulty:
- A kinetics plot curving suggests the assumed order is wrong, or the mechanism changes during the reaction.
- An Arrhenius plot curving suggests a composite rate constant or a change of mechanism with temperature.
- An adsorption plot deviating at high pressure suggests the model's assumptions have broken down.
Answering "the data do not fit that model, therefore the assumption behind it fails" is a stronger answer than forcing a line through curved points.
Common data traps
| Trap | What to check |
|---|---|
| Axis not starting at zero | Read the actual values; a steep-looking rise may be small |
| Logarithmic axis | Equal spacing means equal ratios, not equal differences |
| Temperature in Celsius | Convert before using in any proportional relationship |
| Units differing between axes | Convert before computing a slope |
| Extrapolation beyond the data | Valid only if the relationship holds there; state the assumption |
Answering a graph question well
State what the axes represent, name the relationship being tested, say what the slope and intercept correspond to, then give the numerical answer with units. A bare number from a slope calculation scores poorly even when correct, because the marks are distributed across the interpretation.
Where the question asks you to sketch rather than read, label both axes, mark any significant intercept, and indicate the shape correctly at both extremes. Unlabelled sketches lose marks that cost nothing to secure.
Frequently asked questions
How do I find the order of a reaction from data?
Test which plot is linear. If ln[A] against time is straight the reaction is first order; if 1/[A] against time is straight it is second order; if [A] against time is straight it is zero order.
Why plot ln k against 1/T rather than k against T?
Because the Arrhenius relationship is exponential, and taking logarithms linearises it. A straight line is far easier to read a slope from than a curve.
What if the points do not fit a straight line at all?
That is a result. Say which model fails and what that implies about the assumptions, rather than forcing a line through the data.
Should I use all the points to find a slope?
Use two well-separated points on the best line through the data, not two adjacent points. Widely spaced points reduce the effect of reading error on the slope.
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