A graph is not decoration at the end of an experiment. It is where the answer lives — in the gradient, the intercept, or the area underneath. Drawing it properly is half the skill; knowing what to pull out of it is the other half.
📚 What you need to know
Sketch graphs have no scale but must still be labelled.
Every real graph needs a title, labelled axes, units and linear scales with no jumps.
The plotted points should fill at least half the grid.
Independent variable on the x-axis, dependent on the y-axis.
A line of best fit can be straight or curved. It shows the trend, not every point.
Interpolation reads inside the data; extrapolation extends beyond it.
Gradient of a curve is found by drawing a tangent, then using a large triangle.
Straight line equation: y = mx + c, where m is the gradient and c the y-intercept.
Uncertainty bars show the absolute uncertainty of each plotted value.
Rules for drawing a graph
These are the things examiners tick off, one at a time.
A clear title saying what is plotted against what.
Both axes labelled, with the quantity and its unit.
Linear scales going up in sensible steps, with no sudden jumps partway along.
The plot fills the grid. Rule of thumb: if you could double the scale and still fit every point on, your scale is too small.
Points marked with small crosses, so the exact position is visible.
Drawn in pencil, so a misplotted point can be fixed.
The independent variable is the one you chose and controlled. The dependent variable is the one that responded. If you set the concentrations and measured the rates, concentration goes on the x-axis — every time.
Lines of best fit
A line of best fit does not have to be straight, and it does not have to pass through every point. What it has to do is show the trend.
It should pass through or close to the majority of the points.
Where the data scatters, points should be spread evenly on both sides of the line.
Never join the points dot-to-dot. That claims the data does something between the points that you never measured.
Decide deliberately whether the origin is a real data point. If it is, it anchors the line beautifully, because you know it exactly.
Interpolation and extrapolation
Two words for reading values off a line, and they are not equally safe.
Extrapolation is not banned. Calorimetry depends on it. But you must be able to justify why the trend should continue into the region you are reading.
The classic legitimate extrapolation. In a calorimetry experiment the mixture starts cooling before it has finished reacting, so you extend the cooling line backwards to the moment of mixing to find the temperature rise that would have happened with no heat loss.
Gradients
The gradient is the answer to a lot of chemistry questions: a rate, an entropy change, a rate constant.
Equation of a straight liney = mx + c so gradient m = Δy ÷ Δx
For a straight line, draw a large triangle on the line and divide the vertical side by the horizontal side. Make the triangle as big as the graph allows — a small triangle magnifies your reading errors.
For a curve, the gradient changes from point to point, so you have to draw a tangent first. Line a ruler up against the curve so it is an equal distance from the curve on both sides of the touching point, then draw the tangent and take its gradient.
The tangent is the red line. It touches the curve at one point only, and its gradient is the rate of reaction at that instant.
🧩 Drawing a tangent that actually works
Mark the point on the curve where you want the gradient.
Lay a ruler against the curve at that point, so the gap between ruler and curve looks equal on both sides.
Draw the tangent long, right across the graph. A short tangent is hard to read.
Build a big triangle on the tangent, not on the curve.
Read both sides off the axes with their units.
Divide, and give the answer a unit made from the two axis units.
Intercepts
An intercept is where the line crosses an axis, and in chemistry it usually carries physical meaning. The best example is a graph of Gibbs energy change against temperature.
Rearranged into y = mx + c
ΔG = −ΔS × T + ΔH
Compare that with y = mx + c. Plotting ΔG against T gives a straight line whose gradient is −ΔS and whose y-intercept is ΔH. The x-intercept is the temperature at which ΔG = 0, which is where the reaction stops being feasible.
Below about 465 K the line sits below zero, so ΔG is negative and the reaction is feasible. Above it, ammonia synthesis stops being spontaneous.
Maxima, minima and areas
Two more features worth naming.
Maxima and minima are the highest and lowest points. At a maximum the gradient goes positive, then zero, then negative; at a minimum it does the reverse. On an energy profile diagram, the maximum is the transition state and the minima are the reactants and products.
Areas under a curve can carry meaning too. Under a Maxwell–Boltzmann distribution, the total area is the total number of particles, and the area to the right of Ea is the number with enough energy to react.
Uncertainty bars
An uncertainty bar is drawn above and below a plotted point, showing the absolute uncertainty in that measurement. Usually they are vertical, for the y-values, but they can be horizontal for the x-values too.
A point with a long bar is telling you it was measured badly. If your line misses that point but passes through its bar, the line is still consistent with the data.
Worked examples
WORKED EXAMPLE
On the ΔG against T graph above, the y-intercept is −46.2 kJ mol–1 and the gradient is +0.0994 kJ K–1 mol–1. Find ΔH, ΔS, and the temperature above which the reaction is no longer feasible.
Match the graph to y = mx + cΔG = −ΔS × T + ΔH, so c is ΔH and m is −ΔS.
Read off ΔHΔH = −46.2 kJ mol–1 (exothermic)Turn the gradient into ΔS−ΔS = +0.0994 → ΔS = −0.0994 kJ K–1 mol–1= −99.4 J K–1 mol–1Find where ΔG = 0T = 46.2 ÷ 0.0994 = 464.8Feasible below about 465 K (192°C)both ΔH and ΔS are negative, which is exactly why temperature decides the outcome
WORKED EXAMPLE
A tangent drawn to a volume-time curve at t = 40 s passes through (10 s, 41 cm3) and (70 s, 95 cm3). Calculate the rate of reaction at 40 s.
Use the two points on the tangent, not on the curveΔV = 95 − 41 = 54 cm3Δt = 70 − 10 = 60 sDivide54 ÷ 60 = 0.90Build the unit from the axes
y-axis is cm3, x-axis is s, so the gradient is cm3 per s.
Rate at 40 s = 0.90 cm3 s–1this is the instantaneous rate at that moment, not the average over the whole reaction
💡 Exam tip
Label both axes with quantity and unit. It is the most reliably awarded graph mark there is.
Use a scale that makes your points fill more than half the grid.
Draw the gradient triangle as large as possible, and show it on the graph.
Take the gradient of a curve from the tangent, never from two points on the curve itself.
Build the gradient’s unit from the two axis units: y-unit per x-unit.
If you extrapolate, say why it is reasonable to assume the trend continues.
⚠️ Common mix-up
Joining the points dot-to-dot. Draw a single line or smooth curve of best fit.
Taking a curve’s gradient from two points on the curve. That gives an average, not the rate at a point.
Using a tiny gradient triangle. Small triangles multiply your reading uncertainty.
Putting the dependent variable on the x-axis. The one you controlled goes on x.
Leaving units off the gradient. A gradient always has a unit unless both axes share one.
Forcing the line through the origin. Only do that if zero really is a data point you trust.
That completes Tool 3. Every mark on this page is one you can secure before you even walk into the exam — label the axes, fill the grid, draw a big triangle, and put a unit on the answer.
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