The graph shows the hydrogen given off when magnesium reacts with excess acid.

• The gradient of the curve is the rate.
• It is steepest at the start, when there are most reactant particles.
• It gets less steep as the reactants are used up.
• It goes flat when one reactant has run out: the reaction has stopped. The final volume (60 cm³ here) depends on how much of that limiting reactant there was.

1. Mean rate over the first 40 s: about 52 cm³ ÷ 40 s = 1.3 cm³/s
2. Mean rate from 20 s to 60 s: (57 − 38) ÷ (60 − 20) = 19 ÷ 40 = 0.48 cm³/s

A mean rate covers a stretch of time. For the rate at one instant, draw a tangent: a straight line that touches the curve at that point without cutting it. Its gradient is the rate then.

1. Tangent at 20 s passes through (0, 16) and (40, 60)
2. gradient = (60 − 16) ÷ (40 − 0) = 44 ÷ 40
3. rate at 20 s = 1.1 cm³/s

Read two points far apart on the tangent, not on the curve. Points close together make a small reading error a big error in the gradient.

When a reaction is repeated with one change, plot both curves on the same axes.

• The steeper curve at the start is the faster reaction.
• If the amounts of reactants are the same, both curves level off at the same final volume, even though one gets there sooner.
• Using more of the limiting reactant raises the final volume; using less lowers it.