Rate graphs and tangents
Reading the curve
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.
- Mean rate over the first 40 s: about 52 cm³ ÷ 40 s = 1.3 cm³/s
- Mean rate from 20 s to 60 s: (57 − 38) ÷ (60 − 20) = 19 ÷ 40 = 0.48 cm³/s
Higher: the rate at one moment
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.
- Tangent at 20 s passes through (0, 16) and (40, 60)
- gradient = (60 − 16) ÷ (40 − 0) = 44 ÷ 40
- 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.
Comparing two curves
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.
Concentration in the simulation
Open the rates of reaction simulation. Set Particles of A to 15 and run it, watching the Product C graph and the Rate readout. Then reset, set Particles of A to 60 and run it again. Which run gives the steeper start, and why do the particles meet more often?
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This question is in Brainlag Plus