4.1.3Unit 4. Rates, Equilibria and Further Organic Chemistry
Reaction Orders – Graphs — IAL Edexcel Linear (Chemistry) Revision Notes & Topical Questions
5 min read 6 parts Lesson 12 of 56 Unit quiz
Part 1 of 6Concentration–Time Graphs
The shape of the graph indicates the order of the reaction with respect to the reactant.
Zero order
- The graph is a straight line sloping downwards, because the rate stays constant as the concentration falls.
First order
- The graph is a curve that falls with a decreasing gradient, since the rate drops in proportion to the concentration.
Second order
- The curve falls more steeply at the start and then flattens more slowly, so the half-life gets longer.
Gradient
- At any time the gradient of the tangent equals the rate of reaction at that moment.
Part 2 of 6Rate–Concentration Graphs
Rate–Concentration Graphs
Zero order
- A horizontal line shows that the rate does not change when the concentration changes.
First order
- A straight line through the origin shows that rate is directly proportional to concentration.
Second order
- A curve through the origin that gets steeper with concentration, showing rate ∝ [A]².
Gradient of first order
- The gradient of the straight line equals the rate constant k.
| Order | Concentration–time shape | Rate–concentration shape |
|---|---|---|
| 0 | Straight line, downward | Horizontal line |
| 1 | Exponential decay curve | Straight line through origin |
| 2 | Steeper curve, longer half-lives | Upward curve through origin |
Part 3 of 6Half-Life
1
The half-life t½ is the time for the concentration of a reactant to fall to half its value.
2
Read the time for the concentration to fall from one value to half of that value, and repeat from other starting points.
3
If successive half-lives are constant, the reaction is first order.
4
If successive half-lives increase, the reaction is probably second order; for zero order they decrease.
5
For a first-order reaction k = ln 2 ÷ t½, which is about 0.693 ÷ t½.
Part 4 of 6Using Graphs in Practice
Draw tangents
- Draw tangents at several concentrations, find their gradients, and then plot the rate against concentration.
Check data
- Compare the shape from your data with the standard shapes, taking care over experimental scatter.
Limit
- A graph shows the order for one reactant only when others are in large excess or held constant.
Rate constant
- For first order, the gradient of the rate–concentration graph gives k directly.
Part 5 of 6Worked Example
Question
- The concentration of a reactant is 0.80 mol dm⁻³ at 0 s, 0.40 mol dm⁻³ at 30 s and 0.20 mol dm⁻³ at 60 s.
- Find the order and k.
- The concentration halves from 0.80 to 0.40 in 30 s, and from 0.40 to 0.20 in a further 30 s.
- The half-life is constant at 30 s, so the reaction is first order.
- k = ln 2 ÷ t½ = 0.693 ÷ 30 = 0.0231 s⁻¹.
Answer First order; k = 0.0231 s⁻¹
Part 6 of 6Exam Checklist & Tips
4.1.3 – Key Points for the Exam
- Half-life The time taken for the concentration of a reactant to fall to half its initial value.
- Tangent A straight line touching a curve at one point and having the same gradient there.
- First order A reaction whose rate is directly proportional to the concentration of one reactant.
- Rate–concentration graph A plot of rate against concentration used to find the order.
- Exponential decay A decrease in which each equal time interval multiplies the quantity by the same fraction.
Common Mistakes
- Drawing a first-order concentration–time graph as a straight line.
- Saying that a constant half-life means zero order, when it indicates first order.
- Reading the half-life only once, rather than checking that two successive half-lives are equal.
- Mixing up rate–concentration and concentration–time graphs when deciding the order.
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