Rate of Reaction Graphs
This topic covers how to interpret graphs that plot the amount of a substance against time to understand how a reaction's speed changes. For the ESAT, you must be able to determine the rate from the graph's gradient and predict how changing reaction conditions will alter the shape of the curve.
Part of the ESAT Chemistry syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- The rate of reaction at any given time is represented by the gradient (steepness) of the curve on a concentration-time or product-volume-time graph.
- The reaction is fastest at the beginning where the curve is steepest, because reactant concentrations are at their maximum.time = 0
- As the reaction progresses, the curve becomes less steep because reactants are being consumed, their concentration falls, and the rate slows down.
- The reaction stops when the graph becomes a horizontal line, which occurs when one of the reactants is completely used up.gradient = 0
- The final height (plateau) of the graph shows the total amount of product formed, which is determined by the amount of the limiting reactant, not the reaction rate.
Diagram
Formulae
Rate = (change in y-axis quantity) / (change in time) To calculate the average rate between two points, or the instantaneous rate by finding the gradient of a tangent to the curve at a single point.
Definitions
- Rate of Reaction
- The change in amount or concentration of a reactant or product per unit of time. On a graph, this is the gradient of the curve.
- Initial Rate
- The instantaneous rate of reaction at the start of the experiment. It is found by calculating the gradient of the tangent to the curve at the origin.t=0
- Limiting Reactant
- The reactant that is completely consumed in a chemical reaction. It determines the maximum amount of product that can be formed.
Worked example
The graph shows the volume of H2 gas produced when excess magnesium ribbon reacts with 100 cm3 of 0.5 M HCl. The reaction produces a final volume of 60 cm3 of H2. Which curve (A, B, or C) best represents the reaction if it were repeated using 50 cm3 of 1.0 M HCl with excess magnesium? The original curve is shown as a solid line.
- 1
Step 1:
Compare the moles of the limiting reactant (HCl) in both experiments.
Initial moles = Volume (dm3) × Concentration = 0.1 × 0.5 = 0.05 mol.
New moles = 0.05 × 1.0 = 0.05 mol - 2
Step 2:
Since the moles of the limiting reactant are the same, the total amount of product (H2 gas) formed will be identical.
The new curve must therefore end at the same final volume of 60 cm3.
- 3
Step 3:
Compare the initial concentrations of HCl.
The new experiment uses 1.0 M HCl, which is double the concentration of the original 0.5 M HCl.
- 4
Step 4:
A higher concentration leads to more frequent successful collisions between reactant particles.
Therefore, the initial rate of reaction will be faster.
- 5
Step 5:
A faster rate is represented by a steeper initial gradient on the graph.
The new curve must start more steeply than the original but finish at the same height.
- 6
Step 6:
Curve A shows a faster initial rate (steeper) and the same final volume.
Curve B shows a slower rate.
Curve C shows a faster rate but a larger final volume.
Therefore, A is the correct answer.
Answer: A
Common mistakes
- ×Confusing the reaction rate with the final yield. A steeper curve means a faster rate, but the final height of the plateau represents the total product formed. A catalyst, for example, increases the rate but does not change the final yield.
- ×Forgetting to check the limiting reactant. When comparing two reactions, you must first calculate the moles of the limiting reactant to see if the final amount of product will change. Students often just focus on the change in rate.
- ×Misinterpreting the y-axis. Remember that if the y-axis shows the concentration of a *reactant*, the curve will slope downwards, and the reaction stops when it flattens at or above zero.
No-calculator tips
- ✓To compare rates, you don't need to calculate them. Simply compare the steepness of the curves by eye; a steeper line means a faster rate.
- ✓To calculate a gradient for an instantaneous rate, draw a tangent and form the largest possible right-angled triangle. Choose points on the axes that are easy to read and divide, for example, ending a time interval on 10s or 60s.
- ✓To find the time taken for half the reaction to complete (the half-life), find the final y-value, divide it by two, and read the corresponding time from the x-axis. This is a quick way to compare rates between two curves.