Interpret and use simple rate equations
Use rate = k[A]ᵐ[B]ⁿ for orders of zero, one or two and relate concentration changes to rate changes.
A Level; Cambridge International Chemistry 9701, 2028–2030 syllabus, Topic 26. Rate laws are empirical unless an elementary step is explicitly stated. Written practice is self-checked
Before you begin
- Use AS collision theory, concentration, graph gradients, and balanced reaction equations.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
If a zero-order reactant concentration doubles, what is the rate factor?
What you will learn
- Substitute concentrations into a rate equation
- Predict rate changes from concentration scaling
- Calculate overall order and interpret each exponent
Each exponent controls one concentration effect
For rate = k[A]ᵐ[B]ⁿ, if [A] is multiplied by f while other concentrations and temperature stay fixed, rate is multiplied by fᵐ. A zero-order reactant has no effect on rate in that range; first order gives a proportional effect; second order gives a squared effect.
The syllabus restricts m and n to 0, 1 or 2 for these simple rate equations. The overall order is m+n, not the sum of the balanced-equation coefficients.
Use fixed conditions when comparing rates
Rate comparisons assume k is unchanged, so temperature and other experimental conditions must be the same. If a concentration changes by a factor, raise that factor to the corresponding order.
For example, doubling a second-order reactant makes the rate four times as large when all else is constant. Doubling a zero-order reactant leaves the rate unchanged in the stated concentration range.
Pause and explain
A second-order reactant is doubled while other conditions are fixed. What happens to rate?
Worked example
For rate = k[A][B]², what happens to rate if [A] doubles and [B] is halved at constant temperature?
Show the worked solution
- The [A] factor changes by 2¹.
- The [B] factor changes by (1/2)².
- Multiply the two rate factors.
Answer Rate factor = 2 × 1/4 = 1/2. The rate halves.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
For rate = k[A]²[B], find the rate factor if [A] is halved and [B] triples.
Give me a hint
Raise each concentration factor to its order, then multiply.
Compare my reasoning
- A contributes (1/2)² = 1/4.
- B contributes 3¹ = 3.
- Multiply the factors.
Rate factor = (1/4)×3 = 0.75; the rate becomes three-quarters of its original value.
Look for these in your work
- Powers applied
- Factors combined
- Direction interpreted
For rate = k[A]⁰[B]², state the overall order and the effect of doubling both concentrations.
Give me a hint
Use each exponent separately.
Compare my reasoning
- Overall order is 0+2.
- Doubling [A] gives factor 2⁰ = 1.
- Doubling [B] gives factor 2² = 4.
Overall order = 2; the rate becomes four times as large because [A] has zero order and [B] is doubled at second order.
Look for these in your work
- Overall order calculated
- Zero-order effect identified
- Second-order effect applied
A student doubles [A] and halves [B] in rate = k[A][B]² and predicts the rate doubles. Correct the prediction.
Give me a hint
Calculate each concentration factor raised to its order.
Compare my reasoning
- A contributes a factor of 2.
- B contributes (1/2)² = 1/4.
- Multiply 2×1/4.
The combined factor is 0.50, so the rate halves rather than doubles.
Look for these in your work
- Both changes included
- Exponent on B used
- Combined change correct
Common mistakes
- Changing k when only concentration changes
- Using the exponent as an additive factor
- Forgetting that two simultaneous concentration changes multiply
- Assuming the rate equation is the balanced reaction
What can you explain now?
If a zero-order reactant concentration doubles, what is the rate factor?
Compare with the explanation
1
A factor raised to the zero power is 1.
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Make it stick
How do concentration scaling factors and reaction orders combine to predict a rate change?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.