Calculating rates of reaction
The rate of reaction is how quickly reactants are converted to products. We can measure it by looking at the change in mass, volume of gas produced or change in concentration over time.
The rate equation
rate = quantity changed ÷ time taken
Units depend on the quantity:
- mass: g/s
- volume of gas: cm³/s or dm³/s
- concentration: mol/dm³/s
Mean rate
If 50 cm³ of gas is collected over 100 s: mean rate = 50/100 = 0.5 cm³/s
This averages the rate over the whole time.
Instantaneous rate from a graph
A graph of "amount of product vs time" usually starts steep and flattens out. The instantaneous rate at any point is the gradient of the tangent to the curve at that point.
To find an instantaneous rate:
- Draw a tangent line at the point of interest.
- Choose two points on the tangent.
- Calculate gradient = Δy / Δx.
- Include units (e.g. cm³/s).
Why rate decreases over time
As reactants are consumed:
- Their concentration drops.
- Frequency of successful collisions decreases.
- Rate decreases.
When the curve levels off, the reaction has stopped (one or more reactants exhausted, or equilibrium reached).
✦Worked example— Worked example — collecting gas
A student measures volume of CO₂ from CaCO₃ + HCl:
- After 10 s: 12 cm³.
- After 30 s: 28 cm³.
- After 60 s: 40 cm³.
- After 120 s: 50 cm³ (and stops).
Mean rate over the first 30 s = 28/30 = 0.93 cm³/s. Mean rate over 30–60 s = (40−28)/(60−30) = 12/30 = 0.4 cm³/s — slower as concentration falls.
Methods of measuring rate
- Gas syringe for gas volume.
- Mass loss with electronic balance for reactions producing gas.
- Disappearing-cross for cloudy precipitate (e.g. Na₂S₂O₃ + HCl).
- Colour change with a colorimeter for accurate timing.
⚠Common mistakes
- Forgetting the units in your final rate.
- Picking two points NOT on the tangent when finding instantaneous rate from the graph.
- Saying "the reaction has stopped" when the rate is just slow — only when the curve is exactly flat.
- Confusing time on x-axis with rate — rate is the gradient, not a y-value.
Links
Sets up C6.2 (factors affecting rate), C6.3 (catalysts). Used in C3.7 (concentration calculations) when graphing.
AI-generated · claude-opus-4-7 · v3-deep-chemistry