Calculating Rates of Reaction

The rate of reaction measures how fast a chemical reaction happens. A fast reaction, such as an explosion, is over in a fraction of a second; a slow one, such as iron rusting, takes years.

To measure a rate you track how a quantity changes over time. You can either measure how much of a reactant is used up, or how much product is made. Both give the same information because as reactants disappear, products appear.

Rate of reaction is a measure of the quantity of reactant used, or quantity of product formed, over time.

Two quantities are commonly measured:

• Mass using a balance (for example, if a gas escapes, the flask gets lighter).
• Volume of gas using a gas syringe or an inverted measuring cylinder.

The choice depends on the reaction. If a gas is given off, you can either weigh the flask as it loses mass or collect the gas and measure its volume.

The mean rate is the average rate over a period of time. It is found with a simple division:

$\text{mean rate}=\frac{\text{quantity of reactant used}}{\text{time}}\text{or}\frac{\text{quantity of product formed}}{\text{time}}$

The units depend on how you measured the quantity:

Quantity measured	Unit of quantity	Unit of rate
Mass	grams (g)	g/s
Volume of gas	cubic centimetres (cm³)	cm³/s
Amount (Higher Tier)	moles (mol)	mol/s

(Higher Tier only) Measuring the amount in moles, giving a rate in mol/s, is assessed only at Higher Tier. Foundation candidates use mass (g/s) or gas volume (cm³/s).

Time is usually measured in seconds, so the "per second" appears in each unit.

A student reacts marble chips with dilute hydrochloric acid and collects the carbon dioxide gas produced. After 40 seconds, 60 cm³ of gas has been collected. Find the mean rate over this period.

Write down what you know:

• Quantity of product formed = 60 cm³
• Time = 40 s

Substitute into the formula:

$\text{mean rate}=\frac{60{\text{ cm}}^3}{40\text{ s}}=1.5{\text{ cm}}^3/\text{s}$

The mean rate is 1.5 cm³/s.

A second student measures a reaction by loss of mass. The flask loses 2.4 g of mass in 120 seconds:

$\text{mean rate}=\frac{2.4\text{ g}}{120\text{ s}}=0.02\text{ g/s}$

The mean rate is 0.02 g/s. Always write the correct unit: the number alone does not answer the question.

Plotting the quantity against time produces a curve that tells you how the rate changes as the reaction proceeds. The typical shape rises steeply at first, then bends and flattens.

Three features carry the marks:

• Steepness (gradient) shows the rate. The steeper the line, the faster the reaction at that moment.
• The start is steepest because the concentration of reactants is highest, so the reaction is fastest.
• The flat part means the reaction has stopped. It levels off when a reactant is used up, so no more product forms.

Point on the graph	What it tells you
Steep section (start)	Reaction is fast; reactants are being used quickly
Curve is bending	Reaction is slowing as reactants run low
Flat (horizontal)	Reaction has finished; no more product forms

If two reactions are plotted on the same axes, the one with the steeper starting line has the faster rate. If both reach the same final height, the same amount of product was made overall, just at different speeds.

The mean rate averages over a whole period, but the rate is not constant. To find the rate at a single moment, draw a tangent to the curve at that point.

A tangent is a straight line that just touches the curve at one point, matching its steepness there. To draw one well:

• Place a ruler so it touches the curve at the chosen time.
• Angle the ruler so the gap between the ruler and the curve is equal on both sides of the touch point.
• Draw a long straight line so it is easy to read values from it.

A steep tangent means a fast rate; a shallow tangent means a slow rate. Near the end of the reaction the tangent is almost flat, showing the rate has fallen close to zero.

At Foundation Tier you can compare rates by comparing how steep the tangents are. Higher Tier requires the actual number, calculated from the gradient.

(Higher Tier only) Calculating the rate at a specific time from the gradient of a tangent is assessed only at Higher Tier.

A tangent has been drawn to a gas-volume curve at 20 seconds. Two points are read from the tangent line:

• Point A: (10 s, 20 cm³)
• Point B: (30 s, 80 cm³)

The gradient of the tangent is the rate at that instant:

$\text{rate}=\frac{\text{change in volume}}{\text{change in time}}=\frac{80-20}{30-10}=\frac{60{\text{ cm}}^3}{20\text{ s}}=3{\text{ cm}}^3/\text{s}$

The rate at 20 seconds is 3 cm³/s.

To keep the calculation accurate, choose two points on the tangent line that are far apart, not points on the curve itself. A larger triangle reduces the error in reading the values.

1. Forgetting the unit

A rate is a number with a unit: g/s, cm³/s or (Higher Tier) mol/s. Writing "1.5" instead of "1.5 cm³/s" throws away a mark. Match the unit to the quantity you measured.

2. Reading points off the curve instead of the tangent

When finding a gradient, both points must lie on the straight tangent line, not on the original curve. Points taken from the curve give the wrong gradient.

3. Saying the reaction "stops going" when the graph flattens

The flat part means no more product is being made because a reactant has run out, not that the graph is broken. State that the reaction has finished.

4. Confusing mean rate with rate at a point

Mean rate divides total quantity by total time. Rate at an instant needs a tangent. A question asking for the rate at 30 s wants the tangent method, not a division of the totals.

5. Drawing a tiny gradient triangle

A small triangle magnifies reading errors. Extend the tangent and pick two widely spaced points to make the gradient calculation reliable.