Rates and Yields
Rate of Reaction
The rate of reaction tells you how quickly a reaction proceeds. It is calculated from:
$$\text{rate} = \frac{\text{quantity of reactant used or product formed}}{\text{time taken}}$$
The units of rate depend on how the quantity is measured. If you measure the volume of gas produced in cm3 over time in seconds, the rate has units of cm3/s. A common student error is to measure volume in cm3 but record time in minutes, and then forget to convert — always check your units match.
Rate of reaction can be increased by: raising temperature, increasing concentration (or pressure for gases), increasing surface area of solid reactants, or using a catalyst. Rate = quantity of reactant or product ÷ time.
Collision Theory
Collision theory explains why rate changes when conditions change. A reaction only occurs when particles: (1) collide with each other, and (2) have at least the activation energy. If either condition is not met, particles bounce off without reacting.
Each factor affects either the frequency of collisions or the proportion that have enough energy:
- Temperature — raising temperature gives particles more kinetic energy. They move faster, collide more frequently, and a greater proportion exceed the activation energy.
- Concentration / Pressure — more particles in a given volume means more frequent collisions.
- Surface area — breaking a solid into smaller pieces exposes more surface, increasing the area available for collisions.
- Catalyst — provides an alternative reaction pathway with a lower activation energy. More collisions now have sufficient energy to succeed. The catalyst is not used up and does not appear in the overall equation.
Three common methods to measure reaction rate:
- Gas collection — gas produced is collected in a gas syringe or over water in an inverted measuring cylinder. Volume is recorded at intervals.
- Mass loss — the reaction vessel sits on a balance; mass decreases as gas escapes. Mass is recorded at intervals.
- Colour/turbidity change (Higher tier) — used for reactions that produce a precipitate or change colour. The “disappearing cross” experiment (sodium thiosulfate + hydrochloric acid) measures the time for a cross beneath the flask to become invisible as sulfur precipitate forms. Rate = 1 ÷ time.
A reaction between marble chips and hydrochloric acid produces CO2 gas. After 20 s, 30 cm3 of gas has been collected. After 40 s, 50 cm3. Calculate the mean rate between 20 s and 40 s.
Rate = change in volume ÷ change in time = (50 − 30) cm3 ÷ (40 − 20) s = 20 ÷ 20 = 1.0 cm3/s.
Note: the units are cm3/s because volume was measured in cm3 and time in seconds. The same rate written per minute is 60 cm3/min, because there are 60 seconds in a minute. Always convert the time to the unit you want before you divide.
Catalysts lower the activation energy by providing an alternative reaction pathway. More collisions have sufficient energy to succeed. The catalyst is not used up and does not appear in the overall equation.
Yield and Atom Economy
Percentage yield compares what you actually obtained to what you could theoretically obtain:
$$\text{percentage yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100$$
Yield is rarely 100%. Reasons include: the reaction may not go to completion, some product is lost in filtering or transferring, or a reversible reaction may not fully favour the products. In industry, maximising yield while controlling costs is a key challenge.
Atom economy measures how efficiently atoms from reactants end up in the desired product:
$$\text{atom economy} = \frac{\text{relative formula mass of desired product}}{\text{sum of relative formula masses of all reactants}} \times 100$$
A high atom economy means less waste. Addition reactions (where all reactants become one product) have 100% atom economy. Reactions that produce by-products have lower atom economy. Green chemistry aims to maximise atom economy to reduce waste and cost.
Consider the reaction: \(CaCO_3 \rightarrow CaO + CO_2\). The desired product is CaO (\(M_r = 56\)). The only reactant is CaCO3 (\(M_r = 100\)), so the total mass of reactants = 100. Atom economy = (56 ÷ 100) × 100 = 56%. This means 44% of the atom mass ends up as the waste gas CO2.
Why Yield and Rate Both Matter
In industry, the goal is not simply to achieve the fastest possible rate or the highest possible yield — it is to produce the most product economically over time. A reaction that runs very quickly but has a low yield may be less profitable than a slower reaction with a high yield, depending on the cost of raw materials and energy. Conversely, a reaction with a high theoretical yield but a very slow rate may not be commercially viable without a catalyst to speed it up.
Industrial chemists therefore optimise conditions to balance rate and yield together. For example, using a catalyst simultaneously increases rate (without reducing yield) while allowing lower temperatures — reducing energy costs. Recycling unreacted starting materials back into the reaction vessel can also improve the overall yield over time, even if the yield at any single pass is moderate. These economic and environmental factors make the design of industrial chemical processes genuinely complex, and they illustrate why chemistry has real-world importance beyond the laboratory.