Collision Theory: Concentration and Pressure – Rate of Chemical Reactions (Senior 3 Chemistry) | Ganzaa

Rate of Chemical Reactions

Lessons

Senior 3 · Chemistry

Rate of Chemical Reactions

4 lessons

Lesson 2 of 4

Collision Theory: Concentration and Pressure

25 min

A glowing splint and pure oxygen

A wooden splint that has just been blown out glows red in air, then slowly dies. Push the same glowing splint into a jar of pure oxygen and it bursts back into flame: the test for oxygen you met in S2. The wood has not changed; only the gas around it has. Air is about 21% oxygen by volume, so pure oxygen packs nearly five times as many oxygen molecules into each cubic centimetre, and nearly five times as many strike the hot wood every second. To see why that matters, you need a model of what happens when particles react.

Collision theory

The particles of liquids and gases are always moving (the kinetic theory, S1). Two particles can react only if:

they collide, and
they collide with at least a minimum amount of energy, the activation energy, enough to start breaking the bonds in the reactants. (Molecules must also meet the right way round.)

Most collisions fail these tests and the particles simply bounce apart. A collision that does lead to a reaction is called an effective (or successful) collision. The rate of a reaction depends on how many effective collisions happen each second:

$\text{rate} \propto \text{number of effective collisions per second}$

So there are only two ways to speed up a reaction: make collisions happen more often, or make a larger fraction of them effective. Concentration, pressure and particle size work the first way; temperature and catalysts work the second (Lessons 3 and 4).

Definition

Collision theory: the model that a reaction happens only when reactant particles collide with enough energy (and the right orientation). The more effective collisions per second, the faster the reaction.

Activation energy, $E_{a}$ : the minimum energy that colliding particles must have for a reaction to take place. Example: a mixture of methane and air does not react at room temperature, because few collisions have energy $\ge E_a$ ; a spark supplies the energy to start it.

Effective collision: a collision that has at least the activation energy and so produces new substances.

An energy profile shows the activation energy as a hill that the reactants must climb before they can fall to the products (Figure 2.1). Even an exothermic reaction, which gives out energy overall, needs this push to begin.

Effect of concentration

The concentration of a solution is the amount of solute in each cubic decimetre (Unit 6 treats it in detail). In a more concentrated acid the acid particles are more crowded, so more of them strike the surface of a solid, or meet another dissolved particle, every second (Figure 2.2). The energy of each collision is unchanged; collisions simply happen more often, and so do effective ones.

An experiment shows the effect. Excess marble chips are added to two portions of hydrochloric acid that contain the same amount of acid, $0.0050\,\mathrm{mol}$ , at different concentrations, and the carbon dioxide is collected in a gas syringe.

$\mathrm{CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + H_2O(l) + CO_2(g)}$

Table 2.1: Volume of carbon dioxide ( $\mathrm{cm^3}$ ) with excess marble chips (illustrative results)

time (s)	A: $25\,\mathrm{cm^3}$ of $0.20\,\mathrm{mol\,dm^{-3}}$ acid	B: $50\,\mathrm{cm^3}$ of $0.10\,\mathrm{mol\,dm^{-3}}$ acid
0	0	0
30	26	15
60	42	27
90	51	36
120	56	43
150	59	48
180	60	52
210	60	55
240	60	57
270	60	58
300	60	59
330	60	60
360	60	60

Curve A starts more steeply than B: the more concentrated acid reacts faster.
Both curves end at $60\,\mathrm{cm^3}$ : the acid is the limiting reactant, and both portions contain the same amount of it. Concentration changes how fast the gas comes, not how much.
B takes longer to finish (about 330 s instead of 180 s).

Worked example

Problem. (a) Use the tangents in Figure 2.3 to find the initial rates of A and B, and compare them. (b) Show that both experiments should give $60\,\mathrm{cm^3}$ of carbon dioxide. (Molar volume $24\,\mathrm{dm^3\,mol^{-1}}$ .)

Solution. (a) A: $\frac{55 - 0}{50 - 0} = 1.1\,\mathrm{cm^3\,s^{-1}}$ . B: $\frac{44 - 0}{80 - 0} = 0.55\,\mathrm{cm^3\,s^{-1}}$ . Halving the concentration of the acid halved the initial rate: $\frac{1.1}{0.55} = 2$ .

(b) A: $n(\mathrm{HCl}) = \frac{25}{1000} \times 0.20 = 0.0050\,\mathrm{mol}$ . B: $\frac{50}{1000} \times 0.10 = 0.0050\,\mathrm{mol}$ . From the equation, 2 mol HCl give 1 mol $\mathrm{CO_2}$ , so each gives $0.0025\,\mathrm{mol}$ of $\mathrm{CO_2}$ :

$V = 0.0025 \times 24\,000 = 60\,\mathrm{cm^3}$

Effect of pressure

Pressure matters only for reactions of gases. Squeezing a gas into a smaller volume packs the same particles closer together, so its concentration rises (Figure 2.4). At the same temperature, halving the volume doubles the pressure and doubles the concentration, so the particles collide more often and the reaction is faster. Industrial gas reactions, such as the Haber process in Unit 2, are run at high pressure partly for this reason.

Changing the pressure has almost no effect on a reaction between solids and liquids, because their particles are already touching and cannot be squeezed closer.

Worked example

Problem. A syringe holds $0.0040\,\mathrm{mol}$ of a gas in $100\,\mathrm{cm^3}$ . The gas is compressed to $50\,\mathrm{cm^3}$ at the same temperature. Find the concentration before and after, and state the effect on the rate of a reaction of the gas.

Solution. $100\,\mathrm{cm^3} = 0.100\,\mathrm{dm^3}$ , so before:

$c = \frac{0.0040}{0.100} = 0.040\,\mathrm{mol\,dm^{-3}}$

After: $c = \frac{0.0040}{0.050} = 0.080\,\mathrm{mol\,dm^{-3}}$ . The concentration has doubled, so its particles collide more often and the reaction goes faster.

Warning

Common mistakes. (1) Higher concentration does not make particles collide harder or move faster; it makes collisions more frequent. (2) A faster reaction does not give more product: the final amount is set by the limiting reactant. (3) Pressure has no effect on a reaction with no gaseous reactants, such as zinc with dilute sulfuric acid; the hydrogen there is a product.

Tip

How often, or how hard? Concentration, pressure and particle size change how often particles collide. Temperature mainly changes how hard they collide, and a catalyst lowers the energy needed. In an exam answer, always say "more frequent collisions" or "more collisions per second".

FuseSchool: Rates of Reaction, Part 2 (6 min). Watch for the reason particles must collide with enough energy before they react, and for the ways a rate is measured.

✦

Practice

State the two conditions a collision must meet to be effective.
Define activation energy, and mark it on a sketch of the energy profile of an exothermic reaction.
Use collision theory to explain why magnesium reacts faster with $2.0\,\mathrm{mol\,dm^{-3}}$ hydrochloric acid than with $0.5\,\mathrm{mol\,dm^{-3}}$ acid.
Experiment C uses $25\,\mathrm{cm^3}$ of $0.10\,\mathrm{mol\,dm^{-3}}$ hydrochloric acid with excess marble chips. (a) What final volume of carbon dioxide forms? (b) How does its initial rate compare with A's in Figure 2.3?
$0.0060\,\mathrm{mol}$ of a gas fills $150\,\mathrm{cm^3}$ . Find its concentration, and its new concentration when it is squeezed into $50\,\mathrm{cm^3}$ at the same temperature.
Explain why raising the pressure does not speed up the reaction of zinc with dilute sulfuric acid.
Use collision theory to explain why a glowing splint relights in pure oxygen but not in air.
A student says: "Doubling the concentration of the acid doubles the volume of hydrogen I get from one piece of magnesium ribbon." The acid is in excess. Evaluate the claim.

Show answersHide answers

The particles must collide, and the collision must have at least the activation energy (with the right orientation).
The minimum energy colliding particles need in order to react. On the profile it is the height from the reactants' level up to the peak of the curve.
The $2.0\,\mathrm{mol\,dm^{-3}}$ acid has more acid particles per $\mathrm{dm^3}$ , so more of them hit the magnesium surface each second. More frequent collisions give more effective collisions per second, so the rate is greater.
(a) $n(\mathrm{HCl}) = 0.025 \times 0.10 = 0.0025\,\mathrm{mol}$ , $n(\mathrm{CO_2}) = 0.00125\,\mathrm{mol}$ , $V = 0.00125 \times 24\,000 = 30\,\mathrm{cm^3}$ . (b) About half of A's initial rate (the same as B's), because the concentration is half of A's.
$\frac{0.0060}{0.150} = 0.040\,\mathrm{mol\,dm^{-3}}$ ; $\frac{0.0060}{0.050} = 0.12\,\mathrm{mol\,dm^{-3}}$ , three times as great.
The reactants are a solid and a solution. Pressure changes the concentration only of gases, and hydrogen is a product, not a reactant.
Pure oxygen has nearly five times as many oxygen molecules per $\mathrm{cm^3}$ as air (21% oxygen), so oxygen molecules strike the hot wood far more often. The burning becomes fast enough to give a flame.
Wrong. Magnesium is the limiting reactant, so the volume of hydrogen is fixed by the amount of magnesium. The more concentrated acid gives the same volume, faster.

Sources and credits

Chemistry 2e, 12.5: Collision Theory and 12.2: Factors Affecting Reaction Rates (collision theory and activation energy), Paul Flowers, Klaus Theopold, Richard Langley and William R. Robinson, OpenStax, via LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Video: Rates of Reaction, Part 2, FuseSchool, embedded from YouTube.
The diagrams, graph, table, worked examples and Practice items were drawn and written by Ganzaa; the results in Table 2.1 are illustrative.

time (s)	A: $25\,\mathrm{cm^3}$ of $0.20\,\mathrm{mol\,dm^{-3}}$ acid	B: $50\,\mathrm{cm^3}$ of $0.10\,\mathrm{mol\,dm^{-3}}$ acid
0	0	0
30	26	15
60	42	27
90	51	36
120	56	43
150	59	48
180	60	52
210	60	55
240	60	57
270	60	58
300	60	59
330	60	60
360	60	60

time (s)	A: $25\,\mathrm{cm^3}$ of $0.20\,\mathrm{mol\,dm^{-3}}$ acid	B: $50\,\mathrm{cm^3}$ of $0.10\,\mathrm{mol\,dm^{-3}}$ acid
0	0	0
30	26	15
60	42	27
90	51	36
120	56	43
150	59	48
180	60	52
210	60	55
240	60	57
270	60	58
300	60	59
330	60	60
360	60	60

1A glowing splint and pure oxygen

2Collision theory

3Effect of concentration

4Effect of pressure

A glowing splint and pure oxygen

Collision theory

Effect of concentration

Effect of pressure

time (s)	A: $25\,\mathrm{cm^3}$ of $0.20\,\mathrm{mol\,dm^{-3}}$ acid	B: $50\,\mathrm{cm^3}$ of $0.10\,\mathrm{mol\,dm^{-3}}$ acid
0	0	0
30	26	15
60	42	27
90	51	36
120	56	43
150	59	48
180	60	52
210	60	55
240	60	57
270	60	58
300	60	59
330	60	60
360	60	60