Temperature and Particle Size – Rate of Chemical Reactions (Senior 3 Chemistry) | Ganzaa

Rate of Chemical Reactions

Lessons

Senior 3 · Chemistry

Rate of Chemical Reactions

4 lessons

Lesson 3 of 4

Temperature and Particle Size

25 min

Beans in a pressure cooker

Dry beans, eaten in many Rwandan homes, need long boiling in an open pot, but a pressure cooker softens them in a fraction of the time. Its sealed lid traps the steam, the pressure inside rises, and the water boils at about 120 °C instead of 100 °C. Cooking is a set of chemical changes in the starch and proteins of the beans, and they run faster at the higher temperature. (Where water boils below 100 °C, as high on a mountain, cooking is slower still.) A fridge works the other way: milk stays fresh for days in the cold because the reactions of the bacteria that sour it slow right down.

Effect of temperature

Heating gives particles more kinetic energy, so they move faster. That has two effects:

they collide more often; and, much more important,
a larger fraction of the collisions have energy equal to or greater than the activation energy, so a larger fraction are effective.

A useful rule of thumb: for many reactions near room temperature, a rise of 10 °C roughly doubles the rate. Cooling slows a reaction down in the same way, which is why food keeps longer in a fridge.

An experiment: the disappearing cross

Sodium thiosulfate solution reacts with hydrochloric acid to give a fine precipitate of sulfur, which slowly makes the solution cloudy:

$\mathrm{Na_2S_2O_3(aq) + 2HCl(aq) \rightarrow 2NaCl(aq) + SO_2(g) + S(s) + H_2O(l)}$

The flask stands on a cross drawn on paper (Figure 3.1). The same volumes of the same solutions are warmed to different temperatures and mixed; the temperature of the mixture is read, and the time for the cross to disappear is measured. The cross vanishes when the same amount of sulfur has formed each time, so a shorter time means a faster reaction, and $\frac{1000}{\text{time}}$ can be used as a measure of the rate.

Warning

Safety. The reaction gives off sulfur dioxide, a toxic gas that can trigger an asthma attack. Work in a well-ventilated room, do not heat the solutions above 50–60 °C, and pour the mixture away as soon as each run ends. Wear eye protection.

Table 3.1: Time for the cross to disappear (illustrative results)

temperature (°C)	time (s)	rate, $\frac{1000}{\text{time}}$ ( $\mathrm{s^{-1}}$ )
20	120	8.3
30	62	16.1
40	31	32.3
50	17	58.8
60	9	111.1

Worked example

Problem. Use Table 3.1. (a) How many times faster is the reaction at 40 °C than at 20 °C? (b) Does this agree with the rule of thumb? (c) Estimate the time at 70 °C from the rule of thumb, and say why the experiment is not done at that temperature.

Solution. (a) The rate is proportional to $\frac{1}{\text{time}}$ , so

$\frac{\text{rate at } 40\,^\circ\mathrm{C}}{\text{rate at } 20\,^\circ\mathrm{C}} = \frac{120}{31} = 3.9$

The reaction is about 4 times as fast.

(b) Yes: a 20 °C rise is two 10 °C steps, and $2 \times 2 = 4$ .

(c) Halving the 60 °C time gives about $\frac{9}{2} \approx 4.5\,\mathrm{s}$ , too short to time accurately. Hot solutions would also give off much more sulfur dioxide.

Effect of particle size (surface area)

A solid can react only at its surface: the particles inside a lump cannot be reached until the outer layers have reacted. Cutting a solid into smaller pieces exposes more surface, so more particles can be hit each second, and the reaction is faster (Figure 3.3). The smaller the pieces, the larger the total surface area; a powder reacts fastest of all.

In an experiment, 0.30 g of small marble chips and 0.30 g of large chips are each added to $50\,\mathrm{cm^3}$ of $1.0\,\mathrm{mol\,dm^{-3}}$ hydrochloric acid, which is in excess, and the carbon dioxide is collected (Figure 3.4).

Table 3.2: Volume of carbon dioxide ( $\mathrm{cm^3}$ ) (illustrative results)

time (s)	small chips	large chips
0	0	0
20	30	12
40	49	23
60	60	33
80	66	41
100	70	48
120	72	54
140	72	59
160	72	63
180	72	66
200	72	68
220	72	70
240	72	71
260	72	72

Definition

Surface area: the total area of the outside of a solid that is in contact with the other reactant. For a cube of side $a$ , the surface area is $6 a^{2}$ . Example: a 1 cm cube has $6 \times 1^2 = 6\,\mathrm{cm^2}$ ; cut into 8 cubes of side 0.5 cm it has $8 \times 6 \times 0.5^2 = 12\,\mathrm{cm^2}$ , twice as much.

Worked example

Problem. (a) Use the tangents in Figure 3.4 to find the initial rate with small and with large chips. (b) Explain why both curves level off at the same volume, and check that volume. ( $\mathrm{CaCO_3} = 100$ ; molar volume $24\,\mathrm{dm^3\,mol^{-1}}$ )

Solution. (a) Small chips: $\frac{54}{30} = 1.8\,\mathrm{cm^3\,s^{-1}}$ . Large chips: $\frac{62}{100} = 0.62\,\mathrm{cm^3\,s^{-1}}$ . The small chips start about $\frac{1.8}{0.62} \approx 2.9$ times as fast.

(b) The acid is in excess, so the marble is the limiting reactant, and both runs use the same mass of it. $n(\mathrm{CaCO_3}) = \frac{0.30}{100} = 0.0030\,\mathrm{mol}$ , which gives $0.0030\,\mathrm{mol}$ of $\mathrm{CO_2}$ :

$V = 0.0030 \times 24\,000 = 72\,\mathrm{cm^3}$

When surface area becomes dangerous

A lump of iron does not burn in a flame, but steel wool, made of very thin iron threads, burns with bright sparks. A sack of flour burns slowly, but flour dust spread through the air, with every grain surrounded by oxygen, can burn almost instantly: a dust explosion. Flour and maize mills, sugar factories, sawmills and coal mines guard against this by removing dust and keeping sparks and flames away. The same idea is used safely every day: small dry sticks are used to light a fire before larger logs are added, and food is chewed into small pieces so that digestive enzymes can work on a larger surface.

Warning

Common mistakes. (1) Smaller particles mean a larger surface area, not a smaller one. (2) For temperature, "the particles collide more" is not enough: the key point is that more collisions have at least the activation energy. (3) Changing particle size or temperature does not change the final amount of product when the same amounts of reactants are used.

Tip

Hotter: faster and harder. Smaller: more surface. A 10 °C rise roughly doubles the rate; crushing a solid exposes more particles to collisions.

Rugby School Chemistry: Effect of Temperature, Sodium Thiosulfate and Hydrochloric Acid. Watch the cross disappear faster each time the starting temperature is raised.

✦

Practice

Give two reasons why raising the temperature increases the rate of a reaction. Which is more important?
In the disappearing-cross experiment, why must the same volumes of the same solutions, and the same cross, be used at every temperature?
Use Table 3.1 to find how many times faster the reaction is at 50 °C than at 20 °C.
A reaction takes 80 s at 25 °C. Use the rule of thumb to estimate the time at 35 °C and at 45 °C.
Find the surface area of a cube of side 2 cm, and the total surface area of the 8 cubes of side 1 cm made by cutting it.
In Figure 3.4, after how many seconds has each reaction finished? Calculate the average rate over the whole reaction for the small chips.
Explain why flour dust in a mill can explode, although a sack of flour burns only slowly.
A student says: "Milk keeps longer in a fridge because the cold kills the bacteria." Evaluate this statement.

Show answersHide answers

The particles move faster, so they collide more often; and a larger fraction of collisions have at least the activation energy. The second is more important.
To make it a fair test: only the temperature may change. The cross disappears when the same amount of sulfur has formed, so the times can be compared only if everything else is the same.
$\frac{120}{17} = 7.1$ times.
About 40 s at 35 °C and about 20 s at 45 °C (the rate doubles, so the time halves, for each 10 °C).
$6 \times 2^2 = 24\,\mathrm{cm^2}$ ; $8 \times 6 \times 1^2 = 48\,\mathrm{cm^2}$ .
Small chips at 120 s, large chips at 260 s. Average rate for the small chips $= \frac{72}{120} = 0.60\,\mathrm{cm^3\,s^{-1}}$ .
Spread in the air, each tiny grain is surrounded by oxygen, so the surface area in contact with oxygen is enormous. The burning is so fast that the gases expand violently: an explosion. In a sack only the outside of the flour meets the air.
Not correct. Cold slows down the reactions of the bacteria, so the milk sours more slowly; it does not kill them. When the milk warms up again, souring speeds up again.

Sources and credits

Chemistry 2e, 12.2: Factors Affecting Reaction Rates (temperature and surface area), Paul Flowers, Klaus Theopold, Richard Langley and William R. Robinson, OpenStax, via LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Photo: Pressure cooker - Hawkins, Contura Model - 3 litres - 1.jpg, Cantons-de-l'Est, licensed under CC BY-SA 4.0, via Wikimedia Commons.
Photo: Burning steel wool.jpg, AgrisR, licensed under CC BY-SA 4.0, via Wikimedia Commons.
Photo: Dust explosion 04.jpg, Hans-Peter Scholz, licensed under CC BY-SA 3.0, via Wikimedia Commons.
Video: Effect of Temperature: Sodium Thiosulfate and Hydrochloric Acid, Rugby School Chemistry, embedded from YouTube.
The diagrams, graphs, tables, worked examples and Practice items were drawn and written by Ganzaa; the results in Tables 3.1 and 3.2 are illustrative.

time (s)	small chips	large chips
0	0	0
20	30	12
40	49	23
60	60	33
80	66	41
100	70	48
120	72	54
140	72	59
160	72	63
180	72	66
200	72	68
220	72	70
240	72	71
260	72	72

time (s)	small chips	large chips
0	0	0
20	30	12
40	49	23
60	60	33
80	66	41
100	70	48
120	72	54
140	72	59
160	72	63
180	72	66
200	72	68
220	72	70
240	72	71
260	72	72

1Beans in a pressure cooker

2Effect of temperature

3An experiment: the disappearing cross

4Effect of particle size (surface area)

5When surface area becomes dangerous

Beans in a pressure cooker

Effect of temperature

An experiment: the disappearing cross

Effect of particle size (surface area)

When surface area becomes dangerous

time (s)	small chips	large chips
0	0	0
20	30	12
40	49	23
60	60	33
80	66	41
100	70	48
120	72	54
140	72	59
160	72	63
180	72	66
200	72	68
220	72	70
240	72	71
260	72	72