Topic 9 · page 5 of 15

Concentration, pressure and surface area

Concentration, gas pressure and the surface area of a solid all raise the rate in the same way. They put more reactant particles where they can collide, so collisions are more frequent, while the energy of the particles is unchanged.

12 min read9.1

Read first: Collisions and activation energy

Three factors raise the collision frequency without changing how much energy the particles have. For each of them the explanation has the same shape: the change, why collisions are more frequent, and so more successful collisions per second.

Concentration 9.1

In a more concentrated solution there are more particles in the same volume. They are closer together, so a given particle meets others more often.

Doubling the concentration of a reactant roughly doubles the number of collisions per second. The fraction of collisions with energy of at least EaE_\text{a} stays the same, because the temperature is the same. So the number of successful collisions per second rises in proportion, and the rate rises.

Pressure of a gas 9.1

At a higher pressure the same number of gas molecules is squeezed into a smaller volume. That is a higher concentration, so the explanation is the same as above. You can see this from the ideal gas equation, pV=nRTpV = nRT. At constant temperature, the concentration of a gas is

c=nV=pRT c = \frac{n}{V} = \frac{p}{RT}

so the concentration is proportional to the pressure.

Worked examplePressure and concentration

Show that doubling the pressure of a gas at 298 K doubles its concentration. (R = 8.31 J mol⁻¹ K⁻¹)

  1. At 100 kPa = 100 000 Pa: c = p ÷ RT = 100 000 ÷ (8.31 × 298) = 40.4 mol m⁻³
  2. 40.4 mol m⁻³ ÷ 1000 = 0.0404 mol dm⁻³
  3. At 200 kPa the same working gives 80.8 mol m⁻³ = 0.0808 mol dm⁻³, twice as much.

Pressure only matters when gases take part in the step that controls the rate. Solids and liquids hardly change volume when squeezed, so the pressure has no effect on a reaction between aqueous solutions.

Surface area of a solid 9.1

A solid can only react where it is touching the other reactant, so only the particles on its surface are available. Cutting the solid into smaller pieces exposes more particles without changing how much solid there is.

A 4 cm cube is shown whole, cut into 8 cubes of side 2 cm, and cut into 64 cubes of side 1 cm. The total volume is 64 cubic centimetres each time. The total surface area doubles at each stage: 96, 192 and 384 square centimetres.
Same volume, more surface: each cut that halves the side doubles the total surface area.

Worked exampleSurface area of a cut cube

A cube of side 4 cm is cut into cubes of side 2 cm. Find the total surface area before and after.

  1. Before: one cube, 6 faces of 4 × 4 cm = 6 × 16 = 96 cm²
  2. After: 8 cubes, each with 6 faces of 2 × 2 cm = 6 × 4 = 24 cm². Total = 8 × 24 = 192 cm²
  3. The volume is 8 × 2³ = 64 cm³, the same as 4³. The surface area has doubled.

This is why marble powder fizzes faster than marble chips in acid. The same mass of marble has much more surface in contact with the acid, so collisions between acid particles and the marble surface are more frequent. A powder gives a faster rate but the same total amount of gas, since the mass of marble has not changed.

Writing the explanation 9.1

Check yourself

  1. Explain why increasing the concentration of hydrochloric acid increases the rate of its reaction with magnesium.
  2. Explain why increasing the pressure increases the rate of a reaction between two gases.
  3. Explain why changing the pressure has almost no effect on the rate of a reaction between two aqueous solutions.
  4. A cube of side 2.0 cm is cut into cubes of side 1.0 cm. Calculate the total surface area before and after cutting.
  5. Excess acid is added to 5.0 g of marble chips in one experiment and to 5.0 g of marble powder in another. Compare the initial rates and the final volumes of gas.
  6. A student says that increasing the concentration speeds up the reaction because the particles move faster. Correct her.

Answers cover these until you have tried the questions

  1. There are more acid particles in the same volume, so they collide with the magnesium surface more frequently. The energy of the particles has not changed, so a greater number of successful collisions occurs per second.
  2. A higher pressure puts the same number of molecules in a smaller volume, so the concentration is higher. The molecules collide more frequently, so more successful collisions per second.
  3. Liquids and solutions are almost incompressible, so raising the pressure does not change the concentrations, and the collision frequency is unchanged.
  4. Before: 6 × 2.0² = 6 × 4.0 = 24 cm². After: 8 cubes, each 6 × 1.0² = 6 cm², so 8 × 6 = 48 cm². The total surface area doubles.
  5. The powder has a larger surface area, so its initial rate is higher (a steeper initial gradient). The final volume of gas is the same, because the mass of marble is the same.
  6. The particles do not move faster; their energy is unchanged. A higher concentration means more particles in the same volume, so collisions are more frequent.