Activation energy and catalysisEdexcel International A Level Chemistry: Revision notes

The activation energy, Ea, is the minimum energy colliding particles need for a reaction to occur. At a given temperature the molecules have a range of energies. Raising the temperature increases the proportion of molecules with energy equal to or greater than Ea, so more collisions per second are successful. Even a 10 K rise can roughly double the rate, and the rate constant k increases with temperature.

A catalyst provides an alternative route with a lower activation energy, so a greater proportion of molecules can react at the same temperature.

The Arrhenius equation relates the rate constant to temperature: k = A e^(−Ea/RT), where A is a constant, Ea is the activation energy in J mol⁻¹, R is 8.31 J K⁻¹ mol⁻¹ and T is the temperature in kelvin.

Taking natural logs gives ln k = ln A − Ea/RT. This has the form y = c + mx, so a graph of ln k against 1/T is a straight line with gradient = −Ea/R. Then Ea = −gradient × R.

The equation is given if needed, but you must be able to use it.

Subtracting the Arrhenius equation at two temperatures gives ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂).

Worked example. k = 1.5 × 10⁻³ s⁻¹ at 298 K and 6.0 × 10⁻³ s⁻¹ at 318 K.

ln(k₂/k₁) = ln 4.0 = 1.386. 1/298 − 1/318 = 2.11 × 10⁻⁴ K⁻¹.

Ea = 8.31 × 1.386 ÷ 2.11 × 10⁻⁴ = 54 600 J mol⁻¹ = 54.6 kJ mol⁻¹.

The same equation can predict k at a new temperature if Ea is known. A graph using several temperatures is more reliable than two points, because it averages out errors.

A common method uses sodium thiosulfate and hydrochloric acid, which form a sulfur precipitate. The time t for a cross to disappear is measured at several temperatures.

• Use the same volumes and concentrations each time.
• Bring each solution to temperature in a water bath, mix them, and record the temperature and time.
• Use at least five temperatures over about 20 to 60 °C.
• Rate is proportional to 1/t.
• Plot ln(1/t) against 1/T (T in kelvin). The gradient is −Ea/R, so Ea = −gradient × 8.31.

Limitations include judging when the cross disappears and the temperature changing during the reaction.

In many industrial gas-phase reactions the catalyst is a solid (heterogeneous catalyst), for example iron in the Haber process. The reaction takes place on its surface:

• Reactant molecules are adsorbed onto active sites, which weakens bonds and holds them close together.
• The reaction occurs through a route with a lower activation energy.
• The products are desorbed, freeing the sites.

The catalyst is used as pellets or a finely divided solid to give a large surface area, and the rate increases with surface area. The catalyst lets the reaction run at a lower temperature, saving energy. It is easy to separate from the gaseous products.