AQA Chemistry A-level Year 2
A second-order rate constant has units mol−1 dm3 s−1. Rearranging the rate equation: rate k = [A][B] allows units of concentration to cancel: s−1 (mol dm−3) s−1 = −3 −3 (mol dm )(mol dm ) (mol dm−3)
= mol−1 dm3 s−1
Higher-order reactions A general form of the rate equation for two reactants A and B is: rate = k[A]m[B]n If n = 1 and m = 2 (or vice-versa) the reaction is third order overall. If n = 2 and m = 2 (or any other integers that add up to 4) the reaction is fourth order overall. The units for third-order and fourth-order rate constants can be derived using the method shown above. Table 1 on page 12 shows the units of all orders of reaction from order 0 to order 4. The experimental determination of orders of reaction and rate equations is dealt with in the next section.
Number of molecules
The effect of changes in temperature on rate constant T1 T2
At T2, many more molecules have energy greater than Ea compared with T1 T2 > T1
Ea
Energy
Fig 4 Molecules with energies greater than Ea at different temperatures. The curve for T2, the higher temperature, is broader and has a lower peak than the curve for T1. Apart from the origin through which curves at all temperatures pass (there are never any molecules with exactly zero energy), the curve for a higher temperature always lies to the right of that for a lower temperature.
An increase in temperature increases the rate of a reaction. According to kinetic theory, the mean kinetic energy of the particles is directly proportional to the temperature. At higher temperatures, particles have more energy; they move about more quickly, there are more collisions, and these collisions are more energetic. The increased energy of the collisions is a much more important factor in affecting the rate than is the relatively slight increase in the collision rate when the temperature is raised. Fig 4 shows what happens to the distribution of energies in molecules of a gas when the temperature is increased from T1 to T2. For a fixed sample of gas, the total number of molecules is unchanged and the total area under the curve remains constant (Collins Student Support Materials: AS/A-Level year 1 – Organic and Relevant Physical Chemistry, section 3.1.5.2). To the right of the maximum, the curve at higher temperature T2 lies above the one at lower temperature T1; at the higher temperature there are more molecules with greater energy than there are at the lower temperature. Particles will react only if, on collision, they have more than a minimum amount of energy known as the activation energy.
Definition The activation energy of a reaction is the minimum energy required for the reaction to occur.
Fig 4 shows that, when the activation energy for a reaction is Ea, the number of molecules with energy in excess of Ea is much greater at the higher temperature T2 than at the lower temperature T1. The number of collisions between 8
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