Effect of temperature on reaction rates and the concept of activation energy — practice questions

(A sketch would show two curves. Both start at (0,0). The curve for $T_2$ has a lower peak which is shifted to the right of the $T_1$ peak. The $T_2$ curve crosses the $T_1$ curve and has a fatter 'tail' at high energies. The total area under both curves is the same. A vertical line is drawn to represent $E_a$.)

Explanation:

1. The axes are labelled 'Number of molecules' (y-axis) and 'Kinetic energy' (x-axis).
2. At the higher temperature, $T_2$, the average kinetic energy of the molecules is greater. This is shown by the peak of the $T_2$ curve being shifted to the right.
3. The area under the curve to the right of the activation energy ($E_a$) line represents the number of molecules with sufficient energy for a successful collision.
4. As shown by the sketch, the shaded area under the $T_2$ curve to the right of $E_a$ is significantly larger than the corresponding area under the $T_1$ curve.
5. Therefore, at the higher temperature $T_2$, a greater proportion of molecules have energy greater than or equal to the activation energy.
6. This leads to a much higher frequency of successful collisions, and thus a faster rate of reaction. (A smaller additional effect is that particles also collide more frequently overall).

(A sketch would show one Boltzmann distribution curve. Two vertical lines are drawn on the x-axis: one for the uncatalysed activation energy, $E_a$, and another to its left for the catalysed activation energy, $E_{a(\text{cat})}$.)

Explanation:

1. A catalyst, such as manganese(IV) oxide, increases the rate of reaction by providing an alternative reaction pathway with a lower activation energy.
2. On the Boltzmann distribution curve, this is represented by a new activation energy, $E_{a(\text{cat})}$, which is less than the original activation energy, $E_a$.
3. The distribution of molecular energies (the curve itself) is not affected by the catalyst, as the temperature remains constant.
4. With a lower activation energy barrier ($E_{a(\text{cat})}$), a much larger area under the curve is now to the right of the activation energy line.
5. This means a significantly greater proportion of molecules now possess the minimum energy required for a successful collision.
6. Consequently, the frequency of successful collisions increases, leading to a faster rate of reaction.