Exercise 3 solution (1) Crush the solid to a powder: SPEEDS UP. More surface area means more particles exposed, so more collisions with the solution (Reaction rate article: rate increases as surface area does). (2) Cool by 10 C: SLOWS DOWN. Lower average kinetic energy, so fewer collisions have the activation energy. By the page's rule of thumb the rate constant roughly halves for a 10 C fall (approximate) (check). (3) Add a suitable catalyst: SPEEDS UP. It gives a pathway with a lower activation energy, so more collisions succeed. It is not used up, and it does not change the overall energy change. (4) More dilute solution: SLOWS DOWN. Lower concentration means fewer collisions, so fewer successful ones (Collision theory article). Raise by 20 C: two steps of 10 C, each roughly doubling the rate constant: 2 x 2 = 2^2 = 4 (Python: 4.0). So about four times faster, as a rough estimate only.