Rates and surface area to volume ratio

Dividing lumps

For a given mass of a solid, large lumps have smaller surface area to volume ratios than smaller lumps or powders. If a large lump is divided or ground into a powder:

  • its total volume stays the same
  • the area of exposed surface increases
  • the surface area to volume ratio increases

Lumps vs powders

The greater the frequency of successful collisions, the greater the rate of reaction. If the surface area to volume ratio of a reacting solid is increased:

  • more reactant particles are exposed at the surface
  • the frequency of collisions between reactant particles increases
  • therefore the rate of reaction increases

Note that the mean energy of the particles does not change. However, since the frequency of collisions increases (they happen more often), the frequency of successful collisions also increases.

Graphs

The rates of two or more reactions can be compared using a graph of mass or volume of product formed against time. The graph shows this for two reactions.

Graph of total mass of product against time from start of reaction, for large and small surface area.

The gradient of the line is equal to the rate of reaction. The faster reaction with the powder:

  • gives a steeper line
  • finishes sooner

Note that the amount of product does not change when the reaction rate changes. The same amount of product is formed, but in a shorter time. Therefore, both lines on the graph finish in the same value of mass or volume, but the reaction with the higher surface area to volume ratio reaches this mass or volume sooner.

curriculum-key-fact
Make sure you answer questions in terms of surface area to volume ratio, rather than just surface area. This is because the surface area also depends on the mass of solid reactant used.