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
3 cubes. 1cm cube: SA = 6 sq cm, Vol = 1 cubic cm, SA: Vol ratio = 6:1. 2cm cube: SA = 24 sq cm, Vol = 8 cubic cm, SA:Vol ratio =  3:1. 3cm cube: SA = 54 sq cm, Vol =27 cubic cm, SA: Vol ratio = 2:1A solid divided into smaller lumps has a higher surface area to volume ratio than the same mass of solid divided into larger lumps

Lumps vs powders

The greater the rate 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 rate 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 rate of collisions increases (they happen more often), the rate 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 horizontal line shows that no more product is being made - the reaction has finished
  • the mass of product formed is not affected by the rate of reaction

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

  • gives a steeper line
  • finishes sooner
curriculum-key-fact
Always refer to 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.