Surface Area to Volume Ratio

Chemistry: AQA GCSE Higher, topic 2.3.20

Nanoparticles - Surface Area to Volume Ratio

Nanoparticles have special properties because of their high surface area to volume ratio.

As particles get smaller, their surface area to volume ratio increases.
E.g. decreasing the length of a cube’s side by a factor of 100 increases its surface area to volume ratio by a factor of 100.

This allows for smaller amounts of nanoparticles to be used for a desired purpose compared to using normal-sized particles.
This means that they are cheaper and more efficient to use.

Using nanoparticles can also change the properties of the material completely.
E.g. ‘normal’ gold particles are extremely unreactive, but gold nanoparticles can be very efficient catalysts for many processes.

If the side length of a cube is decreased by a factor of 100, what happens to its surface area to volume ratio?
Which type of gold particle can be used as an efficient catalyst?
Why can smaller amounts of nanoparticles be used to achieve the same effect as normal-sized particles?
Why can gold nanoparticles work as efficient catalysts, even though normal-sized gold particles are extremely unreactive?
A chemist wants to use the smallest possible mass of metal to coat a surface for a reaction. Why would using metal nanoparticles, rather than normal-sized metal particles, help achieve this?