There are spiders that are able to live on the surface of the water. Explain the chemistry that is involved in

allowing the spiders to live on the surface of the water without drowning.

Water is a polar molecule meaning that it contains one end that is slightly positive and the other end that is slightly negative. This enables it to make hydrogen bonds with other molecules of water and as you can imagine in a sea or lake you have zillions of molecules of water. They create a network of hydrogen bonds, and because a spider is tiny and it's mass is small, it can live on the surface of water without breaking that network of H-bonds.

In a nutshell, spiders that can tread water do so because of fine clusters of hairs on their tarsai (feet) called setae.
These non wetting hairs can displace enough water to support the small mass of the spider.
Paulina has a more 'in depth' response of how this works.
The electrostatic properties of this setae also allow some spiders to climb smooth surfaces such as glass.