Question

at a depth of 100m underwater the water pressure is equal to 10 atm of pressure. what is the partial pressure of N2 at a pressure of 10 atm?

Answer 1

In air at 10atm?

Dry Air is about 78 percent Nitrogen, so partial pressure at 10atm=7.8 atm

The issue always underwater vs above water, is that air below water as in a casson is wet air, fully saturated, so water vapor reduces the partial pressures of the other gases slightly. Your question is not clear on what gases are present in the mixture.

Answer 2

the gas is still about 80% N2
so 8 atm

It would also be 2 atm O2 instead of 0.20 atm O2 or ten times the O2 pressure. Both the high partial pressure of N2 and of O2 cause problems for divers and for deep diving for extended times mixtures with lower O2 content and Helium instead of Nitrogen are used (HELIOX). For example see: http://oceanexplorer.noaa.gov/technology/diving/technical/technical.html