The human lungs can function satisfactorily up to a limit where the pressure difference between the outside and inside of the lungs is 1/21 of an atmosphere. If a diver uses a snorkel for breathing, how far below the water can she swim? Assume the diver is in salt water whose density is 1052 kg/m3

Answer 1

This question is very misleading because in fact free diving with a snorkel you can go down many, many meters. However you do not breathe while doing so, but hold your breath and your lungs get smaller compressing the air inside. (Your buoyancy also decreases and the deeper you go the faster your descent.
That said:
1 atm = 10^5 Pascal or Newton/m^2

water per meter pressure =rho g
= 1052 kg * 9.81 = 10,320 N/m^3
so
10,320 d = (1/21)10^5
216,722 d = 10^5 = 100,000
d = .461 meters
By the way, that is an awfully long snorkel