Calculating Gas Volume and Molecule Count in Lungs During Submarine Emergency

[mexqwerty]

A submarine has run into trouble and is stuck at the bottom of the ocean. Several people are on board and must make their way to the surface without any diving gear. The air pressure aboard the submarine is 3.500 atm. The air temperature inside the submarine is 17.52 °C and you can take body temperature (inside the lungs) to be 37.70 °C.

The second person to leave also takes a breath as deep as possible by exhaling as far as possible (leaving a volume of 1.140 L in their lungs), and then slowly inhaling to increase their lung volume by 4.740 L. His body temperature is also 37.70 °C.
(i) How many particles of air do their lungs contain after inhaling?
(ii) This person breathes out all the way to the surface in order to maintain a constant lung volume. How many moles of gas remain in the lungs?

The answers are 4.86e23 and 0.23mol respectively but I don't know how to get them.

I don't have an idea of how to do (i) and for (ii), I'm using PV=nRT (n=PV/RT) but I can't get the right answer. Values I used:
P = 3.500 atm
V = 1.140L +4.740 L
R = 8.315
T = 37.70+273 K

And I got n=7.97e-3 mol which is not right. Am I supposed to do something else?

 

[Chestermiller]

For the units of the other parameters in the problem, the value you used for the gas constant is not correct. Also, you need to multiply by avigodro's number to convert moles to molecules.