Answer 1
for oxygen:
multiply 37 by 16 (atomic mass of oxygen)
=592 (moles)
then multiply 63 by 14 (atomic mass of nitrogen)
=882 (moles)
add them
592+882=1474 (total number of moles in the compound)
divide (number of moles of oxygen) by (total number of moles in the compound)
592/1474 = 0.402 and this mole fraction ur for oxygen
answer 2
The mole fraction is the number of moles of one of the components of the solution divided by the total number of moles of the solution. Since you know the percentage composition, it will be easy.
Assuming constant temperature and pressure, Avogadro says that equal volumes of gas contain equal number of molecules (and therefore equal number of moles of gas).
To simplify, imagine that you have a sample of the gas solution containing exactly 100 moles of gas. 37% of the volume (and therefore 37% of the moles of gas) is oxygen.
This means 37 mol of oxygen in 100 mol of solution. The mole fraction = 37/100 = 0.37.