A container of gas is at a pressure of 3.7 X 10(to the fifth) Pa. How
much work is done by the gas if its volume expands by 1.6 m3?
 
This is the equation i thought fit best for this question:
Work done by the net force = final kinetic energy - starting kinetic energy

You need more information about the type of expansion.  Is it
adiabatic?  Isothermal?  Or is the pressure somehow kept constant
during the expansion?

Also... is the gas ideal?

I'm guessing it's probably an ideal gas under going isobaric expansion
in which case,

W = integral (pressure* dVolume) = pressure * integral (dVolume) =
pressure * DeltaVolume

(deltaVolume is the change in volume)

If it's not isobaric and the gas is ideal,

Then PV = nRT (ideal gas law) => P = nRT/V

W = integral (nRT/V * dVolume)

If you assume the expansion is isothermal, then temperature has no
dependence on volume, pressure by definition:

W = nRT * integral (dV/V) = nRT * ln (Vol_f/Vol_i)  

n = number of moles of the gas
R = 'universal' gas constant 8.3145 J/(Mol*K)

Hope that helps..