The formula weight (FW) of a gas can be determined using the following form of the ideal gas law

FW = gRT / PV

where g is the mass in grams, R is the gas constant, T is the temperature in Kelvin, P is the pressure in atmospheres, and V is the volume in liters.

In a typical analysis the following data are obtained (with estimated uncertainties in parentheses)

g = 0.118 g (± 0.002 g)
R = 0.082056 L atm mol^–1 K^–1 (± 0.000001 L atm mol^–1 K^–1)
T = 298.2 K (± 0.1 K)
P = 0.724 atm (± 0.005 atm)
V = 0.250 L (± 0.005 L)

(a) What is the compound’s formula weight and its estimated uncertainty? (b) To which variable(s) should you direct your attention if you wish to improve the uncertainty in the compound’s molecular weight?