Verified answer

Start with the ideal gas equation

PV = nRT

we know that moles (n) = mass (m) / molar mass (M)

substitute this into the equation and we get

PV = mRT / M

Now, we also know that density (d) = mass (m) / volume (V)

so rearrange the modified gas equation such that m/V (density) is on one side by itself

m/V = PM / RT

density = PM / RT

P = pressure = 51.6 kPa

M = molar mass = ? g/mol

R = gas constant = 8.3145 kPa L mol^-1 K^-1

T = temp in Kelvin = 275 K

density (d) = 0.963 g/L

solve for M

M = dRT / P

= 0.963 gL^-1 x 8.3145 kPaLmol^-1K^-1 x 275 K / 51.6 kPa

= 42.7 g/mol (3 sig figs)