How would you find the molecular weight of an unknown gas?

Question

Wyatt Atkins · Accepted Answer

I would determine the mass of a fixed volume of the gas at a known temperature and pressure and then use the Ideal Gas Law to calculate the molar mass.

AN EXAMPLE The mass of the flask filled with an unknown gas at 25.0 °C and 265 Torr is 143.289 g, while the mass of an evacuated 255 mL flask is 143.187 g. Resolution The ideal gas law is #color(blue)(|bar(ul(color(white)(a/a)PV = nRT color(white)(a/a)|)))" "# Since #n = "mass"/"molar mass" = m/M#, we can write the Ideal Gas Law as #color(blue)(|bar(ul(color(white)(a/a)PV = m/MRTcolor(white)(a/a)|)))" "# We can change things around to get #M = (mRT)/(PV)# #m = "143.289 g - 143.187 g" = "0.102 g"# #R = "0.082 06 L·atm·K"^"-1""mol"^"-1"# #T = "(25.0 + 273.15) K" = "298.75 K"# #P = 265 color(red)(cancel(color(black)("torr"))) × "1 atm"/(760 color(red)(cancel(color(black)("torr")))) = "0.3487 atm"# #V = "0.255 L"# ∴ #M = ("0.102 g" × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 298.15 color(red)(cancel(color(black)("K"))))/("0.3487" color(red)(cancel(color(black)("atm"))) × 0.255 color(red)(cancel(color(black)("L")))) = "28.1 g/mol"# There are 28.1 g/mol of molar mass. ∴ 28.1 u is the molecular mass.

Natalie Anton · Answer

undefined To find the molecular weight of an unknown gas, you can use the ideal gas law equation: $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the ideal gas constant, and $T$ is temperature. Rearrange the equation to solve for $n$, the number of moles. Then, use the equation $n = \frac{m}{M}$, where $m$ is the mass of the gas and $M$ is the molar mass. Solving for $M$ gives the molecular weight of the unknown gas.