A 0.642 g sample of an unknown gas was collected over water at 25.0 degrees C and 1.04 atm. The collection cylinder contained 151.3 mL of gas after the sample was released. How do you find the molar mass of the unknown gas?

1 Answer
Dec 29, 2016

Answer:

The molar mass of the gas is 103 g/mol.

Explanation:

We can use the Ideal Gas Law to solve this problem.

#color(blue)(bar(ul(|color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "#

Since #n = m/M#, we can rearrange this equation to get

#PV = (m/M)RT#

And we can solve this equation to get

#M = (mRT)/(PV)#

Since you are collecting the gas over water,

#P_"atm" = P_"gas" + P_"water"#

At 25.0 °C, the partial pressure of water is 0.0313 atm

# P_"gas" = P_"atm" - P_"water" = "1.04 atm - 0.0313 atm" = "1.009 atm"#

Thus, in your problem,

#m = "0.642 g"#
#R = "0.082 06 L·atm·K"^"-1""mol"^"-1"#
#T = "25.0 °C" = "298.15 K"#
#P = "1.009 atm"#
#V = "151.3 mL" = "0.1513 L"#

#M = (0.642 color(red)(cancel(color(black)("g"))) × "0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1")))"mol"^"-1" × 298.15 color(red)(cancel(color(black)("K"))))/(1.009 color(red)(cancel(color(black)("atm"))) × 0.1513 color(red)(cancel(color(black)("L")))) = "103 g/mol"#