Question

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?

Answer 1

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"`