(8.000x10^-1) g of a gas is collected in the lab and found to have a volume of (8.9000x10^-1) L when the pressure is (9.600x10^1) kPa and the temperature is (3.00x10^2) K. According to this collected data what is the molar mass of the gas?

1 Answer
Ernest Z.
May 6, 2017

According to these data, the molar mass of the gas is 23.4 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)#

In your problem,

#m = 8.000 × 10^"-1"color(white)(l) "g" #
#R = "8.314 kPa·L·K"^"-1""mol"^"-1"#
#T = 3.00 × 10^2color(white)(l) "K"#
#P = 9.600 × 10^1 color(white)(l) "kPa "#
#V = 8.9000 × 10^"-1"color(white)(l) "L "#

∴ #M = (8.000 × 10^"-1"color(white)(l)"g" × 8.314 color(red)(cancel(color(black)("kPa·L·K"^"-1")))"mol"^"-1" × 3.00 × 10^2 color(red)(cancel(color(black)("K"))))/(9.600 × 10^1 color(red)(cancel(color(black)("kPa"))) ×8.900 × 10^"-1" color(red)(cancel(color(black)("L")))) = "23.4 g/mol"#

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