Question

A sample of carbon monoxide gas is collected in a 100 mL container at a pressure of 688 mmHg and a temperature of 565°C. How many grams of this gas is present this given sample?

Answer 1

The mass of `"CO"` is 0.0369 g.

Explanation:

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

`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 rearrange this to get

`m = (MPV)/(RT)`

`M = "28.01 g·mol"^"-1""`
`P = 688 color(red)(cancel(color(black)("mmHg"))) × "1 atm"/(760 color(red)(cancel(color(black)("mmHg")))) = "0.9053 atm"`
`V = "0.100 L"`
`R = "0.082 06 L·atm·K"^"-1""mol"^"-1"`
`T = "(565 + 273.15) K" = "838.15 K"`

∴ `m = (28.01 "g"·color(red)(cancel(color(black)("mol"^"-1"))) × 0.9053 color(red)(cancel(color(black)("atm"))) × 0.100 color(red)(cancel(color(black)("L"))))/("0.0.082 06" color(red)(cancel(color(black)("L·atm·K"^"-1""mol"^"-1"))) × 838.15 color(red)(cancel(color(black)("K")))) = "0.0369 g"`

∴ The mass is 0.0369 g.