Question

How do you solve gas laws problems with the given "at STP" and with mass?

Answer 1

I like to use the Ideal Gas Law.

Explanation:

The Ideal Gas Law is:

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

where

• `P` is the pressure
• `V` is the volume
• `n` is the number of moles
• `R` is the universal gas constant
• `T` is the temperature

We can rearrange the Ideal Gas Law to get

`V = (nRT)/P`

Also,

`"Moles" = "mass"/"molar mass" = m/M`

∴ `V = (m/M) (RT)/P = (mRT)/(PM)`

EXAMPLE

What is the volume of 10.0 g of hydrogen at STP?

Solution

Remember that STP is defined as 0 °C and 1 bar.

`m = "10.0 g"`
`R = "0.083 14 bar·L·K"^"-1""mol"^"-1"`
`T = "(0 + 273.15) K" = "273.15 K"`
`P = "1 bar"`
`M = "2.016 g·mol"^"-1"`

`V = (mRT)/(PM) = (10.0 color(red)(cancel(color(black)("g"))) × "0.083 14" color(red)(cancel(color(black)("bar"))) ·"L"· color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 273.15 color(red)(cancel(color(black)("K"))))/(1 color(red)(cancel(color(black)("bar"))) × 2.016 color(red)(cancel(color(black)("g·mol"^"-1")))) = "113 L"`