Question

What is the volume, in liters, occupied by 260 moles of `N_2` gas?

Answer 1

The volume at STP is 5900 L.

Explanation:

You don’t give the temperature or pressure, so I shall assume the gas is at STP.

We can use the Ideal Gas Law to calculate the volume at STP.

The Ideal Gas Law is:

`color(blue)(|bar(ul(PV = nRT)|)`,

where

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

We can rearrange the Ideal Gas Law to get

`V = (nRT)/P`

STP is 1 bar and 0 °C.

`n = "260 mol"`
`R = "0.083 14 bar·L·K"^"-1""mol"^"-1"`
`T = "273.15 K"`
`P = "1 bar"`

`V = (nRT)/P = (260 color(red)(cancel(color(black)("mol"))) × "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")))) = "5900 L"`