Question

If 49.5 moles of an ideal gas occupies 37.5 liters at 479 K, what is the pressure of the gas?

Answer 1

The pressure of the gas is 51.9 atm.

Explanation:

This looks like a good time to apply the Ideal Gas Law:

`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

`P = (nRT)/V`

`n = "49.5 mol"`
`R = "0.082 06 L·atm·K"^"-1""mol"^"-1"`
`T = "479 K"`
`V = "37.5 L"`

`P = (nRT)/V = (49.5 color(red)(cancel(color(black)("mol"))) × "0.082 06" color(red)(cancel(color(black)("L")))"·atm·"color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 479 color(red)(cancel(color(black)("K"))))/(37.5 color(red)(cancel(color(black)("L")))) = "51.9 atm"`