Question

(8.8400x10^-1) mol of an ideal gas has a pressure of (1.50x10^2) kPa and temperature of (2.5700x10^2) K. What is the volume of the gas?

Answer 1

The volume of the gas is `1.26 × 10^1 color(white)(l)"L"`.

Explanation:

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

`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`

In this problem,

`n = 8.8400 × 10^"-1"color(white)(l) "mol"`
`R = "8.314 kPa·L·K"^"-1""mol"^"-1"`
`T = 2.5700 × 10^2 color(white)(l)"K"`
`p = 1.50 ×10^2 color(white)(l)"kPa"`

`V = (8.8400 ×10^"-1" color(red)(cancel(color(black)("mol"))) × 8.314 color(red)(cancel(color(black)("kPa")))·"L"·color(red)(cancel(color(black)("K"^"-1"·"mol"^"-1"))) × 2.5700× 10^2color(red)(cancel(color(black)("K"))))/(1.50 × 10^2 color(red)(cancel(color(black)("kPa")))) = 1.26 × 10^1 color(white)(l)"L"`