Question

A 21-liter cylinder contains 1.5 moles of an ideal gas at 311 K. What is the pressure of the gas?

Answer 1

`P = "1.8 atm"`

Explanation:

This is a pretty straightforward ideal gas law equation practice problem.

As you know, the ideal gas law equation looks like this

`color(blue)(PV = nRT)" "`, where

`P` - the pressure of the gas
`V` - the volume it occupies
`n` - the number of moles of gas
`R` - the universal gas constant, usually given as `0.0821 ("atm" * "L")/("mol" * "K")`
`T` - the temperature of the gas, always expressed in Kelvin

So, the problem provides you with

• the volume of the gas, `V = "21 L"`
• the number of moles of gas, `n = 1.5`
• the absolute temperature of the gas, `T = "311 K"`

Since you know the value of `R`, you can use this information to find the pressure `P`. First, rearrange the ideal gas law equation to isolate `P` on one side

`PV = nRT implies P = (nRT)/V`

Next, make sure that the units given to you match those used in the expression of the universal gas constant.

`{:(color(red)("Need"), color(white)(aaaaa), color(blue)("Have")), (color(white)(aaaa), color(white)(aaaa), color(white)(aaaa)), (color(white)(aa)"L", color(white)(aaaa), color(white)(aa)"L"color(white)(aaaaaa)color(green)(sqrt())), ("moles", color(white)(aaaa), "moles"color(white)(aaaaa)color(green)(sqrt())), (color(white)(aa)"K", color(white)(aaaa), color(white)(aa)"K"color(white)(aaaaaa)color(green)(sqrt())) :}`

The units given to you match those used for `R`, so you're good to go. Plug in your values to get

`P = (1.5 color(red)(cancel(color(black)("moles"))) * 0.0821("atm" * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 311color(red)(cancel(color(black)("K"))))/(21color(red)(cancel(color(black)("L"))))`

`P = "1.824 atm"`

Rounded to two sig figs, the number of sig figs you have for the volume and number of moles of gas, the answer will be

`P = color(green)("1.8 atm")`