Question

Ideal gas law problem check?

If I have 4.1 moles of a gas at a pressure of 5.6 atm and a volume of 12 liters, what is the temperature?
I want to check that I completed this problem right before continuing with the rest of my problems to ensure I'm doing them correctly. Thanks!

Answer 1

The temperature is `2.0xx10^2` `"K"`.

Explanation:

Equation for the ideal gas law:

`PV=nRT`,

where:

`P` is pressure, `V` is volume, `n` is moles, `R` is the gas constant (varies with units for pressure), and `T` is temperature in Kelvins.

Known

`P="5.6 atm"`

`V="12 L"`

`n="4.1 moles"`

`R="0.082056 L atm K"^(-1) "mol"^(-1)"`

Unknown

`T`

Solution

Rearrange the equation to isolate `T`. Plug in the known values and solve.

`T=(PV)/(nR)`

`T=(5.6color(red)cancel(color(black)("atm"))xx12color(red)cancel(color(black)("L")))/(4.1color(red)cancel(color(black)("mol"))xx0.082056 color(red)cancel(color(black)("L")) color(red)cancel(color(black)("atm")) "K"^(-1) color(red)cancel(color(black)("mol"))^(-1))=2.0xx10^2` `"K"` (rounded to two significant figures)

Answer 2

`T = 199.73 K`

Explanation:

Use the formula

`PV = nRT`

re-arranging for temperature:

`T =( PV)/(nR)`

Plug-in values:

Remember R is a constant = `0.08206 (L*atm)/(mol *K)`

`T = ((5.6 atm)(12 L)) / ((4.1 mol) (0.08206 (L*atm)/(mol *K))`

cancel units and solve:

`T = 199.73 K`