Question

A gas sitting in a 5L container at 12 degrees celcius at 3atm, how many moles do you have?

Answer 1

A bit over half a mole....

Explanation:

We simply solve the Ideal Gas equation...

`n=(PV)/(RT)`

`=(3*atmxx5.0*L)/(0.0821*(L*atm)/(K*mol)*(12+273.15)*K)`

`=??*mol...`

Answer 2

`0.641435498778218\approx 0.641\ \text{moles}`

Explanation:

From ideal gas equation

`PV=nRT`

where:

• `P` is absolute pressure of gas

• `V` is volume of gas

• `n` is number of moles of gas

• `R=8.314\ \text{J/mole K}` is universal gas constant.

• `T` is absolute temperature of gas

`n=(PV)/(RT)`

Setting the values

• `P=3\ "atm"=3 xx 101325\ "Pa"`,

• `V=5\ "L"=5 xx 10^{-3}\ "m"^3`

• `R=8.314 \ \text{J/mole K}`

• `T=12^0 "C"=12+273=285\ "K"`

we get, the number of moles

`n=\frac{3\times 101325\times 5\times 10^{-3} }{8.314\times 285}`

`=0.641435498778218\ \text{moles}`

`\approx 0.641\ \text{moles}`

Answer 3

You have `"0.6 mol"` of gas.

Explanation:

Use the ideal gas law equation:

`PV=nRT`,

where:

`P` is pressure, `V` is volume, `n` is moles, `R` is the gas constant, and `T` is the temperature in Kelvins.

Known

`P="3 atm"`

`V="5 L"`

`R="0.08206 L atm K"^(-1) "mol"^(-1)`

`T="12"^@"C + 273.15"="285 K"`

Unknown

`n`

Solution

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

`n=(PV)/(RT)`

`n=(3color(red)cancel(color(black)("atm"))xx5color(red)cancel(color(black)("L")))/(0.08206color(red)cancel(color(black)("L")) color(red)cancel(color(black)("atm")) color(red)cancel(color(black)("K"))^(-1) "mol"^(-1)xx285color(red)cancel(color(black)("K")))="0.6 mol"`
(rounded to one significant figure)