Question

What is the amount of carbon dioxide gas (in mol) that occupies 100ml at 27degree Celsius at a pressure of 200kpa?

Answer 1

`"0.008 mol"`

Explanation:

Convert pressure in `"kPa"` to `"atm"`

`"200 kPa" = 200 cancel"kPa" × "1 atm"/(101.325 cancel"kPa") = "1.974 atm"`

Use ideal gas equation

`"PV = nRT"`

`"n" = "PV"/"RT" = "1.974 atm × 0.1 L"/"0.0821 L atm / (mol K) × 300 K" = "0.008 mol"`

Answer 2

The amount of `"CO"_2` is `"0.008 mol"`.

Explanation:

Use the equation for the ideal gas law:

`PV=nRT`,

where:

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

Organize your data:

Known

`P="200 kPa"`

`V=100"mL"xx("1 L")/(1000"mL")="0.1 L"` (one sig fig)

`R="8.31447 L kPa K"^(-1) "mol"^(-1)"`

`T="27"^@"C + 273.15"="300 K"`

Unknown

`n`

Solution

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

`n=(PV)/(RT)`

`n=((200color(red)cancel(color(black)("kPa")))xx(0.1color(red)cancel(color(black)("L"))))/((8.31447color(red)cancel(color(black)("L")) color(red)cancel(color(black)("kPa")) color(red)cancel(color(black)("K"))^(-1) "mol"^(-1))xx(300color(red)cancel(color(black)("K"))))="0.008 mol"` (rounded to one significant figure)

The amount of `"CO"_2` is `"0.008 mol"`.