Question

What is the volume of an ideal gas at STP, if its volume is `"2.85 L"` at `14^@ "C"` and `"450 mm Hg"`?

Answer 1

The volume at STP is `~~"1200 L".`

Explanation:

This is an example of the combined gas law, which combines Boyle's, Charles', and Gay-Lussac's laws. It shows the relationship between the pressure, volume, and temperature when the quantity of ideal gas is constant.

The equation to use is:

`(P_1V_1)/T_1=(P_2V_2)/T_2`

https://en.wikipedia.org/wiki/Gas_laws

Housekeeping Issues

Current STP

Standard temperature is `"0"^@"C"` or `"273.15 K"`, and standard pressure after 1982 is `10^5` `"Pa"`, usually written as `"100 kPa"` for easier use.

The Kelvin temperature scale must be used in gas problems. To convert temperature in degrees Celsius to Kelvins, add `273.15` to the Celsius temperature.

`14^@"C"+273.15="287.15 K"`

The pressure in `"mmHg"` must be converted to `"kPa"`.

`"1 mmHg"` `=` `"101.325 kPa"`

`450color(red)cancel(color(black)("mmHg"))xx(101.325"kPa")/(1color(red)cancel(color(black)("mmHg")))="45600 kPa"`

I'm giving the pressure to three sig figs to reduce rounding errors.

Organize the data:

Known

`P_1="45600 kPa"`

`V_1="2.85 L"`

`T_1="287.15 K"`

`P_2="100 kPa"`

`T_2="273.15 K"`

Unknown

`V_2`

Solution

Rearrange the combined gas law equation to isolate `V_2`. Insert the data and solve.

`(P_1V_1)/T_1=(P_2V_2)/T_2`

`V_2=(P_1V_1T_2)/(T_1P_2)`

`V_2=((45600color(red)cancel(color(black)("kPa")))xx(2.85"L")xx(273.15color(red)cancel(color(black)("K"))))/((287.15color(red)cancel(color(black)("K")))xx(100color(red)cancel(color(black)("kPa"))))="1200 L"` (rounded to two significant figures)