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

1 Answer

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)