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

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)