A gas has a volume of 240.0mL at 25.0 celecuis and 600.0mmHg. Calculate it’s volume at STP?

1 Answer
Apr 6, 2018

The final volume is #"1.8 mL"#.

Explanation:

Use the equation for the combined gas law:

#(P_1V_1)/T_1=(P_2V_2)/T_2#,

where:

#P_1# and #P_2# are the initial and final pressure, respectively, #V_1# and #V_2# are the initial and final volume, and #T_1# and #T_2# are the initial and final temperature in Kelvins.

Current STP is #0^@"C"# or #"273.15 K"#, and #"100 kPa"# or #"1 bar"#.

Organize the data:

Known

#P_1="600.0 mmHg"#

#V_1="240 mL"#

#T_1="25.0"^@"C + 273.15 = 298.2 K"# #larr# Temp must be in Kelvins.

#P_2=100 color(red)cancel(color(black)("kPa"))xx(750"mmHg")/(1color(red)cancel(color(black)("kPa")))="75000 mmHg"# #larr# Converting standard pressure to #"mmHg"#.

#T_2="273.15 K"#

Unknown

#V_2#

Solution

Rearrange the equation to isolate #V_2#. Plug in the known values and solve.

#V_2=(P_1V_1T_2)/(T_1P_2)#

#V_2=((600.0color(red)cancel(color(black)("mmHg")))xx(240"mL")xx(273.15color(red)cancel(color(black)("K"))))/((298.2color(red)cancel(color(black)("K")))xx(75000color(red)cancel(color(black)("mmHg"))))="1.8 mL"# (rounded to two significant figures)

Note:

If your teacher is still using #"1 atm"# for pressure at STP, then #P_2="760 mmHg"#, and #V_2="170 mL"#.