A gas under a pressure of 74 mmHg and at a temperature of 75°C occupies a 500.0-L container. How many moles of gas are in the container?

1 Answer
Aug 18, 2017

#"1.7 mols ideal gas"#.


Anytime you see a bunch of units in a row, it's probably an ideal gas problem. The first order of business is to convert all these to more usual units. Consider the universal gas constant:

#R = "0.082057 L"cdot"atm/mol"cdot"K"#.

The units of pressure, volume, and temperature are given directly in the units of #R#!

For the units to work out, the pressure #P# could be rewritten in #"atm"#:

#P = 74 cancel"mm Hg" xx "1 atm"/(760 cancel"mm Hg") = "0.0974 atm"#

It is always reasonable to use the temperature #T# in #"K"# for general chemistry, and in this case it makes the units work out...

#75^@ "C" + 273.15 = "348.15 K"#

The volume #V# is in normal units. We do want it in #"L"#, just as we wanted #P# in #"atm"#. Thus, we can now use the ideal gas law:

#bb(PV = nRT)#

where #n# is the mols of ideal gas.

So, to two significant figures, the mols are:

#color(blue)(n) = (PV)/(RT)#

#= ("0.0974 atm" cdot "500.0 L")/("0.082057 L"cdot"atm/mol"cdot"K" cdot "348.15 K")#

#=# #color(blue)ul"1.7 mols ideal gas"#