# 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

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

It is always reasonable to use the temperature

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

The volume **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"#