What is the number of moles in 500 L of #He# gas at STP?

1 Answer
Jan 17, 2016

Answer:

#"20 moles"#

Explanation:

The important thing to realize here is that you're working under STP conditions, which implies that you can use the molar volume of a gas at STP to find how many moles of helium will occupy that volume.

Now, the molar volume of a gas represents the volume occupied by one mole of a gas under some specific conditions for pressure and temperature.

Starting from the ideal gas law equation

#color(blue)(PV = nRT)#

you can say that the molar volume of gas at a pressure #P# and a temperature #T# will be equal to

#V/n = (RT)/P#

Now, Standard Temperature and Pressure conditions are defined as a pressure of #"100 kPa"# and a temperature of #0^@"C"#. Under these specific conditions, the molar volume of a gas will be equal to

#V/n = (0.0821 * (color(red)(cancel(color(black)("atm"))) * "L")/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 0)color(red)(cancel(color(black)("K"))))/(100/101.325color(red)(cancel(color(black)("atm"))))#

#V/n = "22.7 L/mol"#

This of course implies that one mole of any ideal gas will occupy #"22.7 L"#.

In your case, the volume of the gas is said to be equal to #"500 L"#. This means that you will have

#500 color(red)(cancel(color(black)("L"))) * "1 mole He"/(22.7color(red)(cancel(color(black)("L")))) = "22.026 moles He"#

Rounded to one sig fig, the number of sig figs you have for the volume of the gas, the answer will be

#n_(He) = color(green)("20 moles")#

SIDE NOTE Many textbooks and online sources still list STP conditions as a pressure of #"1 atm"# and a temperature of #0^@"C"#.

Under these conditions for pressure and temperature, one mole of any ideal gas occupies #"22.4 L"#. If these are the values for STP given to you by your instructor, make sure to redo the calculations using #"22.4 L"# instead of #"22.7 L"#.