Chemistry Grades and Chemistry Help

In the ideal gas law pressure and temperature are fairly easy to understand from a molecular point of view.  Pressure is when gas molecules hit the wall and bounce off.  Temperature is how fast they move.  P and T are essentially independent of each other.  Volume can be more difficult to interpret.  The question “how big of a container do you need to hold this much gas” is certainly a good test question, but in a real experiment you start with a container and ask questions about what is inside it.  It has almost no microscopic relevance.  The microscopic feature which is relevant is:  how close are the gas molecules to each other ?

Volume and amount are closely coupled together, and perhaps a better form of the ideal gas law would be  n/V = P/RT where n/V is the molar density.  Molar density is the number of moles per unit volume, which is directly related to the typical distance between molecules.  It’s measured in moles/liter and sounds a lot like molarity (the units are the same).  But molarity usually refers to a dilution of some compound dissolved in water.  The molar density of a gas says how many moles are in a standard volume.  For 1 atm at 298 oK the molar density of a gas is 1/22.41 or 0.04462 moles/liter.

If you measure pressure and temperature as independent variables then molar density is a result.  Only 2 of these 3 variables can be independent. As soon as you measure 2 of them the 3rd can be calculated.

If molar density confuses you think about water solutions.  You would almost never ask “how many liters do I need to hold 0.34 grams of a liquid with density 1.119 g/cm3 ?”  While this is an excellent test question, it’s not a real problem we will ever face.  A much more realistic problem is to ask, if 101.2 grams of liquid has a volume of 100 cm3 then how much will 1 gallon weigh ?

This is a good test question :  At 1 atmosphere and 298 oK what is the density of air?

n/V = P/RT = 1/.08206/298.15 = 0.4462 moles/liter,  now just convert moles to grams.  Since air is 80% N2 and 20% O2 a good molar mass to use is 29 g/mole.  So the density of air is about 29 * 0.4462 = 1.3 g/liter.  So an empty 1 liter Coke bottle has 1.3 grams of air inside of it.  1L can hold 1000 g of H2O.  So water is about 770 times as dense as air (1000/1.3).