okay let's check out a few problems regarding the properties of
gases number one says equal masses of methane and oxygen are mixed in an empty
container at 25 degrees Celsius what is the fraction of the total pressure
exerted by oxygen number 2 asks a gas will approach ideal behavior at and then
there are some options here regarding temperature and pressure and then number
3 says the ratio of the rate of diffusion of helium to methane under
identical conditions of pressure and temperature is and again there are some
numerical options here so some different things here about gases you may want to
review some of my tutorials regarding ideal gases and non-ideal gases as well
as diffusion things of that nature and when you're ready give it a try
so for this first one it specifies that we have equal masses of methane and oxygen so in
this kind of a case it might be useful to just go ahead and assume an arbitrary
mass so let's arbitrarily choose 32 grams of each gas and you could choose
any number you like I'll show you why 32 is very convenient because now we can
convert from grams into moles right because moles are going to tell us
something about the total pressure so let's convert our grand valley's into
moles we have 32 grams of oxygen times 1 mole for every 32 grams because 32 grams
is the molar mass of o2 so we have 1 mole of oxygen then we have 32 grams of
methane as well because we have the same mass of each and that will be times 1
mole over 16 grams because a because methane has a molar mass of 16 so that
means we have 2 moles of methane now what we need to understand is that the
partial pressure of oxygen which is what we're looking for here it says what is
fraction of the total pressure exerted by oxygen that's going to be equal to
the mole fraction of oxygen over the total moles because the fraction of the
molecules that are represented by oxygen will represent the fraction of the total
pressure that's how pressure works and so we need to see that we have one mole
of oxygen for every three moles of gas in total because we have one mole of
oxygen for every two moles of methane so one-third of the gas particles in the
sample are oxygen molecules and that means that one-third of the total
pressure is exerted by oxygen now looking at number two were trying to
describe ideal gas behavior now what are the assumptions we're making when we're
talking about an ideal gas well assumption number one is that the
gas particles do not interact right we're saying that these are just little
points and that they don't interact they just fly around and bounce around and so
in terms of temperature this is presuming a higher temperature because
this would mean that the gas particles move very quickly as opposed to them
moving very slowly which would result in them having time to interact with one
another as they pass by one another and collide if two polar gas molecules pass
by each other very slowly they will have time to make electrostatic interactions
so ideal gas behavior precludes higher temperatures assumption number two is
that the gas particles take up negligible volume we ignore the volume
of the gas particles themselves when talking about an ideal gas and so this
would require that we're looking at lower pressures because the gas
particles must be very sparse it must be a lot of empty space in the vessel if it
was very high pressure that would mean the gas had been rather compressed and
that would mean that the gas particles are very close to one another so there
wouldn't be as much empty space and therefore the volume of the gas
particles themselves would be a significant fraction of the total volume
and so we could no longer ignore the volume of the gas particles so we need
high temperatures and low pressures to be able to assume ideal gas
behavior so that's going to be option C high temperature and low pressure now
number three we're looking at the ratio of the rate of diffusion of helium to
methane so what is the equation we're gonna use well we know that the ratio
this ratio that we're describing helium to methane so let's put our helium over
our methane that is going to be equal to the square root of the molar mass of
methane over the molar mass of helium so this is an important equation to
understand when we're looking at diffusion or effusion basically any
aspect of the movement of gaseous particles notice that we have a square
root on the right over the molar masses and we have inverted the order of the
substances so we have methane on top and helium on the bottom so let's go ahead
and plug these in we're gonna put square root of the molar mass of methane which
is 16 over the molar mass of helium which is 4 and that is equal to 2 so
helium will diffuse twice as fast as methane because it has a quarter the
molar mass so that is going to be B 2