okay let's go ahead and take a look at a problem regarding Graham's law of
effusion so the question asks us to consider the
following equilibrium and that is the one between diatomic chlorine or
chlorine molecule and two chlorine atoms which would be two chlorine radicals so
this is the equilibrium between chlorine gas and the dissociated version two
chlorine radicals and then the question asks this equilibrium mixture is
attained at 1200 degrees Celsius and determined by measuring the rate of
effusion through a pinhole so we're trying to figure out how much of each
substance how much of each species is there simply by looking at the rate of
effusion through a pinhole at one point eight zero millimeters mercury pressure
the mixture it fuses one point one six times as fast as Krypton if uses under
the same conditions what fraction of the chlorine molecules have dissociated into
atoms so we should be able to figure something out right we know that whether
we have diatomic chlorine or chlorine radicals where that equilibrium lies is
going to inform how many particles are in the system the number of particles in
the system is going to tell us something about molar mass the average molar mass
of the particles in the system which is going to inform how quickly this mixture
efuses so we have we know some things about
Krypton we know about Graham's law of effusion we know some things about
equilibria so it's a little bit tricky but see if you can figure this one out
so the first thing we're going to do is start with the information we're given
we're told that the mixture efuses one point one six times as fast as Krypton
effuses so just gonna use this ratio we're gonna
call the rate the rate at which Krypton effuses is going to be one and then
therefore one point one six times that will be the rate of effusion of the
mixture or just one point one six now in order to plug numbers into Graham's law
of effusion we also need molar masses so the molar mass of Krypton we can get
that from the periodic table that's 84 but the molar mass of the mixture we
don't know because that's going to be an average molar mass that's representative
of where this equilibrium lies we need to know what proportion of the chlorine
molecules are dissociated into the radicals at any given time at this
temperature so we don't know the molar mass of the mixture so weak but we can
solve for it because we have all the other data so here's Graham's law of
effusion and we can plug things in so let's put our rates of effusion in there
we have one point one six over one and now let's go ahead and square both sides
so we get rid of that square root now let's go ahead and plug in 84 for the
molar mass of Krypton and now we can solve for the molar mass of the mixture
that's going to be sixty two point four two six now take note that the average
mass of a chlorine atom is around 35 point five so the molar mass of Cl2
is 71 and the molar mass of a chlorine radical is thirty five point five and so
this is obviously in between because some of the species are Cl2 and some
of the species are chlorine radical so we're going to take this information and
we're going to do some more math now this time regarding equilibria so let's
set up an icebox so that we can describe the equilibrium that is occurring in
this system now for chlorine we're going to say that we're starting at an initial
concentration of one and then change is going to be minus X because some of the
chlorine molecules are going to dissociate so we're going to lose some
of the chlorine molecules and then the equilibrium value will be 1 minus X be
the one that we started with minus X whatever amount of chlorine molecules
dissociated then for the chlorine radicals we're going to start with zero
but then the change will be 2x because for every one chlorine molecule that
Associates we get two chlorine radicals so zero plus 2x means for the
equilibrium value for chlorine radicals will be 2x now that means that our
totals will be one for initial X for the change and then for our equilibrium we
will have 1 plus X because 1 minus X plus 2x equals 1 plus X that represents
the total number of particles in the system and those particles might be
chlorine molecules and they might be chlorine radicals but in total there is
1 plus X particles now it is the case that the molar mass of Cl2 over the
molar mass of the mixture is going to be equal to this 1 plus X that we just
calculated so let's go ahead and plug in the numbers that we have we know that Cl2
has a molar mass of 71 and the molar mass of the mixture is what we just
calculated that's our sixty two point four two six that's going to be equal to
one plus X now we solve for X and we get zero point one three seven and that
means that thirteen point seven percent of the chlorine molecules have
dissociated to produce chlorine radicals which is what gives us that reduced
average molar mass that is lower than the molar mass of diatomic chlorine so
there's a little bit of practice regarding Graham's law of effusion as well as equilibria to look at this system