I'm going to present a brief introduction to the equilibrium constant, and remember
the equilibrium constant is dimensionless and this is important, so K is dimensionless
and of course this term in the exponential is dimensionless, where delta G is the change
in the Gibbs free energy at standard state conditions. So let's look at a simple A goes
to B plus C reaction, if we write down the equilibrium constant we have to write it in
terms of the activities, activity of B, activity of C, and then reactant, and the hat just
indicating activity in solution, in general, if this were two A goes to B plus C then the
A activity in the denominator would be squared. Let's look at some special cases, first let's
look at the case of ideal gases, and for an ideal gas the activity of B, which is going
to be the ratio of the fugacity of B in solution, in the mixture, over the fugacity of B at
standard state conditions for the pure component, now this is the general definition of activity,
whether it's an ideal gas or a liquid or a solid, if it's an ideal gas then this fugacity
in the mixture is going to be the partial pressure of B and the typical standard state
is an ideal gas, pure component, at one bar pressure and the same temperature and so the
fugacity then of pure component is going to be one bar, and then the partial pressure
would be the mole fraction times the total pressure divided by one bar and so this would
be the activity of B that we would substitute in to this equation, if all three are gases,
so if A B and C are ideal gases then our equilibrium constant, mole fraction of B, mole fraction
of C, and then pressure squared divided by pressure, so we'd have pressure, where we
have to keep in mind the pressure is in units of bar and this is dimensionless. So if we're
at a constant temperature and we're looking at this same reaction, A goes to B plus C
and we were to increase the pressure, so if we somehow, piston and cylinder arrangement
for example, we raised the pressure, what this equilibrium expression tells us is this
term must decrease because this is a constant, at constant temperature the equilibrium constant
does not change, so increasing the pressure for this reaction sends the reaction back
towards reactants, and that's what this equilibrium expression tells us, we decrease the mole
fractions of B and C and we increase the mole fraction of A. So let's look at the case where
we instead have a liquid as one of the species and so now liquid phase, if component B is
a liquid well it's activity again is the ratio of fugacities and the fugacity of component
B would be the mole fraction, the activity coefficient to account for it being a non-ideal
mixture, the saturation pressure of B and then we may have to have a correction if we're
at very high pressures, the Poynting correction, we're going to forget about that for now and
assume we're at just moderate pressures, so the pressure is not effecting the fugacity
of the liquid significantly and the standard state is the pure liquid at the same temperature
and one bar so one bar, close to an ideal gas, the fugacity is close to the saturation
pressure and so we can see that the mole fraction in the liquid phase time the activity coefficient
is going to be activity and the activity would be the mole fraction if we're an ideal solution,
an ideal solution then, the activity coefficients are one. If it were a pure liquid, let's assume
B exists as a liquid and the other components are in different phases, then the activity
of B, again that's the fugacity of B in the mixture but now it's a pure component, fugacity
of B at standard conditions, same temperature, so the only difference is the pressure and
if we're not at very high pressures the fugacity does not change very much so to reasonable
approximation the activity is one in the equilibrium expression, and we have the exact same thing
if it's a pure solid, the activity of B if it's a pure solid is also approximately one,
so if we have, for example, a reaction where A is a solid and B is a solid and C is a gas
and A and B are immiscible, so they exist as two separate solid phases, that's critical,
they're separate solid phases, activity of B is then one, the activity of A is also one
and the equilibrium constant is just, and let's say it's an ideal gas, it's just the
pressure of C times one and divided by one, so the equilibrium constant, pressure of C
where again we have to use units of bar because we understand it's the pressure of C divided
by one bar so for the case where the solids are not miscible so A and B are solids that
don't mix, the equilibrium constant simplifies quite a bit.