Hello, today we're going to talk
about chemical equilibrium. But first just a word
about chemical reactions. Chemical reactions involve an exchange of
atoms due to collisions between molecules and/or atoms. An example is the reaction of
CO with O2 to produce CO2. Of course, in order to make the number
of atoms add up it has to be half an O2. So CO plus one-half O2 goes to CO2, and the common question would be what
are the relative amounts of CO and CO2 at equilibrium for some mixture
at a given temperature and pressure. So this is a question of
chemical equilibrium. And the equilibrium composition of
chemically reacting mixture is going to be the one that maximizes or minimizes
the appropriate fundamental relation. And for most problems of interest, we seek the composition at
a given temperature and pressure. So as a result, the Gibbs function is
the appropriate fundamental relation. So the Gibbs function can be
written as H minus TS or as, if we normalize it on
the number of moles per mole. It would be G is, lowercase g is equal
to lowercase h minus T lowercase s. And I have a bar over the lowercase letters to indicate that
there are molar quantities. So it's useful to write
the Gibbs function for particular species i at a given
temperature T, as g super zero for the given species i,
at the given temperature. Plus a correction term which corrects for the change in entropy, the pressure
dependence of the change in entropy between the given partial pressure and
some reference pressure. Usually that reference pressure and
tables is atmospheric pressure. So, Gibbs super zero is called
the Gibbs function of the pure substance at the standard state
pressure and given temperature. So, the Gibbs function can be
written as the Gibbs function of formation plus the change in
the Gibbs function between the actual temperature and
the reference temperature. And like the enthalpy of formation,
it's a zero for the element ,for elements in their naturally occurring
state at the reference condition. And we'll look at a table of this later. So the equilibrium condition
is going to be when the mixture Gibbs function goes to zero. So we write dG of the mixture
is equal to zero, where G of the mixture is equal to
the number of moles times the Gibbs energy of this particular species
summed over all the species. And just substituting
in the relationship for the Gibbs function from
the previous slides. And then taking the derivative we get at
dG of the mix which has to be zero is equal to the sum over the dNi. And there was a change in the number
of moles of species i times the Gibbs function for that species at the given
temperature and initial partial pressure. So that some therefore is zero. Now when we write the reaction
CO plus one-half O2 goes to CO2. It's really a statement
of conservation of atoms. There's one carbon and
two oxygens on each side. The coefficients one and
one-half on the left and one on the right are called
the stoichiometric coefficients. More generally you might write
a reaction as little aA, little bB plus whatever the other reactants are goes
to little eE plus little fF, and so on. So if that reaction proceeds
in one essay toward the right, then the change in the number of moles
of each species is directly proportional to its stoichiometric coefficients times
the progress of reaction variable that here we have called alpha. So for example, dNA would be minus
alpha a, dNE would be plus alpha e. So if we substitute this into
the equation for dG of the mixture, we obtain the following
equation delta G super zero at the given temperature is equal
to minus RT ln case K sub p. K sub p is called the pressure
based equilibrium constant. Delta G, large G super naught
T is written as the sum of the stoichiometric coefficients
times G super naught of the species. And it would be positive values for the products and
negative values for the reactants. So that the pressure based
equilibrium constant is equal to the expression on the bottom. In other words, it's equal to the partial
to a ratio of partial pressures of each of the products and the reactants,
divided by their reference pressure, all raised to the appropriate
stoichiometric coefficient. So this pressure based equilibrium
constant K sub p, here it is written for the example that we've been using
of CO plus one-half O2 goes to CO2. So then Kp would be equal to P of
CO2 over the reference pressure divided by P of Co, divided by
the reference pressure times PO2 divided by the reference
pressure to the power one-half. And K sub p, we will find is tabulated for
many, many species. So, it turns out that sometimes it's more
useful to have the equilibrium constant in terms of concentrations, molar
concentration, moles per unit volume. And typically concentration is
represented as with brackets. So for example,
x sub i within the square brackets is the molar concentration of species x. So that can be written as
the mole fraction of species i times p over RT, or
the partial pressure of i divided by RT. So then you can define an equilibrium
constant based on molar concentrations in terms of the pressure based equilibrium
constant, not shown on the bottom line. And this can be more generally
written as shown whether these are the stoichiometric coefficients. So the concentration based
equilibrium constant can be written say as the concentration
of E to the power little e. Concentration of F to the power little
f etc, for the products divided by the concentration of A to littl a,
times the concentration of B to little b, etc, or more generally in terms
of those products as shown. So, equilibrium constants are tabulated
in a number of sources in particular, in the NIST database janaf.nist.gov. JANAF stands for Joint Army Navy. It used to have two ends, used to be
Joint Army, Navy, NASA, Air Force. Now they're just called the JANAF tables. And these were developed back
starting in the Second World War when people needed thermochemical
properties because of the development of the jet engine and
rocket propulsion systems, and so on. And it was originally published as a book,
I have to book and then various supplements. But now it's located on the NIST website,
and we will in a moment,
explore that website for a bit. So, here is the web page for
the NIST JANAF thermochemical tables, it's just janaf.nist.gov. And it should show as a periodic table
here, and some other data links. You can actually download the most
recent version of the tables as a PDF. But you can also just go in here, and I'm
just going to put in CO2, carbon dioxide. And if I select that, I get the table, and this I believe is the table that
I showed in the previous slide. And so it lists as a function of
temperature, and this is by the way all for ideal gases up to a fairly high
temperature, 6,000 degrees Kelvin. And it gives the specific heat, the entropy gives this function
delta minus G, minus H over T. It gives the change in
enthalpy from the reference temperature, which is to 98.15K. And it gives the enthalpy of formation
that gives energy of formation and the log of the of
the equilibrium constant. So, and I believe it's the log to
the base ten, although you can get that, all that information from this website or
from the document itself. So, let's go back and put in oxygen O2 and we will see that oxygen, all of the enthalpy and
the Gibbs energy of formation. And therefore the internal energy of
formation would all be zero because oxygen O2 is the natural
occurring state of oxygen atoms at the standard reference state of
one atmosphere and 298.15 Kelvin. So again, you can get the specific heat. You can get the change in enthalpy with
respect to 298.15 Kelvin and so on. So that's it. Thanks, and have a great day.