Chemical Equilibrium and Reaction Quotients Video Lecture | Physical Chemistry

hey it's professor Dave, let's look at
chemical equilibria.
sometimes chemical reactions are not unidirectional,
they are reversible. the reactants create the
products which then go right back and
create reactants. this means there is
both a forward and reverse reaction. when
the rates of the forward and reverse
reactions are the same this system is
at dynamic equilibrium. chemistry is
happening but because the reactions are
happening at the same rate there doesn't
appear to be any activity. there is a
balance. we learned how to use
stoichiometry to discuss limiting
reagents and how much of the products to
expect but these were for unidirectional
reactions where we assume that all the
reactants make products and then the
reaction is over. with equilibria it's a
little more complicated to calculate
what the concentrations of each
substance will be at equilibrium so
we're going to have to do a little bit
of math to be able to describe the
system. for example let's look at this
equilibrium let's say we start with one
mole of PCl5, allow the system to reach
equilibrium, and then once at equilibrium
we measure that there are 0.135 moles of
PCl3. so how much of the other two
things are there? to answer this we can
make something called an icebox. these
letters stand for initial, change, and
equilibrium. we set them up like this. for
initial we put the initial amount of
each thing we started with, just one mole
of reactant so we put one there and
zeros for the products since there
wasn't any of those at first. then for
the change we don't know exactly how
much the change was to get to
equilibrium so we call it x. for the
reactant we put negative x because
that is being depleted and in this case
all of the stoichiometric coefficients
are one so as x moles of reactant are
being depleted
x moles of each product are being formed.
we would make these two or three x as
necessary if the coefficients were
different. and for the products x is
positive because these are being formed.
then lastly we add up the initial and
the change to give the amounts present
at equilibrium. for the reactant this is
1-x and for the products it is simply
x. we measured the final concentration
of PCl3 as 0.135 which here
will correspond to x and we therefore know
all the other concentrations by plugging
in x
simple, no? well it can get trickier as we
will see but first let's learn about
equilibrium expressions. every
equilibrium has an equilibrium constant
Kc. it will be given by the
concentrations of the products each
raised to the power of their
stoichiometric coefficients over the
concentration of the reactants each
raised to the power of their
stoichiometric coefficients. this is
called the equilibrium constant
expression. one thing this constant tells
us is whether the products or reactants
are favored in the equilibrium. if Kc
is much greater than one that means the
numerator is bigger so we are creating
more products. if Kc is much less than
one that means the denominator is bigger
and we are creating more reactants. when
we write this expression we only take
into account gases and aqueous species
solids and pure liquids will not be
included in the expression. for example
here
notice how carbon is not included in the
expression since it doesn't make sense
to discuss a solid in terms of a
concentration. sometimes we may want to
predict which way a mixture will go
given some non equilibrium quantities. to
do this we plug in non equilibrium
values into the Kc expression to
calculate the reaction quotient, Q. if
Kc is bigger than Q, Q is more on
the reactant side so it'll make more
products to equilibrate. if Kc is
smaller than Q, Q is more on the
product side so it'll make more
reactants to equilibrate. when Kc
equals Q the system is at equilibrium.
let's try a more difficult icebox. given
the following information
calculate the equilibrium concentrations
of each substance in terms of molarity
remember that molarity is moles per
liter. so we set up our icebox and
calculate the concentration of our
reactant. that'll be the initial value and
zero for the products. now here the change
will be different for each substance
because of the stoichiometry
for every two moles of reactant we get
one mole of each product so we have to
subtract 2x here and add x here.
then equilibrium is just the sum of
initial and change
plug them into the equilibrium
expression and solve for x. luckily on
the right
both the numerator and denominator are
squared so we can take the square root
of both sides. if it wasn't this
convenient we may have had to use the
quadratic equation. but as is we can
solve for x and use that to determine
all the equilibrium concentrations. let's
check comprehension
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