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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