Chemical Equilibrium & Beer’s Law | Intro & Theory


experiment 17 in CHEM 1212 is titled
Chemical Equilibrium and Beer’s Law. The principles and
concepts of chemical equilibrium are going to be
really important to you throughout your study of chemistry and if your future career involves
chemistry in any way shape or form you will use chemical equilibrium. I
guarantee it; so this experiment is really important.
With that in mind this video has two major parts. First of
all I’m gonna give a general introduction to
chemical equilibrium talk about how to think about it not just how the equilibrium constant is
defined and the relationship to free energy, but also
how to think about it at the molecular level and think about the processes that are
occurring when a system is in chemical equilibrium. In part two, we’ll get a little bit closer
to the actual experiment and we’ll talk about measuring equilibrium constant K or K_C or K_eq. The purpose in this
experiment is going to be really to measure the
equilibrium constant of the reaction of iron(III) cation with thiocyanate anion.
So let’s start with discussing chemical equilibrium in general. I’d like to use as a context
the reaction that we’re going to be investigating in this experiment which
is the coordination of the thiocyanate anion, SCN-, to the iron(III) cation, Fe3+, to form a complex [Fe(SCN)]2+. that’s easy enough for us to dream up
this reaction and write it as you see here, and cross our fingers that when we mix the
reactants they’ll actually form the product that we’ve drawn. In practice it’s not this simple to
design a working chemical reaction because it’s just as possible that the
reverse reaction might occur: the complex might break apart to form Fe3+ and SCN-. A
key question we have as chemists is, how do we know which direction—the forward, or the way
we’ve written it or the reverse direction—is more likely what we can say in general is that after an
infinite amount of time, so that effects due to differences in rate are essentially taken off the
table, both reactants and products will be present and the
relative amounts tell us whether the forward direction is
favored—in which case we’ll see more products— or the reverse direction is favored, in which
case we’ll see more reactants (or we may not see the reactants move toward product at all). This stage in which the rates of the forward and reverse reactions are equal and the amounts of reactants and
products are not changing the time is called chemical equilibrium and to
explore equilibrium in a little more detail, I want to think about it in terms of three
energies, because that’s really the origin of this state we see at chemical
equilibrium. So I’ll start with a free energy axis G that
runs vertically, low energy at the bottom, high energy at the top, and we can
imagine putting down the reactants and products on this energy graph. So the starting
materials here Fe3+ and SCN- are a
little bit higher in energy than the products, let’s just say
hypothetically. Now the forward direction corresponds to
moving from the higher energy reactants to the lower energy products and once we
reach the state of chemical equilibrium it’s really important to see that for
every event going from the reactants to products for every R to P event there is a corresponding event in the reverse direction that converts
products back to starting materials. So for every
conversion of a reactant to product there is a corresponding product to
reactant event. For every forward reaction there is a
reverse reaction event. This means that if we start with say four reactant molecules and 8 product molecules at the state of
chemical equilibrium, these amounts are not changing: for every
pair of reactant molecules that’s converted to products, one of the
product modules forms a pair of reactants. So at chemical equilibrium, the
amounts reactants and products are static. More correctly, the concentrations of the
reactants and products are static. Put another way, the rates of the
forward reaction R to P and the reverse reaction P to R are equal at this point. Notice however
that the amounts (in other words the numbers of moles) of R and P are not equal. I put a little
asterisk here because the one time they do end up
being equal is when the reactants and products are identical. But literally in any other case when the
reactants and products are different in any way shape or form, the amounts of
reactants and products at equilibrium are not equal. Furthermore there’s no
guarantee that we have more products than reactants or vice versa! That depends on the nature
of the particular chemical system we’re looking at. So if we think of a general reaction a
molecules of R going to b molecules of P, we can quantify the nature of the
equilibrium state using the equilibrium constant K_C. this is the molarity or the
concentration of P raised to the b power divided by the
concentration of R raised to the a power. And for more
than one product or more than one reactant we just add factors raised to their
respective stoichiometric coefficient to either the numerator or the
denominator respectively. Now K_C tells us at a sufficiently large
time whether we’ll have more products or
more reactants around, and so the equilibrium constant is a really
valuable piece of information the tells us whether a reaction will
work or not to some degree so a question we have then is, how do we
actually measure this? How can we study a chemical reaction to
measure K_C so that when another chemist comes along and wants to run this reaction to say
synthesize the complex for some application we can say to that chemist “yes, this
reaction will work and will go to products” or “no, don’t even try it; it’s not going to
move from reactants when you mix the iron(III) and the thiocyanate.” So in the remainder of this video we’ll explore how to measure K_C. So how
do we go about measuring K_C for the coordination of thiocyanate to iron(III)? Well, I see this is as basically a four-step
process two of the steps are quite easy and two of the
steps are a little bit more computationally involved. Step 1 is
simply to mix the reactants in known concentrations or known
molarities. We need to know these molarities for a later step, but of course setting up the reaction and
running it is going to be the key first step. The second step which is the easiest of
all is simply to wait go grab coffee go hang out with friends
go see a movie go do whatever you want to do, and take all
the time in the world. We need to give the reaction enough time
so that the forward and reverse reactions attain equal rates. Remember in general
those rates won’t be equal to start, and need to let the reaction, sort of adjust its
concentrations so that the rates of the forward and
reverse processes are equal and we’ve attained chemical equilibrium.
Once equilibrium has been achieved the next step is to measure the
concentrations of reactants and products. Once we have those in hand we can simply
plug those in to the equilibrium expression to
calculate K_C. Now I won’t talk about determining
equilibrium expressions—you talk about this in lecture in great detail— and I’ll just go ahead and tell you that the
equilibrium constant for this reaction is equal to the
concentration of the complex or the product divided by the concentration of Fe3+ times the concentration of SCN-.
This is the so-called equilibrium expression for this reaction. Truthfully once you understand how to
write equilibrium expressions the trickiest part in this entire
process actually becomes step 3, measuring concentrations. Measuring
concentrations is a little bit trickier than it sounds because we can’t simply
peer into a solution and visually identify
the number of moles of a molecule within a solution. So
concentration has to be measured indirectly, and the way we’ll measure it
indirectly is by using Beer’s law. Beers law
remember relates the absorbance of a colored
species within a solution to the concentration of that species
within the solution. In a nutshell it says that the more
molecules of absorbing substance you have in a solution, the larger absorbance
you’ll see, and they’re linearly related, so it relates A or the absorbance to (in our
case) the concentration of the only absorbing
species, which is the product. Only the complex absorbs light; Fe3+ and SCN- are for all intents and
purposes transparent, particularly at the wavelength where [Fe(SCN)2+] absorbs the strongest. So we’ll focus on the
concentration of the species in applying Beer’s law. And because we
knew the concentrations in the starting materials from step 1, we’ll be able to just
apply Beer’s law to the product and back-calculate the equilibrium
concentrations of the reactants. The constants you see in front of the
molarity of the complex term on the right-hand side of this equation are epsilon and l. l is just the path length
that the light travels as it traverses the solution for us, because all of our cuvettes are standardly built, it will be one centimeter across the board and so we
can essentially ignore that component in this equation, and the
epsilon is what’s called the molar absorptivity, and it’s really the
proportionality constant the tells us how much a mole [per liter] of [Fe(SCN)]2+ actually absorbs. We’ll measure this in
part A and to do that will generate a curve
that shows the absorbance as a function of the [Fe(SCN)]2+
concentration, which will be known. The curve we’ll get
will be a line and the slope of this line is the value
of epsilon. In part B we’ll prepare reactions with
known concentrations of the starting materials and unknown concentrations of the product,
and we’ll measure absorbance to determine the
concentration of the product. So we might measure an absorbance like you
see here in red, and we can project that onto the x-axis in a graphical way or we can use algebra to back-calculate the concentration of [Fe(SCN)]2+. From there, as I mentioned before, the
equilibrium concentrations of Fe3+ and SCN- can be determined from
their initial concentrations and the concentration of the product
that we just measured. The idea there is to use the stoichiometry of the reaction, and appreciate the fact that the only thing
that’s consuming iron and thiocyanate is the formation of the complex. So for
every molecule of complex that we have one molecule of Fe3+ and one molecule of SCN- has been taken away. With
the equilibrium concentrations of the
product, Fe3+, and SCN- in hand, we can just plug
back into the K_C expression that you see in the
middle of the slide here to determine the value of K_C. We’ll do
this with several different starting concentrations to illustrate that the value of K_C
that we calculate in each case is approximately the same even
though we’re varying the starting concentrations of Fe3+ and SCN-.

1 thought on “Chemical Equilibrium & Beer’s Law | Intro & Theory

  • Man this is the most awesome video in Equilibrium out there. Your content is gold! God bless you. You just earned a subscriber

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