Reading Notes
for Chapter 13
These are Dr. Bodwin's reading notes for Chapter 13 of "Chemistry
2e" from OpenStax.
I am using a local .pdf copy that was downloaded in May 2020.
Chapter
Summary:
Up to this point, we've discussed chemical reactions as if they either
"go" or "don't go". In reality, all
reactions occur, we just have to determine how far they go. The term equilibrium
is used commonly enough that we all probably have some sense of what it
means, but how does it apply to chemical reactions? By building upon
collision theory and our discussions of kinetics, we can begin to
understand what chemical equilibrium is and how to interpret it.
Equilibrium
& Equilbrium Constants:
We've actually talked about equilibrium before. Recall the discussion
of vapor pressure;
when the rate at which liquid molecules escape to the gas phase is
equal to the rate at which gas molecules condense into the liquid
phase, we observe a constant pressure that we called vapor pressure.
This is an equilibrium!
There are many ways to think about equilibrium. Consider the simple
example described here.
The most important thing to remember about equilibrium is that it is
dynamic; the forward reaction is always
happening, and the reverse reaction is always happening.
Because equilibrium is dynamic, it doesn't matter if we start with all
reactants, or if we start with all products, or if we start with some
mixture of reactants and products, the equilibrium that we react (and
the equilibrium constant) will be the same in all of these cases.
Equilibrium
Constants - Key Points:
Based upon the balanced chemical equation.
Always positive.
Have no units.
Pure solids and pure liquids do not appear in K
NOTE: For now, "pure solids and pure
liquids do not appear in K" works for us, so feel free to lock that
into your brain as a "rule". Are you curious why it's true? Formally speaking,
equilibrium constants have activities,
not concentrations. You get an activity by dividing a concentration in
units of "M" by "1 M", so we can just use the molar concentrations
directly. That's also why equilibrium constants have no units. What
about pure solids and liquids? By definition, their activity is "1", so
although in the most formal sense they do appear in the equilibrium
constant, they are just multiplying and/or dividing by 1 raised to some
power. One raised to any power is... 1. And number multiplied or
divided by 1 is... unchanged. So for the level that we are studying
equilibrium, we can just ignore pure solids and liquids in constructing
our equilibrium constants.
K>1 is product-favored.
K<1 (but always greater than zero...) is reactant-favored.
K values can vary greatly and are usually best expressed using
scientific notation.
Think about scale when evlautating "differences". Because K values can
be so large, differences become, well, different. For example, an
equilibrium constant of 238.8 is not really all that different from an
equilibrium constant of 295.3; it is
different from an equilbrium constant of 4.286E5!
Most of the equilibria we will discuss are in solution, so we will use
Kc. If the reaction is in the gas phase, we could use KP and use
partial rpessures instead of concentrations.
We will look at an entire alphabet soup of "different" K values.
Although each different subscript describes a different type of
reaction, these K values are all conceptually the same, they all mean
the same thing, and they all follow the same rules. Don't make them all
into completely new things!
Reaction
Quotient:
Mathematically, the reaction quotient, Q, has the same form as the
equilibrium constant for a reaction.
By comparing Q to K, you can determine if the reaction is at equilibrium, or if the reaction
has to shift toward products
to reach equilibrium, or if the reaction has to shift toward reactants to reach equilibrium.
Manipulating Equilibrium & Equilibrium Constants:
Changing the reaction we're looking at changes the equilibrium constant, but often in mathematically calculcable ways.
The heart of equilibrium is that all reactions are reversible (to some
extent). If a reaction is reversed, reactants become products and
products become reactants. This "flips" the numerator and denominator
of the equilibrium constant ratio, so the value of K is also inverted.
Coefficients in balanced chemical equations appear as exponents in the
equilibrium constant expression, so multiplying all the coefficients in
a reaction by a constant raises the K value to that power.
LeChatelier's Principle:
Equilibrium is a balancing act. The concentrations of reactants and products are balanced.
If a system at equilibrium experiences a "stress", the equilibrium will shift to relieve that "stress" if possible.
In this case, "stress" can be:
- Adding or removing a reactant or product - This action will change the concentration. If you add something, the reaction will shift away from what you add. If you remove something, the reaction will shift toward
- Changing temperature - This is the same (essentially) as adding
or removing a reactant or product, you just have to think of "heat" as
a reactant or product. For an endothermic reaction, heat is a reactant; for an exothermic reaction, heat is a product.
- Changing pressure - If the pressure is changing without changing the amount of reactants or products, then the equilibrium will shift to relieve the pressure, if possible.
Remember from ideal gas behavior, gas particles move randomly and
independently, regardless of which gas particle it is. Assume a
reaction with 4 total gas particles on the reactant side and 2 total
gas particles on the product side. If this reaction is at equilibrium
and the pressure is increased, the equilibrium will shift toward the side with fewer gas particles; if the pressure is decreased, the equilibrium will shift to the side with more
gas particles. EXCEPTION: If the number of gas particles is the same on
both sides, changing the pressure will not shift the equilibrium.
LeChatelier's Principle is the chemistry version of a concept that
shows up in a LOT of places. For the biology/ecology crowd, the concept
of "carrying capacity" for predators and prey is just a different
version of LeChatelier's Principle. This concept comes up in a number
of ways in economics and finance; if you experience the stress of
losing your job, you will (hopefully!) shift your spending habits to
re-establish an equilibrium where your income and expenses are balanced.
Catalysts and Equilibrium:
All of chemistry can be lumped into either thermodynamics or kinetics.
Thermodynamics compares the energy of reactants to the energy of
products. Enthalpy is a thermodynamic concept. Whether a reaction is
endothermic or exothermic is not really a factor in the rate of the reaction.
Kinetics explores the activation energy of a reaction, and activation energy determines rate.
Equilibrium is a thermodynamic concept. Catalysts affect the kinetics. Addition of a catalyst to a reaction does not affect the equilibrium of the reaction, it just affects how quickly the reaction reaches equilibrium.
Equilibrium Calculations:
The
calculations required to answer equilibrium questions are not
especially difficult BUT organizing the information can be a challenge.
The easiest way to keep things organized is by using a table.
Your textbook (and many sources) refer to these as "ICE Tables".
Personally, I don't care for that term, so I am unlikely to use it, but
if it helps you keep things straight, then go for it. I will always use a table of initial concentrations, changes in concentration, and final concentrations to understand equilibrium.
Your textbook has some good examples of an initial/change/equilibrium
concentration table starting with Example 13.7. Use tables. Even if you
think you "got this", use a table. Even when you've done 284 sample
problems, use a table. The 30 seconds it will take you to write out a
table and use it to solve your problem is WAY less than the 20 minutes
it will take you to find the error without a table if you get the
problem wrong.
When we're doing equilibrium problems, we have to be able to use some
"super powers" to stop and start time at will. When we mix up a bunch
of chemical to start a reaction, we have to think about mixing
everything together but not
allowing the reaction to start. That's how we get the initial
concentrations. Then, we press the magic button and "allow" the
reaction to occur. In reality, the reaction starts as soon as the first
bits of reactants are mixed together, but to make it easier for us to
understand, we get to use this time-stopping super power to help.
Equilibrium problems will require you to exercsie your algebra muscles to rearrange equations. You may also end up having to use tools like the quadratic formula
to find some answers. This is why setting up your problem clearly is so
important - it helps me (and you!) find where things start going wrong
in a problem.
Simplifying Assumptions:
Some
equilibrium calculations can get a little "thick", but we can often
make some assumptions that will simplify our calculations. Some
important notes about assumptions:
- Always clearly state the assumption you are making.
- Always circle back and check that you assumptions are valid.
Specifically for equilibrium calculations, the assumptions we make are
actually related to the concept of significant figures (everyone's
favorite concept!!).
- For reaction with very small equilibrium constants (very reactant-favored),
the amount of reactant lost is often very small, so we can disregard
the loss of reactant. For example, if my initial concentration of "A"
is 1.284M and in my equilibrium table I have the term (1.284-x)M, if x
is very small, then I can assume
that (1.284-x)M is equal to 1.284M. For a non-chemistry analogy, if I
have a dump truck full of gravel and I remove 4 pieces of that gravel
from the truck... I still pretty much have a dump truck full of gravel.
- For reactions with very large equilibrium constants (very product-favored), the
amount of product formed will probably be very close to the theoretical
yield. That lets us treat some of the values a bit differently as well.
Assumptions are nice because they simplify the math, and we can always make an assumption as long as we check that it is valid. If the assumption ends up not
being valid, we haven't really lost much time and effort, and we can
crank through the "ugly" math that we were hoping to avoid.
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