—
In which Hank shows you that, while it may seem like the Universe is messing with us, equilibrium isn’t a cosmic trick. Here, he shows you how to calculate equilibrium constant & conditions of reactions and use RICE tables all with some very easy, not-so-scary math.
—
—
Transcript Provided by YouTube:
00:00
Last week, I told you about equilibrium, which is proof,
00:02
if you ever needed proof, that the universe is trying to mess with us,
00:05
because even though we think and talk about chemical reactions as being a straightforward process,
00:10
often times they’re also going backwards.
00:12
At the same time, the reactants are combining to form products like nitrogen and hydrogen to make ammonia,
00:16
or hydrogen and fluorine to make hydrogen fluoride.
00:18
The products are also breaking back apart into the reactants.
00:21
So there’s a sweet spot.
00:23
One particular ratio of reactants to products where the products form at the same rate that they break down.
00:28
When a reaction hits that spot, it’s said to be in its equilibrium state.
00:31
A bit of a kick in the head.
00:32
But of course you’re not totally at chemistry’s mercy;
00:35
you can tinker with chemical equilibrium by altering the concentration of the substances
00:39
and their temperature and if they’re gases, the pressure on them.
00:41
For example, adding pressure to the Haber Process that we use to create ammonia essentially
00:45
shifts the position of equilibrium,
00:48
so the result of the reaction is more ammonia being produced than nitrogen and hydrogen.
00:52
But, wouldn’t it be a lot more helpful if you knew
00:54
how much pressure you’d have to add to produce the exact amount of ammonia you needed,
00:59
or how much hydrogen fluoride it takes to refine a certain volume of gasoline.
01:03
Math, of course, is the way to answer questions like these, so today I’m going to show you some simple,
01:07
totally non-scary calculations that will help you get a handle on chemical equilibrium.
01:12
[Theme Music]
01:21
The first and most important thing you need to do equilibrium calculations is the equilibrium constant.
01:27
This number is unique for every reaction and represents
01:30
a molar ratio of products over reactants when a reaction is at equilibrium.
01:36
Equilibrium constants are easy to set up but hard to explain,
01:39
so let’s start with an example using this obviously fake chemical equation.
01:43
The capital letters stand for the reactants and the products
01:46
and the lowercase letters stand for their coefficients.
01:49
The equilibrium constant, or Keq, is equal to the product of the molar concentration of the products
01:53
divided by the product of the molar concentration of the reactants.
01:56
Each concentration is raised to the power of its coefficient in the balanced equation.
02:00
Now this is important; we’re using the coefficients as exponents here
02:04
because we’re multiplying all the products and all the reactants,
02:08
not adding them like you would do in a balanced equation.
02:11
Generations of students have messed up test scores by getting this part wrong, but you will not do that.
02:18
So again, it’s the product of the products of the product of the reactants and the coefficients become exponents.
02:24
Actually pretty simple.
02:25
The square brackets in the formula are used by chemists to represent molar concentration,
02:29
or molarity: moles of solute per liter of solution.
02:32
These equilibrium constant equations and the constants themselves
02:36
are one of the few places where you don’t need to write them with every number.
02:39
Just remember to convert everything into molarities before plugging numbers into the equation.
02:42
One last thing before we do a calculation: as we learned in the last episode,
02:45
a change in temperature changes the position of equilibrium.
02:49
Therefore, the equilibrium constant is only true for a specific temperature.
02:53
Constants are normally calculated at 25 degrees Celsius, which is close enough for most situations,
02:57
but the temperature should always be mentioned along with the constant.
03:00
Fortunately for us, chemists have already figured out the equilibrium constants for most common reactions.
03:05
Carbonic acid, for instance, which is basically just carbon dioxide dissolved in water,
03:10
dissociates to form carbonate ions and hydrogen ions.
03:12
You’ll see this reaction again later when we talk in depth about carbon and the planet’s carbon cycles.
03:17
More importantly, right now, the reaction is perfectly reversible with an equilibrium constant of 1.66 x 10^-17.
03:25
For this reaction, Keq equals the product of the molar concentration of the carbonate ion
03:31
and the molar concentration of the hydrogen ion,
03:33
which is squared because hydrogen’s coefficient in the balanced equation is 2,
03:37
all divided by the molar concentration of carbonic acid.
03:40
Now, let’s not be boring and throw a bunch of numbers around.
03:42
What you need to see is that the quotient on the right must always yield the same number because it’s a constant.
03:49
So, if the amount of CO2 in the atmosphere increases leading to more H2CO3 in the earth’s water,
03:54
the concentration of carbonate ions and/or hydrogen ions must also increase so the total will match the Keq.
04:01
You should also notice that any change to the concentration of hydrogen ions
04:04
will have a huge effect on the denominator because its square.
04:08
So an increase in hydrogen ions, like if the water were somehow acidified by an outside source,
04:12
would require a huge decrease in carbonate ions or a huge increase in carbonic acid —
04:18
carbon dioxide pulled in from the atmosphere to satisfy the equilibrium condition again.
04:21
We can attack this problem from another direction, too, depending on what information we have to begin with.
04:26
Chemists often know not only the equilibrium constant for a reaction,
04:29
but also how much of each reactant is available.
04:32
And all they need to figure out is exactly how much of each substance will be present at equilibrium.
04:36
This type of calculation is easiest using a format called a RICE table.
04:40
RICE stands for Reaction, Initial, Change, and Equilibrium.
04:43
On the R line at the top of the table, we write the chemical equation of reaction,
04:48
leaving space between each part so we’ll have room to add more information below.
04:52
On the I line we write the initial concentrations of each substance.
04:55
Some of those will almost always be zero, since products generally aren’t present until the reaction begins.
05:01
The C line is where we map out how much of each substance will change during the reaction.
05:05
We often don’t know exactly how much this is until we do the math,
05:08
so we start out with x, where the amount is unknown.
05:11
The E line is where we put the final result: how much of each substance will be present at equilibrium.
05:16
Since the final amount is just the initial amount plus any changes that have occurred,
05:21
this line is the sum of the initial line and the change line.
05:24
Let’s do this for hydrogen fluoride, or HF, an integral part of the process of refining gasoline.
05:30
It can be formed in the gaseous state by an equilibrium reaction between hydrogen gas and fluorine gas.
05:36
Start by writing the balanced equation.
05:38
For our initial concentrations,
05:39
let’s use 3.00 mol of H2 and 6.00 mol of F2 in a 3.00 liter container at a certain temperature.
05:47
That makes the initial concentration of H2 3 moles in 3 liters, or a 1.00 molar solution.
05:52
Similarly, the initial concentration of the F2 is 6 moles per 3 liters, or 2 molar.
05:57
No HF has formed yet, so it’s initial concentration is 0.
06:01
So what we’re trying to figure out is how much of the hydrogen and the fluorine
06:03
will react to form hydrogen fluoride under these conditions.
06:06
So we’ll call the change ‘x’ for now.
06:08
Since 1 mole of H2 and 1 mole of F2, combine to form 2 moles of HF.
06:13
We can say that the H2 and F2 will each lose ‘x’ moles per liter while the HF gains 2x moles per liter.
06:20
That’s on the change line of your table.
06:22
So that leaves the equilibrium line where you write your totals.
06:25
For H2 we have a total of 1.00 – x molar. For F2 the total is 2.00 – x.
06:32
For the HF the total is 2x molar.
06:35
Now we apply these figures to our formula for the equilibrium constant.
06:39
Based on the table in the back of my textbook, the Keq for this reaction is 115 at the given temperature.
06:44
We plug in the numbers from our RICE table and solve for x.
06:47
And we end up with this. Which you probably recognize as a quadratic equation.
06:51
Just so you know that doesn’t happen with every equilibrium calculation, but it’s an extremely common result.
06:56
To solve the quadratic equation we have to use the quadratic formula.
06:59
And to do that we have to think of the coefficients of our equation as a, b, and c in that order.
07:05
Then we plug them in the corresponding positions in this formula:
07:09
-b +/- the square root of b2 – 4ac, all divided by 2a.
07:15
Once we finally get all the numbers in the right places,
07:17
it becomes a matter of grinding through some basic algebra.
07:20
And because of the way the quadratic formula works, we’ll get 2 possible answers.
07:24
To figure out which one is the right one, think back to the beginning of the problem.
07:28
I said the initial concentration of the H2 was 1 molar, and the initial concentration of the F2 was 2 molar.
07:35
And x is the amount that each one lost, right?
07:38
Well neither the H2 nor the F2 could possibly lose 2.13 moles per liter
07:43
when they both started with less than that already.
07:45
So clearly, the correct answer has to be 0.968 molar.
07:50
Using that then, we can calculate the actual equilibrium amounts for each substance.
07:54
At equilibrium, under these specific conditions the concentration of HF is 2x,
07:59
or 2 x 0.968, which equals 1.94 molar.
08:02
The concentration of hydrogen will be 1 – 0.968 or 0.032 molar.
08:07
And the concentration of fluorine will be 2 – 0.968 or 1.03 molar.
08:12
As we learned last week, those values can be shifted.
08:16
For instance, to maximize the hydrogen fluoride production by adding or removing some of the substances.
08:21
Or by changing the pressure or temperature on the system.
08:24
That’s why these calculations are so valuable to scientists.
08:27
Just a little bit of algebra allows us to maximize the benefit that we receive from
08:31
the things that nature is already doing anyway.
08:33
If the universe really is try to take advantage of us, we’ve certainly figured out how to take advantage right back.
08:37
So the next time you’re wondering why you learned this stuff in math class, now you know.
08:41
Thanks for watching this episode of Crash Course Chemistry.
08:43
Today you’ve learned some mathematical tools to help us make more efficient use of equilibrium reactions in real life.
08:49
You’ve learned how to calculate an equilibrium constant, Keq.
08:52
You’ve learned how to calculate the equilibrium conditions of reactions just from knowing their initial conditions.
08:57
And you’ve learned that a RICE table isn’t just a place where you eat sushi.
09:01
And you may even have learned a little bit about the quadratic equation.
09:04
This episode was written by Edi González. The script was edited by Blake de Pastino.
09:08
And our chemistry consultant was Dr. Heiko Langner.
09:11
It was filmed, edited, and directed by Nicholas Jenkins. The script supervisor was Katherine Green.
09:15
The sound designer is Michael Aranda. And our graphics team is Thought Café.
—
This post was previously published on YouTube.
—
Photo credit: Screenshot from video