Leah here from leah4sci.com/mcat and in this video we're going to look at limiting reactants
including how to calculate product yield and excess reagent.
When I learned this topic in general chemistry, I found it very confusing because we focus
only on the Math and not the logic.
It only became clear once I understood what was happening and that's exactly what I wanna
focus on today, but first what is a limiting reactant?
The limiting reactant also called the limiting reagent is the thing that's used up first
in a balanced reaction, say have a reaction in which one molecule of A reacts with two
molecules of B to give me product C, I have a beaker here with a random number of A and
B and I want to know which is going to run out first, is it A or B?
According to the balance reaction we have one A for every two B, so that means if I
use one A or two B, I get one product, A, two B, two products, three, four, five, and
look at that, I have two A's and I only have one B. I can't suddenly mix it up and say
"You know why what for the final we'll use two A's and one B", No.
For that last one I can use half of A with that one B, leaving me with 1.5 A remaining,
this means that when B is used up, I still have 1.5 A left over, that means I have an
excess of 1.5 A and in the process of using up all of B, I had 5.5 products or a yield
of 5.5 C come out of this reaction.
Let's work through this again, but this time numerically.
If I have A reacting with two B to give me C and my starting reagents include seven molecules
of A and eleven molecules of B. Even though it looks like I have less of A and it looks
like I should run out of A first, when I run a limiting reactant calculation where I showed
you by crossing them out, we realize that we actually run out of B before we run out
of A and that when we use 5.5 of A with eleven of B, we get a total 5.5 of C products.
How did we know that?
When we matched up one A for every two B, we noticed that we were able to use up all
eleven molecules of B and still have a little bit of A left over by comparing them to each
other.
Now in your limiting reactant problems they're going to be more complicated so we want to
use a more mathematical approach, But I wanna make sure you first understand what is going
on here.
To do that, let's use a simple reaction of meal Prepping sandwiches because who doesn't
love food?
In order to meal prep these sandwiches, we need to follow a very specific and exact recipe
and in this recipe, lets keep it healthy, we'll start with 2 slices of bread which we'll
call reactant B, 3 slices of turkey which we'll call reactant T and 5 pieces of lettuce
which we'll call reactant L. Now you take your recipe to the supermarket but they don't
sell them in sandwich kits that has 2 to 3 to 5 bread turkey to lettuce, they come in
different types of containers, say you buy a pre-sliced loaf of bread that has 18 slices,
we have 18 B, you buy a package of cut turkey and realize you have 20 slices, that's 20
T and after separating and washing some [00:4:04] you realized that you have a total of 25 usable
slices of lettuce, 25 L.
So how many sandwiches does this give us for the week?
Well it looks like we have the least amount of bread so we'll probably run out of bread
first, is bread my limiting reactant?
Let's not jump to conclusions, let's calculate.
The first thing we need is a balanced equation and for this equation we have 2 B reacts with
3 T and 5 L to give us 1 S for one sandwich.
With this balanced equation we now have a ratio of reactants as follows, 2 B to 3 T
to 5 L. For every 2 breads we use 3 turkey and 5 lettuce to get one product, one sandwich.
Within this topic you can be tested on a couple of different things, you can be asked to find
the limiting reactant or limiting reagent and that's the reactant or the reagent that
gets used up first.
You can be asked to find the product or the yield and that simply how many reactions going
to completion to give us how much product, and then you may be asked to find the excess
reactant or excess reagent and that's the thing that gets left over after the limiting
reactant was completely used up and reacted.
In our previous example because B was used up first, B was our limiting reagent, we have
left over A that means we had 1.5 excess of A and our yield was 5.5 of our product C.
Knowing this, we have 2 ways that we can approach calculation, the first is comparing the mole
ratios of reactants to each other, like we did with earlier example of every A cancelled
2 of B and the second is calculating the max product from the reactant from each of the
reactants to see which one gives you less product.
Both of these options work, it's simply a question of what makes sense in this particular
situation and more likely which one you're more comfortable with.
In this video, I'm gonna walk you through both.
For the first method of comparing mole rations, we're going to use slices instead of moles
since we're not going to calculate the exact number of grams in every slice of bread turkey
and lettuce, instead we'll set up a ratio between bread and turkey and then another
ratio to lettuce comparing each reactant to the other one.
The reactant I calculate first doesn't really matter because I like to do a guess and check
method.
I'm guessing that we're going to run out of bread first because we have the lowest number
of bread but i'm not that confident so let me check, I guess bread, now I will check
by comparing it to turkey.
We'll use the given x ratio method which you can on my website leah4sci.com/conversions
or see the link below.
Since we're comparing bread to turkey, we want to start with our given which is 18 slices
of bread and then multiply that by the stoichiometric coefficient or the ratio between bread and
turkey which in this case is 2 bread for every 3 turkey.
I set up my ratio with 2 bread on the bottom and 3 turkey on top, this allows me to cancel
bread and give me an answer in units of turkey, then we run the math, we have 18 x 3 divided
by 2.
Remember on the MCAT you can't use a calculator so we'll use some of the shortcuts that I
teach on the MCAT math series link below, we can simplify 18 divided by 2 as 9 over
1 which gives a simple math as 9 x 3 which is 27 divided 1, 27 turkey.
This is what we need to pay attention to, if we used up all of the slices of bread and
had perfectly stoichiometrical coefficence in each of the sandwiches, we would need a
total of 27 slices of turkey to get through 18 slices of bread.
Problem is we only have 20 slices of turkey, we're going to run out of turkey if we ever
get the 18 slices of bread.
This is key, if the number that you get when comparing the mole ratios to each other is
more than what you have, that thing is not available in a high enough quantity, that
is a limiting reagent.
We haven't accounted for lettuce yet but just between bread and turkey, we know that the
turkey is going to run out before the bread so let’s make a note of that and then we
run another calculation.
Now, looking at turkey and lettuce, I have less turkey, I can guess again that turkey
is my limit but I wanna verify, I want to check by running A turkey to lettuce ratio
just as we did for the bread.
Setting is up is given x ratio, my given is 20 slices of turkey, my ratio is 3 turkey
on the bottom so that I can cancel and 5 pieces of lettuce at the top because I need 5 lettuce
for every 3 turkey.
This math looks a little dicey if we're doing math without a calculator but remember, on
the MCAT close enough is good enough so let’s take some simplifications.
Your first option is to run it all the way through, 20 x 5 is a hundred divided by 3,
this is a ratio that you should know and that is 33.
If you wanted to simplify that 20 is very close to 21, 21 divides by 3 very nicely giving
me 7 over 1, 7 x 5 is 35 and look at that, 35 is very close to 33.
But what is the unit if we cancel turkey?
We're left with lettuce; our answer is in units of lettuce and that's a problem isn't
it?
We do not have 33 pieces of lettuce.
If we used up all of the turkey, we would require 33 pieces of lettuce which we don't
have and that means lettuce is our limited reactant or limiting reagent.
How did we know?
First we prove that if we use up all of the bread, we'll run out of turkey first, bread
is not our limit, then we proved that if we use up all of the turkey we're gonna run out
of lettuce first because we don't have enough, turkey is not our limit.
That leaves lettuce as our limiting reagent.
The second option is finding the total products for each which will require a calculation
that compares the reactant to the products.
That means you're going to require 3 calculations, 1 each for bread, turkey, and lettuce.
Notice in the last attempt, we only have 2 calculations to get our answer, here we need
3 calculations which is something to take into consideration when deciding which way
to go.
So why would you even bother with this method?
But what if the question asks you to find the total in addition to the limiting reagent,
this one is going to find the total in the process of finding the limiting reagent.
Once again we're going to set it up as a given x ratio with one equation for each reactant.
We'll have our 18 breads, 20 turkeys and 25 lettuce
The ratio that we're going to use is simply the reactant compared to the product our first
ratio has 2 slices of bread for every 1 sandwich, bread goes on the bottom so that we can cancel
out, our second reaction has 3 slices of turkey for every 1 sandwich, our third reaction has
5 pieces of lettuce for every 1 sandwich.
What does that give us?
If the breads cancelled and we have 18 divided by 2 we get 9 sandwiches if we used up all
the bread.
For the second example 20 turkeys divided by 3 per sandwich, that's approximately 21,
remember on the MCAT, close enough is good enough and 21 divided by 3 gives us 7 sandwiches
with the lettuce we have 25 lettuce, lettuce cancels and 25 divided by 5 lettuce per sandwich,
25 divided by 5 is 5 giving us 5 sandwiches.
Okay so what does this tell us?
It tells us that if we used up all the bread assuming we had enough of everything else
and bread was the limit, we can get up to 9 sandwiches just by the number of bread alone.
If turkey was our limit and we have enough of everything else, using up all the turkey
would give us approximately 7 sandwiches and if lettuce is our limit and we have enough
of everything else, using up all the lettuce gives us 5 sandwiches, based on this information,
if lettuce gives us 5 sandwiches which is the lowest amount that means that the lettuce
is going to run out first because the lettuce would run out at 5, turkey at 7 and bread
at 9.
This tells us the lettuce is our limit which we already knew from the previous calculation
but this is how we found it here and at the same time we also found that when all of the
lettuce runs out, we have a yield of 5 sandwiches.
Knowing that lettuce is our limit and that it's going to give us a total of 5 sandwiches
the next thing we want to find is the excess of each, to do this we're going to run the
same type of equation again using given x ratio but this time our given is 5 sandwiches
and the ratio is for every 5 sandwiches how much of everything else do I need.
We don't have to run this math for lettuce because we know we're using it up completely,
it's the limiting reagent and when it's used up it's completely gone but I’ll show you
the math just in case.
Our given in this case is our product, 5 sandwiches x the ratio of 1 sandwich for 5 pieces of
lettuce.
Why?
Because if we get a total 5 sandwiches and every sandwich requires 5 pieces of lettuce
how much lettuce will we use, we expect to use it all up?
Let's see.
If we run the math 5 x 5 is 25, sandwiches cancel and certain units of lettuce, 25 lettuce
used up, 25 lettuce provided, completely used up.
We knew that but what about turkey?
If we make 5 sandwiches and every 1 sandwich requires 3 pieces of turkey, how much turkey
do we need?
Units of sandwich cancels, 5 x 3 is 15, 15 turkey required but we're given 20.
So we'll take the 20 turkey that we're given minus the 15 turkey that we used to make the
sandwiches for a total of 5 turkey in excess, now if you were me, you'd probably just eat
the 5 slices of turkey right there while you finish wrapping up your sandwiches but in
the chemical equation, you can't use extra, everything has to be exact.
What about excess bread?
We know we're making 5 sandwiches x the ratio of 1 sandwich requiring 2 slices of bread,
we run the math at 5 x 2 which gives me 10, sandwiches cancel leaving me units of bread,
10 slices of bread are used up in the making of 5 sandwiches, so what does that leave me
for the excess?
If I have a total of 18 slices of bread minus the 10 slices of bread that I used in my meal
prep, 18 - 10 gives me 8 which means I have 8 slices of bread left over and that's not
something you necessarily want inhale during meal prep but hey, maybe you're hungry right?
Now I know we haven't gone into molds yet but does the concept of limiting reactant
makes sense to you from a logical perspective and the type of math that we use in different
situations, do you get where and why before going crazy?
If yes, let's try and practice example but first, give this video a thumbs up and make
sure to subscribe and hit that bell icon so you don't miss out on any new videos then
join me on part 2 where we apply what we learn today but take it a step further by looking
at grams and molds to find limiting reactants, product yields, and excess reagents.
You can find this on my website along with the entire reactions and stoichiometry video
series and practice quiz, go to Leah4sci.com/Reactions or visit the link below.
Again, that's Leah4sci.com/Reactions