## Monday, January 4, 2021

### Finding Molarity

General Chemistry Index

Where are we going with this? This page will assist in developing the ability to perform calculations to determine the composition of a compound or mixture when given the necessary information and to apply lab data to determine the empirical and molecular formula of a compound.

Finding Molarity
This sounds like something someone just made up as a joke…

Seems like a definition should come now. Good news! This is really very, very simple.

Molarity: the number of moles of something (the solute) in a liter of a solution.

 https://en.wikipedia.org/wiki/Molar_concentration

AKA: Molar concentration, because… two names are better than one?

That's it. If you put one mole of something into water, then top it off to exactly one liter, you have something that has a molarity of one.

If you put two moles of something into water, then top it off to exactly one liter, you have something that has a molarity of two.

Hang on for this one! If you put FOUR moles of something into water, then top it off to exactly TWO liters, you have something that has a molarity of two.

Seems like there would be a formula!

Where…

M is molarity,

n is number of moles, and

V is volume…

M = n/V

There's a trick though! Of course there is!

V is the volume you end up with! So you mix stuff such that you end up with some volume. Then you divide. Hence the "top it off to exactly" wording in the examples above.

So… this seems really easy…

It can be slightly more difficult. Suppose you are given grams of solute, not moles? OR! Suppose you are supposed to find the grams needed for some given molarity! Yeah, that! So… Let's do some examples…

EXAMPLE 1

What is the molarity of a 2 liter solution containing 3.4 moles of CuSO4?

Find M where

V = 2 liters
n = 3.4 moles

M = n/V

M = 3.4 moles / 2 liters

= 1.7 M

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EXAMPLE 2

How many grams of K2SO4 are needed to make 2 liters of a 4 Molar solution?

That escalated fast! Let's do it in two steps:

1. How many moles of K2SO4 are needed to make 2 liters of a 4 Molar solution?

2. How much does that many moles of K2SO4 weigh in grams?

Hmm… seems legit.

1. How many moles of K2SO4 are needed to make 2 liters of a 4 Molar solution?

Find n where

V = 2 liters
M = 4

M = n/V

4 moles/liter = n / 2 liters

Multiply both sides of the equation by 2 and handle the unit to clear the fraction on the right, because math.

2 • 4 moles = n

8 moles = n

So we need 8 moles of K2SO4

2. How much does that many moles of K2SO4 weigh in grams?

We know how many moles we need (8 moles), so we need to convert that to grams.

Moles to grams you multiply… grams to moles divide…

grams = natomic mass

Having the number of moles, we now need to find the molecular mass of K2SO4. Using a periodic table (and rounding) we can find the atomic masses of the elements:

K = 39.1 g/mole

S = 32.1 g/mole

O = 16.0 g/mole

So, the molecular mass of K2SO4 is the sum of all those atom masses:

2 • K = 78.2

1 • S = 32.1

4 • O = 64.0

78.2 + 32.1 + 64 = 174.2 g/mole

Okay… so, one mole weighs 174.2 grams. How much does… what was that number again?

So we need 8 moles of K2SO4

Moles to grams you multiply… grams to moles divide…

grams = moles • g/mole
grams = 8 moles174.2 g/mole  <----- moles cancel
grams = 1393.6 g

You need 1393.6 grams of K2SO4 to make 2 liters of a 4 Molar solution?

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EXAMPLE 3

What would be the molarity of a .5 liter solution in which was 18.65 grams of KCl?

Looks like we have two steps again…

1. How many moles are in 18.65 grams of KCl?

2. What is the molarity of a .5 liter solution in which are that many moles of KCl?

Let's do this!

1. How many moles are in 18.65 grams of KCl?

Moles to grams you multiply… grams to moles, divide…

Where n is number of moles, g is mass in grams, and atomic mass is the atomic mass of the substance, then…

n = g atomic mass

Atomic mass of KCl is

1 • K = 39.1
1 • Cl = 35.5

Atomic Mass = 39.1 + 35.5
Atomic Mass = 74.6 g / mole

Now, we can find how many moles there are…

n = gatomic mass
n = 18.65 / 74.6 moles <-- the units reduce to moles because math
n = .25 moles

So, 18.65 grams of KCl is .25 moles.

2. What is the molarity of a .5 liter solution in which are that many moles (.25 moles) of KCl?

Find M where

V = .5 liters
n = .25 moles

M = n/V

M = .25 moles / .5 liters

= .5 M

The molarity of a .5 liter solution in which are 18.65 grams of KCl is 0.5 M.

So, there you go… Essentially, we are taking our understanding of moles and grams and all that, then adding… the solvent.
• Find out how many moles you have and divide by the volume.
• Or flip it around and find out how many moles you need and convert moles to grams.

• In EXAMPLE 2, we made a LOT of a 4 molar solution. Most situations will call for much smaller quantities.

• Solutes actually have a MAXIMUM amount that will dissolve in in a solvent, and when that happens, the solution is said to be saturated.

RESOURCE:

Here's a link to a kinda cool spreadsheet you can copy that will do a lot of the math for you!