Molarity and Dilutions

By Shawn P. Shields, Ph.D.

This work is licensed by Shawn P. Shields-Maxwell under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Molarity

Molarity (M) is a concentration unit that describes how much of a substance is dissolved in solution.

Molarity Example

Suppose we wanted to make a 1.0 M solution of NaCl. What should we do?

Calculate the mass of 1 mole of NaCl, then weigh this amount on a balance.

Molar mass = 22.990g + 35.453g = 58.443 g/mol NaCl

Next, add this amount of NaCl to a flask, and fill it until the volume of the solution (water AND salt) equals one liter.

Molarity Example 2

What is the molarity of a 250 mL solution containing 0.35 moles NaCl?

First, convert mL to L,

Now, calculate the molarity of the solution

Molarity Example 3

Suppose we have 35 mL of a 0.85 M MgCl2 solution. How many moles of MgCl2 are present in the solution?

Convert mL to L

Now, rearrange the molarity equation and solve for moles.

Sig figs!

Molarity Example 4

How many mL of a 1.2 M MgCl2 solution are needed to have 0.35 moles MgCl2?

Rearrange the molarity equation and solve for volume.

Convert L to mLSig figs!

Dilution

Dilution is the process of adding solvent to a more concentrated solution to yield a solution of lower concentration.

The equation for dilution calculations is

Where M1 is the initial molarity, V1 is the initial volume, M2 is the final molarity, and V2 is the final volume.

Dilution

Recall that multiplying a volume in Liters and a molarity gives the moles of the substance.

Therefore, this relationship is simply

moles = moles!

The moles of solute remains constant, but the volume and molarity change.

Dilution Example

How many mL of a 2.5 M HCl stock solution would we need to make 100 mL of 0.80 M HCl?

Dilution Example Solution

How many mL of a 2.5 M HCl stock solution would we need to make 100 mL of 0.80 M HCl?

First, let’s identify what we have and what we are solving for…

M1 is the molarity of the stock solution, but we don’t know how much we need.

M2 is the final concentration (0.80 M) and V2 is the final volume (100 mL).

Dilution Example Solution

How many mL of a 2.5 M HCl stock solution would we need to make 100 mL of 0.80 M HCl?

Plug everything in…

Solve for V1

Watch sig figs… only 1 sf, so the final answer is 30 mL.

What You Should Be Able to Do

Calculate the molarity of a solution

Describe how to prepare a solution with a specific molarity

Use the molarity relationship to solve for moles and/or volume of solution.

Perform dilution calculations