Ch.4 - Chemical Quantities & Aqueous ReactionsWorksheetSee all chapters
All Chapters
Ch.1 - Intro to General Chemistry
Ch.2 - Atoms & Elements
Ch.3 - Chemical Reactions
BONUS: Lab Techniques and Procedures
BONUS: Mathematical Operations and Functions
Ch.4 - Chemical Quantities & Aqueous Reactions
Ch.5 - Gases
Ch.6 - Thermochemistry
Ch.7 - Quantum Mechanics
Ch.8 - Periodic Properties of the Elements
Ch.9 - Bonding & Molecular Structure
Ch.10 - Molecular Shapes & Valence Bond Theory
Ch.11 - Liquids, Solids & Intermolecular Forces
Ch.12 - Solutions
Ch.13 - Chemical Kinetics
Ch.14 - Chemical Equilibrium
Ch.15 - Acid and Base Equilibrium
Ch.16 - Aqueous Equilibrium
Ch. 17 - Chemical Thermodynamics
Ch.18 - Electrochemistry
Ch.19 - Nuclear Chemistry
Ch.20 - Organic Chemistry
Ch.22 - Chemistry of the Nonmetals
Ch.23 - Transition Metals and Coordination Compounds
Jules Bruno


In this video we take a look at the concept of dilutions and the equations associated with dilutions. Any time we are talking about dilutions we use the equation of M₁V₁ = M₂V₂. 

Dilution equation

dilution equation

M₁ here represents the molarity or concentration before dilution has occurred

V₁ represents the volume before dilution has occurred

M₂ represents the molarity or concentration after dilution

V₂ represents your volume after dilution

Some key things in relation to the variables to one another:

M₁ represents your concentration before dilution. It is more concentrated because we haven’t added water yet. Therefore, M₁ is always a larger value than M₂, it is a larger molarity.

V₂, since that’s the volume after we’ve added water, V₂ will be larger than M₁. Since V₂ represents our final volume after we’ve added water, V₂ equals V₁ plus the amount of water you’ve added. That’s the whole process of dilution, adding water.

When exactly are we talking about dilution?

In terms of dilution, they’ll refer to two molarities or two volumes for a single compound. 

For example, you have 50 ml of 0.100 M NaOH and you are going to dilute it so that you get to a new concentration of 0.012 M NaOH. Realize that we are talking about only one compound the whole time and they have given us two molarities. That’s the key to realizing dilution is occurring - referring to one compound and that one compound is either dealing with two molarities or two volumes right from the beginning of the question.

When would we use this dilution formula?

Now, they also could mention or reference as “mixing or adding water to the solution” which represents a dilution and it’s a signal to you that the dilution formula will most likely be used to answer the question.

Remember, when we talk about dilutions it is just simply adding water to a reaction mixture. It causes our solution to become less concentrated so your M₂ is smaller than your M₁. Because you are adding water, the overall volume increases that’s why your V₂ (your final volume) is bigger than V₁ (your initial volume).

Jules Bruno

Jules felt a void in his life after his English degree from Duke, so he started tutoring in 2007 and got a B.S. in Chemistry from FIU. He’s exceptionally skilled at making concepts dead simple and helping students in covalent bonds of knowledge.