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### Course: AP®︎/College Chemistry>Unit 3

Lesson 7: Solutions and mixtures

# Dilution

A common method of making a solution of a given concentration involves taking a more concentration solution and adding water until the desired concentration is reached. This process is known as dilution. We can relate the concentrations and volumes before and after a dilution using the following equation: MV₁ = MV₂ where M₁ and V₁ represent the molarity and volume of the initial concentrated solution and M₂ and V₂ represent the molarity and volume of the final diluted solution. Created by Sal Khan.

## Want to join the conversation?

• can you just multiply the 500 mls by the .125 molars and get the same answer?
• Yes, that's essentially what Sal did. A more simplified way of solving this is by using the dilution formula: (M1)(V1) = (M2)(V2), where M's are molarities and V's are volumes. 1 means the initial state and 2 mean the final state.

So for this problem here where we want 500 mL of a 0.125 M solution of sodium sulfate and start with 1.00 M solution of sodium sulfate, we want to know how much volume of the 1.00 M solution we need to add. So M1 = 1.00 M, M2 = 0.125M, V2= 500 mL, V1= is unknown and what we solve for. So V1 = (0.125 M)(500 mL)/(1.00M) = 62.5 mL. So that's what Sal's doing essentially and what you suggested to do, both are just following the dilution formula.

Hope that helps.
• How can you know when to use the M1*V1=M2*V2 formula?
• Well whenever you are trying to create a more dilute solution you would use that formula. A more dilute solution meaning a solution with a lower concentration than the original. You use this quite often in chemistry when you want to work with a solution with a specific concentration.

Another use for the dilution formula is that it allows you to know how much acid/base to add to an analyte when doing acid/base titrations using strong acids and strong bases.

Hope that helps.
• Why is 500 mL = 0.500L, I thought that 500 has 1 significant figure and 0.500 has 3? Shouldn't it be 0.5L?
• Are molarity and moles the same thing? Do they have the same unit?
(1 vote)
• Molarity and moles are measuring different things and hence have different units.

A mole is the unit for the amount of substance, or how much of something there is. It is defined as an Avogadro's number of particles, or 6.02214076 x 10^(23) particles. In the same way that a dozen of something is 12 particles. So a dozen eggs is 12 eggs, a dozen people is 12 people, a dozen atoms is 12 atoms. A mole of eggs is 6.02214076 x 10^(23) eggs and a mole of atoms is 6.02214076 x 10^(23) atoms. We use such a large number in chemistry because atoms are so small that having even a small amount of atoms like a gram could already be a mole of atoms. So it's more convenient to use moles of atoms instead of saying 6.02214076 x 10^(23) atoms each time we do a calculation.

Molarity is a unit of concentration, with units of moles of solute/ liters of solvent. Concentration being how much of a substance is in a given volume. A solvent being a liquid into which something is dissolved into, which is referred to as the solute. Together a solute and a solvent are called a solution. So if you have a glass of salt water, you have a solution of water where the water is the solvent and the salt is the solute. If you have a lot of salt in the water then it is a concentrated solution which we would express with a large molarity. And a small amount of salt in the water is an unconcentrated solution with a small molarity.

Hope that helps.
• why I don't see the equation M1V1=M2V2
(1 vote)
• Well the dilution formula is in the about of the video.

But Sal used the dilution formula at even though he didn’t explicitly say he did. It's the same math, just expressed differently.
• if we have molars of different compounds, can we use the formula MiVi=MfVf or do we have to relate the molars first?
(1 vote)
• Why is the 1M also equal to 0.0625 moles Na2SO4?
(1 vote)

The molarity of a solution is defined as the number of moles of solute per liter of solution. Therefore, 1M Na2SO4 solution contains 1 mole of Na2SO4 per liter of solution 1.

The molar mass of Na2SO4 is 142.0421 g/mol 1. Therefore, 1 mole of Na2SO4 weighs 142.0421 grams.

To calculate the number of moles of Na2SO4 in a 1M solution, we need to multiply the molarity by the volume of the solution in liters. Since the volume of the solution is not given, we cannot calculate the number of moles of Na2SO4 directly.

However, if we assume that the volume of the solution is 1 liter, then the number of moles of Na2SO4 in the solution would be equal to the molarity of the solution, which is 1 mole/L. Therefore, 1M Na2SO4 solution contains 1 mole of Na2SO4 per liter of solution 1.

If we assume that the volume of the solution is 0.0625 liters (62.5 mL), then the number of moles of Na2SO4 in the solution would be equal to the molarity of the solution multiplied by the volume of the solution in liters. Therefore, 1M Na2SO4 solution with a volume of 0.0625 liters contains 0.0625 moles of Na2SO4 1.

Therefore, 1M Na2SO4 is equal to 0.0625 moles of Na2SO4 when the volume of the solution is 0.0625 liters.

Dont mind the 1's