Concentrations, Molarity and Dilution

Concentration refers to the relative amount of solute or either solution or solvent.  There’s a number ways to express concentration and one way is molarity.  Other ways to express concentration are parts per million.  When you hear about pollution or things like that, you’ll hear PPM of lead or whatever is in the air.

Another way to express concentrations is percent concentrations.  There’s 3 ways to express that.

1. Mass to mass (used in chemistry)

grams of solute per grams of solution times 100 equates to grams of solute per 100g solution.

2. Mass to volume (used in biology)

grams of solute per mL of solution x 100 and that would be equal to grams of solute per 100mL of solution.

3. Volume to volume (least important, deals with liquid dissolving in another liquid)

mL of solute per mL solution x 100 equals mL solute per 100 mL solution.

Example

Let’s say we have 100g of solution and 5% NaCl.  Using #1:  Grams of solute is 5 grams over 100 grams of solution times 100, so we have 5g NaCl and 95g H2O.  Using #2, we can’t figure out.

Molarity

Molarity is moles of solute per liter of solution.

• M = n / V.  When you see it in this context, volume is in liters and n is moles.
• n = MV  If you know the molarity and volume, you could get the moles.
• V = n / M works as well.

Example: Let’s say we have 500mL of 0.2M NaOH. How many grams is that?

First we have to figure out how much sodium hydroxide we have.  If n = MV = (0.20)(0.500L) = 0.10 moles NaOH.

That’s how much we have but we want to know how many grams specifically so we are going to multiply the moles by the formula weight, which is 40.0g.  0.10 moles x 40.0g  = 4.0g NaOH.

1. 4.0 grams of NaOH

2. Add H2O up to 500mL.

What volume of this solution would contain 1.75g of NaOH?

You’re going to look for volume so you’re going to look for V=n/M.  You know the molarity for this solution is 0.2M so you just need to convert your grams into moles and plug it in.

So 1.75g / 40.0g = 0.0438 moles NaOH is our n and M=0.2.

V = (0.2) / (0.0438) = 0.22 Liters = 220mL

Example How many grams of NaOH are in 9.78mL of this solution?

M = 0.2 and V = 9.78mL but V must be in liters so V=0.00978 so the answer is n=MV=(0.2)(0.00978)=0.00196 moles NaOH which we multiply by 40.0g to get 0.0782g NaOH.

Dilution

M₁V₁ = n₁ = n₂ = M₂V₂

M₁V₁ = M₂V₂

This is what you use for any type of dilution problem.

Example If you have 30mL and 2.5M KCl, add 250mL H2O.  What is the new concentration?

V1 = 30mL, M1 = 2.5M, V2 = 280mL, M2 = ?

M2 = M1V1 / V2 = (2.5)(30) / 280 = 0.27 M

Example What volume of water must be added to 85mL of 3.5M Na2CO3 to dilute it to 0.41M?

• M1 = 3.5M
• V1 = 85mL
• M2 = 0.41M
• V2 = ?

(3.5)(85) = (0.41)(V2) => 730mL = V2.  730-85mL = 645mL needs to be added.