1. Molarity and Dilutions
Concentration of Solutions

2. Molarity and Dilutions
E.Q.: How do we calculate the concentration of solute in a solution (molarity)?

3. Molarity (M) = moles of solute / liters of solution
Molarity – Measurement of the concentration of a solution (how much solute is in a volume of solution)
Molarity (M) is equal to the number of moles of solute (n) per liter of solution
Molarity (M) = moles of solute / liters of solution
Units: M = mol / L

4. Molarity
Be careful not to get molarity and moles mixed up. Moles measures the amount of material you have. Molarity measures the concentration of the material.

5. M = 1.00 mole / 1.00 liter = 1.00 mol/L or 1.00 M
Molarity
Suppose we had 1.oo mole of sucrose and proceeded to mix it into some water. It would dissolve and make sugar water. We keep adding water, dissolving and stirring until all the solid was gone. We then made sure that when everything was well-mixed, there was exactly 1.00 liter of solution.
What would be the molarity of the solution?
M = 1.00 mole / 1.00 liter = 1.00 mol/L or 1.00 M
Often, instead of writing the units as mol/L, a capital M is used (M = mol/L)

6. Molarity Examples
1. Calculate the molarity of a solution prepared by mixing 1.5 g of NaCl in mL of water
First calculate the moles of solute in the solution:
1.5 grams NaCl mol NaCl
grams NaCl
= mol NaCl
Next convert mL to L: L
Last, plug the appropriate values into the correct variables in the equation:
M = n / V = mol / L = mol/L or M

7. Molarity Examples
2. Calculate the mass of NaOH needed to prepare 1.00 L of a 1.50 M solution.
To do this, the formula for molarity needs to be rearranged in order to solve for the number of moles:
M = moles / liters moles = M x liters
Numbers are then plugged into rearranged formula:
moles = (1.50 mol/L) x (1.00 L) = mol NaOH
We then find the grams in the 1.50 mol of NaOH by using dimensional analysis
1.50 mol NaOH grams NaOH
1 mol NaOH
= grams NaOH = grams NaOH

8. Molarity Examples
grams of NaOH is used in preparing a 1.5M solution. What volume of solution can be made?
First calculate the moles of solute in the solution:
965 grams NaOH mol NaOH
grams NaOH
= mol NaOH
We now rearrange the formula for molarity to solve for volume (liters):
M = moles / volume volume = moles / M
Numbers are then plugged into rearranged formula:
volume = (24.1 mol) / (1.5 mol/L) = L = 16 L

9. Your Turn……
Sea water contains roughly 28.0 g of NaCl per liter. What is the molarity of sodium chloride in sea water?
What is the molarity of g of H2SO4 dissolved in 1.00 L of solution?
How many moles of Na2CO3 are there in 10.0 L of 2.0 M solution?
What weight (in grams) of H2SO4 would be needed to make mL of 2.00 M solution?
What volume of 18.0 M H2SO4 is needed to contain 2.45 g H2SO4?

10. Dilutions
Dilution: The process of decreasing the concentration of a stock solution by adding more solvent to the solution.
The solvent added is usually the universal solvent, known as water. The more solvent you add, the more diluted the solution will get.
A stock solution is a concentrated solution that will be diluted to a lower concentration for actual use

11. Dilutions The equation for dilution is M1V1=M2V2
stock solution= diluted solution
M1= molarity of the stock solution
M2= molarity of the diluted solution
V1= volume of stock solution
V2= volume of diluted solution
Basically, dilution calculations involve figuring out the final concentration or volume ( depending on what’s given and what’s known) after a volume or concentration has been changed.
In dilution equations, you are given three things and you need to find the fourth component.

12. Dilution Examples
If I add 25 mL of water to 125 mL of a M NaOH solution, what will the molarity of the diluted solution be?
2. If I add water to 100. mL of a M NaOH solution until the final volume is 150. mL, what will the molarity of the diluted solution be?

13. Dilution Examples
I have 345 mL of a 1.5 M NaCl solution. If I boil the water until the volume of the solution is 250 mL, what will the molarity of the solution be?
How much 0.05 M HCl solution can be made by diluting 250 mL of 10 M HCl?