# Molarity

### Molarity

#### Lessons

In this lesson, we will learn:
• The definition of molarity and how to describe it.
• An equation to calculate the concentration of ions in solution.
• An equation to find the change in concentration of a substance in solution.

Notes:
• We now have an understanding of what a solution is and what a solution does to chemical properties when substances are dissolved. These depend on the molarity of substances in solution.

• Molarity measures the number of moles of a substance per unit volume. It is how concentration is measured for chemical substances in solution – it asks "how much stuff in how much space?" for a chemical substance.

• The units of molarity are moles per liter (written mol/L or mol L-1), or mol per cubic decimeter (mol/dm3 or mol/dm3). Both of these are equivalent and are often just given the symbol M.
• Calculating molarity is done by dividing the number of moles by the volume in liters according to the equation:

• $Molarity$ $(mol L^{-1}) =$ ${mol}\over{volume (L)}$

• When answering problems related to molarity, volume is often given in mL in chemical reactions – you'll need to convert from mL to L if you are finding concentration of a solution! This is done by dividing by 1000 (or use the unit conversion method; 1 L = 1000 mL).
• In some problems you may be told the mass of the substance used (mass measured in grams). In this case you need to convert from mass to moles by finding molar mass of the substance. You can then use the unit conversion method to get the number of moles of the substance.
• Remember, concentration is always measured with respect to 1 L of substance, so M can always be written as mol over liters, for example:

• $0.6 M = 0.6$ $mol L^{-1} =$ ${0.6 mol} \over {1L}$

• The molarity equation lets chemists compare the concentration of two different solutions which may have different quantities – solutions with high molarity are called concentrated solutions, while low molarity solutions are called dilute solutions.
• Dilution is when more solvent is added to a solution. This has the effect of increasing the volume of the solution, therefore decreasing molarity (see the molarity equation!). This would be like adding water to a juice drink; the same number of 'juice particles' are spread amongst more water than before so the drink is less concentrated.
• Similarly, removing some solvent, by evaporating it for example, will decrease the volume of your solution and lead to a higher molarity. This would be concentrating your solution; the same amount of 'juice particles' in less water.

• Calculating concentration is also very important for many chemical reactions. Knowing the concentration of solutions, for example acids and alkali, enables chemists to use appropriate amounts of the reactants in experiments. When writing concentration of chemical substances, square brackets [ ] are used.
• For example [HCl] = 0.2 M tells chemists that a solution of hydrochloric acid has a concentration of 0.2 mol per liter.

• Molarity concentrations will often be used to find concentration of ions in solution that react in rather than the formal chemical compounds. This is for two reasons:
1. It is the ions that actually cause the chemical properties and processes in solution to happen.
2. Many ionic compounds dissociate into more than just two oppositely charged ions! For example every molecule of phosphoric acid H3PO4 dissociates in solution into three H+ ions, the particle which actually take part in acid-base reactions. You need to multiply the concentration of the compound by the number of specific ions the compound produces to take this into account.
• For example: A solution of 0.4 M phosphoric acid, H3PO4, is made. As the formula shows, three H atoms are present in each molecule. Therefore in solution each single molecule will dissociate to form three H+ ions, so to find H+ concentration as multiply the concentration by three to find 0.4 * 3 = 1.2 M [H+].

• There is an equation that relates the volume and concentration before and after a dilution has taken place. This equation allows you to measure change in concentration of a solution, whether solvent or another solution is added or removed:
• $M_iV_i$ $=$ $M_fV_f$
Where:
Mi = initial molarity or concentration
Mf = final molarity or concentration
Vi = initial volume or concentration
Vf = final volume or concentration
• Introduction
Molarity and concentration
a)
Definition of molarity

b)
Finding the concentration of a solution

c)
Changing concentration of a solution

• 1.
Apply the formula to find the concentration of solutions.
a)
Find the concentration of a solution where 0.7 mol NaOH is dissolved into 120 mL of water.

b)
Find the concentration of another solution where 0.45 mol HCl is dissolved into 95 mL of water.

c)
Find the concentration of the solution that will be made if 32 grams of NaOH pellets are weighed out and dissolved in a container with 200 mL water.

• 2.
Apply the formula to find changing concentration and volume of solutions.
a)
Find the molarity of this solution.

b)
45 mL extra water is added to dilute this solution. Find the new concentration of this solution.

c)
This solution is diluted down further and the concentration is measured to be 0.55 M. What must the new volume of the solution be?

d)
In a separate experiment, a 50 mL solution of .450 M MgCl2 was mixed with 20 mL of 0.3 M AlCl3. Find the concentration of all the ions present in this combined mixture.