# 4 ways to find molarity

Molarity describes the relationship between the moles of a solute and the volume of a solution. To calculate molarity, you can start with moles and volume, mass and volume, or moles and milliliters. Plugging these variables into the basic formula to calculate molarity will give you the correct answer.

## Steps

### Method 1 of 4: Calculate Molarity with Moles and Volume

#### Step 1. Know the basic formula for calculating molarity

Molarity is equal to the number of moles of a solute divided by the volume of the solution in liters. So, it is written: molarity = moles of solute / liters of solution.

### Example problem: What is the molarity of a solution that contains 0.75 moles of NaCl in 4.2 liters?

#### Step 2. Examine the problem

Finding the molarity requires you to have the number of moles and the number of liters. If the problem offers these values, no preliminary calculations are required.

• Example problem:

• Moles = 0.75 mol NaCl
• Volume = 4.2 L

#### Step 3. Divide the number of moles by the number of liters

The resulting quotient will give you the number of moles per liter of solution, also known as molarity.

### Example problem: molarity = moles of solute / liters of solution = 0.75 mol / 4.2 L = 0.17857142

Round the number of digits after the decimal point to two or three digits, depending on your instructor's preferences. When you write your answer, abbreviate "molarity" with "M" and write the chemical formula of the solute involved.

• Example problem: 0.179 M NaCl

### Method 2 of 4: Calculate Molarity Using Mass and Volume

#### Step 1. Know the basic formula for calculating molarity

Molarity expresses the relationship between the number of moles of a solute per liters of solution, or the volume of that solution. As a formula, molarity is expressed as: molarity = moles of solute / liters of solution.

• Example problem: What is the molarity of a solution obtained by dissolving 3.4 g of KMnO4 in 5.2 liters of water?

#### Step 2. Examine the problem

Finding the molarity requires you to have the number of moles and the number of liters. If you don't have the number of moles but you do have the volume and mass of the solution, you will need to use both figures to calculate the number of moles before continuing.

• Example problem:

• Mass = 3.4 g KMnO4
• Volume = 5.2 L

#### Step 3. Find the molar mass of the solute

To calculate the number of moles based on the mass or grams of the solute used, you must first determine the molar mass of the solute. This can be found by adding the proper molar mass of each element in the solution. Find the molar mass of each element using the periodic table of the elements. Be sure to count the atoms of each element and calculate the molar mass of each of the atoms.

• Example problem:

• Molar mass of K = 39.1 g
• Molar mass of Mn = 54.9 g
• Molar mass of O = 16.0 g (the solution contains 4 oxygen atoms, so count 16 g four times)
• Total molar mass = K + Mn + O + O + O + O = 39.1 + 54.9 + 16 + 16 + 16 + 16 = 158.0 g

#### Step 4. Convert the grams to moles

Now that you have the molar mass of the solute, you must multiply the number of grams of solute in the solution by a conversion factor of 1 mole over the molecular weight (molar mass) of the solute. This will give you the number of moles of the solute for this equation.

• Example problem: grams of solute * (1 / molar mass of solute) = 3.4 g * (1 mol / 158 g) = 0.0215 mol
• The units of grams of the solution and the mass cancel each other out, so you're only left with the molar units.

#### Step 5. Divide the number of moles by the number of liters

Now that you have the number of moles, you can divide this value by the number of liters of solution to find the molarity.

### Example problem: molarity = moles of solute / liters of solution = 0.0215 mol / 5.2 L = 0.004134615

You should round the number of digits after the decimal point to the number of digits required by your instructor. Generally, it will be two or three digits after the decimal point. Also, when you write your answer, abbreviate "molarity" with "M" and write the solute involved.

• Example problem: 0.004 M KMnO4

### Method 3 of 4: Calculate Molarity with Moles and Milliliters

#### Step 1. Know the basic formula for calculating molarity

To find molarity, you will need to calculate the number of moles of solute for a solution per liter of solution. Milliliters cannot be used. The general formula to express molarity is written: molarity = moles of solute / liters of solution

• Sample Problem: What is the molarity of a solution containing 1.2 moles of CaCl2 in 2905 milliliters?

#### Step 2. Examine the problem

Calculating molarity requires you to have the number of moles and the number of liters. If you have the volume in milliliters instead of liters, you will need to convert the volume to liters before continuing with your calculations.

• Example problem:

• Moles = 1.2 mol CaCl2
• Volume = 2905 ml

#### Step 3. Convert the milliliters to liters

Find the number of liters by dividing the number of milliliters by 1000, since there are 1000 milliliters in a liter. Note that you can also simply move the decimal point three places to the left.

### Example problem: 2905 ml * (1 L / 1000 ml) = 2.905 L

#### Step 4. Divide the number of moles by the number of liters

Now that you have the number of liters, you can divide the number of moles of solute by this value to find the molarity of the solution.

• Example problem: molarity = moles of solute / liters of solution = 1.2 mole CaCl2 / 2.905 L = 0.413080895

Round the number of digits after the decimal point to the number of digits your instructor requires (usually two or three digits). When writing your answer, you should also abbreviate "molarity" as "M", and write the solute.

• Example problem: 0.413 M CaCl2

### Method 4 of 4: Additional Practice Problem

#### Step 1. Find the molarity of a solution that is obtained by dissolving 5.2 g of NaCl in 800 m of water

Identify the values given to you in the problem: mass in grams and volume in milliliters.

• Mass = 5.2 g NaCl
• Volume = 800 ml water

#### Step 2. Find the molar mass of NaCl

Do this by adding the molar mass of sodium (Na) and the molar mass of chlorine (Cl).

• The molar mass of Na = 22.99 g
• The molar mass of Cl = 35.45 g
• The total molar mass of NaCl = 22.99 + 35.45 = 58.44 g

#### Step 3. Multiply the mass of the solute by its molar mass conversion factor

In this instance, the molar mass of NaCl is 58.44 g, so the conversion factor is 1 mol / 58.44 g.

### Moles NaCl = 5.2 g NaCl * (1 mol / 58.44 g) = 0.08898 mol = 0.09 mol

#### Step 4. Divide 800 ml of water by 1000

Since there are 1000 milliliters per liter, you will need to divide the number of milliliters in this problem by 1000 to find the number of liters.

• You can also think of this as multiplying 800 ml by a conversion factor of 1 L / 1000 ml.
• To speed up the process, you can simply move the decimal point three places to the left instead of multiplying or dividing anything.
• Volume = 800 ml * (1 L / 1000 ml) = 800 ml / 1000 ml = 0.8 L

#### Step 5. Divide the number of moles of solute by the number of liters of solution

To find the molarity, you divide 0.09 mol, the number of moles of solute NaCl, by 0.8 L, the volume of the solution in liters.