Molarity describes the relationship between the moles of solute and the volume of the solution. To calculate molarity, you can start with moles and volume, mass and volume, or moles and milliliters. Plugging this variable into the basic formula for calculating molarity, will give you the correct answer.
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Method 1 of 4: Calculating Molarity with Moles and Volume
Step 1. Know the basic formula for calculating molarity
Molarity is the number of moles of solute divided by the volume of solution in liters. Thus, it is written as: molarity = moles of solution / liter of solution
Example problem: What is the molarity of a solution containing 0.75 moles of NaCl in 4.2 liters?
Step 2. Research the problem
Finding molarity requires you to know the number of moles and the number of liters. If both are known in this problem, you don't need another calculation.
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Problems example:
- Moles = 0.75 moles of NaCl
- Volume = 4.2 L
Step 3. Divide the number of moles by the number of liters
The result of the division is the number of moles per liter of solution, which is called the molarity.
Example problem: molarity = moles of solute / liter of solution = 0.75 mol / 4.2 L = 0.17857142
Step 4. Write down your answer
Round the number of digits to two or three digits after the comma, depending on your teacher's request. When you write down the answer, abbreviate molarity with M and write down the chemical abbreviation of the solution used.
Problems example: 0.179 M NaCl
Method 2 of 4: Calculating Molarity using Mass and Volume
Step 1. Know the basic formula for calculating molarity
Molarity shows the relationship between the number of moles of solute per liter of solution, or the volume of that solution. In the formula, molarity is written as: molarity = moles of solute / liter of solution
Example problem: What is the molarity of the solution formed by dissolving 3.4 g of KMnO4 in 5, 2 liters of water?
Step 2. Research the problem
Finding molarity requires you to know the number of moles and the number of liters. If you don't know the number of moles, but do know the volume and mass of the solution, you'll need to use these two things to calculate the number of moles before continuing.
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Problems example:
- Mass = 3.4 g KMnO4
- Volume = 5, 2 L
Step 3. Find the molar mass of the solution
To calculate the number of moles of mass or grams of the solution used, you must first determine the molar mass of the solution. This can be done by adding up the molar mass of each element present in the solution. Find the molar mass of each element using the periodic table of the elements.
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Problems example:
- Molar mass K = 39.1 g
- Molar mass Mn = 54.9 g
- Molar mass O = 16.0 g
- Total molar mass = K + Mn + O + O + O + O = 39, 1 + 54, 9 + 16 + 16 + 16 + 16 = 158.0 g
Step 4. Convert grams to moles
Now that you have the molar mass of the solution, you must multiply the number of grams dissolved in the solution by the conversion factor of 1 per weight (molar mass) of the solution. This will give you the number of moles of solution for this equation.
Example problem: grams dissolved * (1/molar mass dissolved) = 3.4 g * (1 mol / 158 g) = 0.0215 mol
Step 5. Divide the number of moles by the number of liters
Since you already have the number of moles, you can divide it by the number of liters of solution to find the molarity.
Example problem: molarity = moles of solute / liter of solution = 0.0215 mol/5, 2 L = 0.004134615
Step 6. Write down your answer
You must round your number a few digits after the comma, as asked by your teacher. Usually, you need to round two or three places after the comma. Also, when you write the answer, shorten the molarity to M and write down the solution used.
Problems example: 0.004 M KMnO4
Method 3 of 4: Calculating Molarity with Moles and Milliliters
Step 1. Know the basic formula for calculating molarity
To find molarity, you must calculate the number of moles of solute per liter of solution. Milliliters cannot be used. The general formula used to find molarity can be written: molarity = moles of solute / liter of solution
Example problem: What is the molarity of a solution containing 1.2 moles of CaCl2 in 2905 milliliters?
Step 2. Research the problem
Calculating molarity requires you to know the number of moles and the number of liters. If you know the volume in milliliters instead of liters, you'll need to convert the volume to liters before continuing to calculate.
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Problems example:
- Moles= 1.2 moles of CaCl2
- Volume = 2905 ml
Step 3. Convert milliliters to liters
Find the number of liters by dividing the number of milliliters by 1000, because there are 1000 milliliters for every 1 liter. Note that you can also move the decimal point to the left three places.
Example problem: 2905 ml * (1 L / 1000 ml) = 2,905 L
Step 4. Divide the number of moles by the number of liters
Since you already know the number of liters, you can divide the number of moles of solute by the number of liters to find the molarity of the solution.
Example problem: molarity = moles of solute / liter of solution = 1.2 moles of CaCl2 / 2.905 L = 0.413080895
Step 5. Write down your answer
Round the number a few digits after the comma as required by your teacher (usually two or three digits after the comma). When writing the answer, you should write the abbreviation for molarity with M, and write down the solution.
Problems example: 0.413 M CaCl2
Method 4 of 4: Additional Practice Problems
Step 1. Find the molarity of the solution formed by dissolving 5.2 g of NaCl in 800 ml of water
Identify the values given in the problem: mass in grams and volume in milliliters.
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- Mass = 5.2 g NaCl
- Volume = 800 ml of 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.
- Molar mass Na = 22.99 g
- Molar mass Cl = 35.45 g
- Molar mass of NaCl = 22.99 + 35.45 = 58.44 g
Step 3. Multiply the dissolved mass by the molar mass conversion factor
In this example, the molar mass of NaCl is 58.44 g, so the conversion factor is 1 mol / 58.44 g.
Moles of NaCl = 5.2 g NaCl * (1 mol / 58.44 g) = 0.08898 mol = 0.09 mol
Step 4. Divide 8000 ml of water by 1000
Since there are 1000 milliliters per liter, you must divide the number of milliliters in this problem by 1000 to find the number of liters.
- You can also multiply 8000 ml by a conversion factor of 1 L / 1000 ml.
- To shorten the process, you can move the decimal point to the left three places, no need to multiply or divide 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 molarity, you need to divide 0.09, the number of moles of dissolved NaCl, by 0.8 L, the volume of the solution in liters.
molarity = moles of solute / liter of solution = 0.09 mol / 0.8 L = 0.1125 mol/L
Step 6. Arrange your answers
Round your answer to two or three decimal places and abbreviate molarity with M.
