How to Calculate Molarity: Easy Step-by-Step Guide

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Learn how to solve molarity problems with our step-by-step guide
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Molarity describes the relationship between moles of a solute and the volume of a solution. [1] To calculate molarity, you can start with moles and volume, mass and volume, or moles and milliliters. Plugging these variables into the basic formula for calculating molarity will give you the correct answer.

Molarity Formula

To calculate the molarity of a solution, divide the moles of solute by the liters of a solution. The answer is expressed in the unit mol/L.

Method 1
Method 1 of 4:

Calculating Molarity with Moles and Volume

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  1. Molarity is equal to the number of moles of a solute divided by the volume of the solution in liters. As such, it is written as: molarity = moles of solute / liters of solution . [2]
    • Example problem: What is the molarity of a solution containing 0.75 mol NaCl in 4.2 liters?
  2. Finding molarity demands that you have the number of moles and the number of liters. If the problem provides each of these figures, no preliminary calculations are needed.
    • Example problem:
      • Moles = 0.75 mol NaCl
      • Volume = 4.2 L
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  3. The resulting quotient will give you the number of moles per liter of solution, otherwise known as molarity. [3]
    • Example problem: molarity = moles of solute / liters of solution = 0.75 mol / 4.2 L = 0.17857142
  4. Round off the number of digits after the decimal point to two or three, depending on your instructor's preference. When you write out the answer, abbreviate "molarity" with "M" and state the chemical abbreviation of the solute involved.
    • Example problem: 0.179 M NaCl
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Method 2
Method 2 of 4:

Calculating Molarity with Mass and Volume

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  1. Molarity expresses the relationship between the number of moles of a solute per liters of solution, or the volume of that solution. In formula form, molarity is expressed as: molarity = moles of solute / liters of solution . [4]
    • Example problem: What is the molarity of a solution made by dissolving 3.4 g of KMnO 4 in 5.2 liters of water?
  2. Finding molarity demands that you have the number of moles and the number of liters. If you are not provided with the number of moles but you do have the volume and mass of the solution, you will need to use these two figures to calculate the number of moles before continuing on.
    • Example problem:
      • Mass = 3.4 g KMnO 4
      • Volume = 5.2 L
  3. Find the molar mass of the solute. To calculate the number of moles from the mass or grams of solute used, you must first determine the molar mass of the solute. [5] This can be done by adding together the separate molar masses of each element found in the solution. Find the molar mass of each element using the periodic table of elements. Make sure that you count the atoms for 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 solute contains 4 O atoms, so count the 16g 4 times.)
      • Total molar mass = K + Mn + O + O + O + O = 39.1 + 54.9 + 16 + 16 + 16 + 16 = 158.0 g
  4. Convert the grams into moles . Now that you have the molar mass of the solute, you need to multiply the number of grams of solute in the solution by a conversion factor of 1 mole over the formula weight (molar mass) of the solute. This will give you the number of moles of the solute for this equation. [6]
    • Example problem: grams of solute * (1/molar mass of solute) = 3.4 g * (1 mol / 158 g) = 0.0215 mol
    • The grams units of the solute and solute mass cancel each other out so you are left with mol units.
  5. Now that you have the number of moles, you can divide this value by the number of liters of solution in order to find the molarity. [7]
    • Example problem: molarity = moles of solute / liters of solution = 0.0215 mol / 5.2 L = 0.004134615
  6. You should round off the number of digits after the decimal point to the place requested by your instructor. Usually, this will be two or three places after the decimal point. Additionally, when you write out the answer, abbreviate “molarity” with “M” and state the solute involved.
    • Example problem: 0.004 M KMnO 4
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Method 3
Method 3 of 4:

Calculating Molarity with Moles and Milliliters

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  1. In order to find molarity, you need to calculate the number of moles of solute for a solution per liter of solution. Milliliters cannot be used. The general formula used to express molarity is written as: molarity = moles of solute / liters of solution . [8]
    • Example problem: What is the molarity of a solution containing 1.2 moles CaCl 2 in 2905 milliliters?
  2. Calculating molarity requires you to have the number of moles and the number of liters. If you are provided with the volume in milliliters instead of liters, you will need to convert the volume into liters before continuing your calculations.
    • Example problem:
      • Moles = 1.2 mol CaCl 2
      • Volume = 2905 ml
  3. Convert the milliliters into liters . Find the number of liters by dividing the number of milliliters by 1000, since there are 1000 milliliters per 1 liter. [9] Note that you could also simply move the decimal point to the left three places.
    • Example problem: 2905 ml * (1 L / 1000 ml) = 2.905 L
  4. Now that you have the number of liters, you can divide the number of moles of solute by this value in order to find the molarity of the solution. [10]
    • Example problem: molarity = moles of solute / liters of solution = 1.2 mol CaCl 2 / 2.905 L = 0.413080895
  5. Round off the number of digits after the decimal point to the amount requested by your instructor (usually two or three places). When you write out the answer, you should also abbreviate “molarity” with “M,” and state the solute.
    • Example problem: 0.413 M CaCl 2
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Method 4
Method 4 of 4:

Additional Practice Problem

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  1. Identify the values provided to you in the problem: mass in grams and volume in milliliters.
    • Mass = 5.2 g NaCl
    • Volume = 800 ml water
  2. Do this by adding together 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 molar mass of NaCl = 22.99 + 35.45 = 58.44 g
  3. 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
  4. Since there are 1000 milliliters per liter, you will need to divide the number of milliliters in this problem by 1000 in order to find the number of liters.
    • You could also look at it as multiplying 800 ml by a conversion factor of 1 L / 1000 ml.
    • To hasten the process, you could 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
  5. In order to find the molarity, you need to divide 0.09 mol, the number of moles of the solute NaCl, by 0.8 L, the volume of the solution in liters.
    • molarity = moles of solute / liters of solution = 0.09 mol / 0.8 L = 0.1125 mol/L
  6. Round your answer off to two or three decimal places and abbreviate molarity with “M.”
    • Answer: 0.11 M NaCl
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  • Question
    What is the formula for a mole?
    Community Answer
    No. of moles = (Given mass of compound in the question)/Molecular mass of the given compound
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  • Question
    What is the difference between molarity and molar mass?
    Community Answer
    Molarity is a measure and unit of concentration. It is used to express concentration of a particular solution. On the other hand, molar mass is a unit of mass. It is the mass of 1 mole of a substance.
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  • Question
    How can I calculate molarity if concentration is given as percentage?
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    Convert the percentage to a decimal by moving the decimal point left two places. For example; 98% would become 0.98, and 6% would become 0.06.
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      References

      1. ↑ https://chem.libretexts.org/Bookshelves/Introductory_Chemistry/Introductory_Chemistry_(CK-12)/16%3A_Solutions/16.08%3A_Molarity
      2. ↑ https://www.omnicalculator.com/chemistry/molarity
      3. ↑ https://www.omnicalculator.com/chemistry/molarity
      4. ↑ https://www.khanacademy.org/science/chemistry/states-of-matter-and-intermolecular-forces/mixtures-and-solutions/a/molarity
      5. ↑ https://www.chem.purdue.edu/gchelp/howtosolveit/Solutions/determinemolarmass.html
      6. ↑ https://chem.libretexts.org/Courses/Harper_College/General_Organic_and_Biochemistry_with_Problems_Case_Studies_and_Activities/06%3A_Moles/6.03%3A_Converting_between_grams_and_moles
      7. ↑ https://www.khanacademy.org/science/chemistry/states-of-matter-and-intermolecular-forces/mixtures-and-solutions/a/molarity
      8. ↑ https://www.khanacademy.org/science/chemistry/states-of-matter-and-intermolecular-forces/mixtures-and-solutions/a/molarity
      9. ↑ https://www.inchcalculator.com/convert/milliliter-to-liter/
      1. ↑ https://www.omnicalculator.com/chemistry/molarity

      About This Article

      Article Summary X

      To calculate molarity, divide the number of moles of solute by the volume of the solution in liters. If you don't know the number of moles of solute but you know the mass, start by finding the molar mass of the solute, which is equal to all of the molar masses of each element in the solution added together. Once you have the molar mass, multiply the number of grams of solute by 1 over the molar mass to convert the grams into moles. Finally, divide the number of moles by the volume of the solution to get the molarity. To learn how to calculate molarity using moles and milliliters, scroll down!

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