How to Calculate the Concentration of a Solution

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In chemistry, a solution’s concentration is how much of a dissolvable substance, known as a solute, is mixed with another substance, called the solvent. The standard formula is C = m/V, where C is the concentration, m is the mass of the solute dissolved, and V is the total volume of the solution. If you have a small concentration, find the answer in parts per million (ppm) to make it easier to follow. In a lab setting, you may be asked to find the molarity , or molar concentration, of the solution instead.

Method 1
Method 1 of 3:

Using the Mass per Volume Equation

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  1. Find the mass of the solute mixed in with the solvent. The solute is the substance that you’re mixing in to form your solution. If you’re given the mass of the solute in your problem, write it down and be sure to label it with the correct units. If you need to find the mass of the solute, then weigh it on a lab scale and record the measurement. [1]
    • If the solute you’re using is a liquid, then you can also calculate the mass using the density formula, where density D = m/V, where m is the mass of the liquid and V is the volume. To find the mass, multiply the density of the liquid by the volume.

    Tip: If you need to use a scale, subtract the mass of the container you’re using to hold the solute or else your calculations will be off.

  2. Record the total volume of the solution. The total volume of the solution is the amount of solvent plus the amount of solute added to it. If you’re finding the volume in a lab, mix the solution in a graduated cylinder or beaker and look at the measurement. Measure the volume from the curve at the top of the solution, or the meniscus, to get the most accurate reading. Record the volume of the solution. [2]
    • If you aren’t measuring the volume yourself, you may need to convert the mass of the solute into volume using the density formula.
    • For example, if you’re finding the concentration of 3.45 grams of salt in 2 liters of water, you would find the volume of salt using the density formula. Look up the density of salt either in a textbook or online and solve the formula for m. In this case, the density of salt is 2.16 g/mL. The formula would read 2.16 g/mL = (3.45 g)/V. Multiply each side by V to get V(2.16 g/mL) = 3.45 g. Then divide the each side by 2.16 to find the volume, or V = (3.45 g)/(2.16 g/mL) = 1.60 mL.
    • Add the volume of the solute to the volume of your solvent, ma. So in this example, 2 L + 1.6 mL = 2,000 mL + 1.6 mL = 2,001.6 mL. You can either leave the measurement in milliliters or convert it back to liters to get 2.002 L.
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  3. Write out the equation C = m/V, where m is the mass of the solute and V is the total volume of the solution. Plug in the values you found for the mass and volume, and divide them to find the concentration of your solution. Don’t forget to label to label your answer with the correct units. [3]
    • In our example for the concentration of 3.45 grams of salt in 2 liters of water, your equation would be C = (3.45 g)/(2.002 L) = 1.723 g/L.
    • Certain problems may ask for your concentration in specific units. Be sure to convert the units before putting them in your final formula.
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Method 2
Method 2 of 3:

Finding Concentration in Percentage or Parts per Million

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  1. Find the mass of the solute in grams . Measure out the mass of the solute that you plan on mixing with your solution. [4] Be sure to subtract the weight of the container you’re using to measure the solute or else your concentration will be inaccurate.
    • If your solute is a liquid, you may need to calculate the mass using the formula D = m/V, where D is the liquid’s density, m is the mass, and V is the volume. Look up the density of the liquid in a textbook or online and then solve the equation for the mass.
  2. The total mass of the solution is the mass of the solvent plus the mass of the solute. Weight the masses using a lab scale or convert the volume of the solvent to mass by using the density formula D = m/V. Add the mass of the solute to the mass of the solvent to find your final volume. [5]
    • For example, if you want to find the concentration of 10 g of cocoa powder mixed with 1.2 L of water, you would find the mass of the water using the density formula. The density of water is 1,000 g/L, so your equation would read 1,000 g/L = m/(1.2 L). Multiply each side by 1.2 L to solve the mass in grams, so m = (1.2 L)(1,000 g/L) = 1,200 g. Add the mass of the cocoa powder to get 1,210 g.
  3. Set up your equation so the concentration C = mass of the solute/total mass of the solution. Plug in your values and solve the equation to find the concentration of your solution. [6]
    • In our example, C = (10 g)/(1,210 g) = 0.00826.
  4. Multiply your answer by 100 if you want to find the percent concentration. If you’re asked to list the concentration in a percentage , take the answer you just found and multiply it by 100. Label your final answer with a percentage sign. [7]
    • In this example, the percent concentration is (0.00826)(100) = 0.826%.
  5. Use the number you found for your concentration and multiply it by 1,000,000 or 10 6 . The number will be how many parts per million the solute is. Label your final answer in ppm. [8]
    • In our example, the ppm = (0.00826)(1,000,000) = 8,260 ppm.

    Tip: Parts per million is usually used for very small concentrations since it’s easier to write and understand than a percentage.

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Method 3
Method 3 of 3:

Calculating Molarity

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  1. Add the atomic masses of the solute together to find the molar mass . Look at the elements in the chemical formula for the solute you’re using. List the atomic mass for each element in the solute since atomic and molar mass are the same. Add together the atomic masses from your solute to find the total molar mass. Label the final measurement in g/mol. [9]
    • For example, if your solute is potassium hydroxide (KOH), find the atomic masses for potassium, oxygen, and hydrogen and add them together. In this case molar mass = 39 +16 + 1 = 56 g/mol.
    • Molarity is used mainly in chemistry when you know the chemical makeup of the solute you’re using.
  2. Find the mass of the solute you’re adding into your solution using a lab scale if you need to. [10] Be sure to subtract the mass of the container so you have an accurate reading. Divide the mass you found by the molar mass so you can find how many moles of the solute you’re using. Label your answer with “mol.” [11]
    • For example, if you want to find the number of moles in 25 g of potassium hydroxide (KOH), then the equation is mol = (25 g)/(56 g/mol) = 0.45 mol
    • Convert the mass of your solute to grams if it isn’t already listed in grams.
    • Moles are used to represent the number of atoms in the solution.
  3. Find the volume of the solvent before you mix in the solute. [12] Use a flask or a graduated cylinder to find the measurement if you aren’t given it. If your measurement is in milliliters, then divide it by 1,000 to convert it to liters. [13]
    • In this example, if you’re using 400 mL of water, then divide it by 1,000 to convert it to liters, which is 0.4 L.
    • If your solvent is already listed in liters, then you can skip this step.

    Tip: You don’t need to include the volume of the solute since it doesn’t usually affect the volume that much. If there is a visible change in volume when you mix the solute with the solvent, then use the total volume instead.

  4. Divide the moles of solute by the volume of the solution in liters. Set up your equation so the molarity M = mol/V, where mol is the number of moles of the solute and V is the volume of the solvent. [14] Solve the equation and label the answer M. [15]
    • In this example, M = (0.45 mol)/(0.4 L) = 1.125 M.
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Calculator, Practice Problems, and Answers

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  • Question
    How do I convert milligrams to moles?
    Community Answer
    First, calculate the molar mass of your substance. (Add the atomic masses of the constituent elements.) Then, convert milligrams to grams by dividing by 1000. Finally, divide the grams of your substance by the Molar Mass.
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  • Question
    If I have a solution with unknown mass, how do I calculate concentration?
    Community Answer
    Calculate the number of moles using the equation c=n/v for the first given solution.Then using the no of moles calculate the mass using equation n=m/Mr.
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  • Question
    If I am given two solutions, what is one way of knowing which one is more/less concentrated?
    Community Answer
    You can perform titrations. Under the Le Chatelier's principle, the more concentrated one will have faster reacting time due to the fact that the more concentrated one has more molecules of that substance, leading to the ultimate truth that the chances of molecules meeting each other is bigger. Note that this method will not work if you are dropping Transition Metals into room-temperature, concentrated HNO3 or H2SO4 since Iron (and other metals) has the property called passivation. It happens when the metal reacts w/ the acid so quickly that the metal forms a salt, preventing the further reaction to the acid.
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      References

      1. ↑ https://www.physiologyweb.com/calculators/mass_per_volume_solution_concentration_calculator.html
      2. ↑ https://www.physiologyweb.com/calculators/mass_per_volume_solution_concentration_calculator.html
      3. ↑ https://www.physiologyweb.com/calculators/mass_per_volume_solution_concentration_calculator.html
      4. ↑ https://www.omnicalculator.com/conversion/ppm
      5. ↑ https://sciencing.com/calculate-concentration-ppm-6935286.html
      6. ↑ https://sciencing.com/calculate-concentration-ppm-6935286.html
      7. ↑ https://chem.libretexts.org/Courses/Los_Angeles_Trade_Technical_College/Chem_51/15%3A_Solutions/15.03%3A_Solution_Concentration_-_Molality_Mass_Percent_ppm_and_ppb
      8. ↑ https://chem.libretexts.org/Courses/Los_Angeles_Trade_Technical_College/Chem_51/15%3A_Solutions/15.03%3A_Solution_Concentration_-_Molality_Mass_Percent_ppm_and_ppb
      9. ↑ https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/04%3A_Reactions_in_Aqueous_Solution/4.05%3A_Concentration_of_Solutions
      1. ↑ Chris Hasegawa, PhD. Retired Science Professor & Dean. Expert Interview. 29 July 2021.
      2. ↑ https://www.khanacademy.org/science/chemistry/states-of-matter-and-intermolecular-forces/mixtures-and-solutions/a/molarity
      3. ↑ Chris Hasegawa, PhD. Retired Science Professor & Dean. Expert Interview. 29 July 2021.
      4. ↑ https://www.inchcalculator.com/convert/milliliter-to-liter/
      5. ↑ https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/04%3A_Reactions_in_Aqueous_Solution/4.05%3A_Concentration_of_Solutions
      6. ↑ Chris Hasegawa, PhD. Retired Science Professor & Dean. Expert Interview. 29 July 2021.

      About This Article

      Article Summary X

      To calculate the concentration of a solution, start by converting the solute, or the substance being dissolved, into grams. If you're converting from milliliters, you may need to look up the solute's density and then multiply that by the volume to convert to grams. Next, convert the solvent to liters. Finally, divide the solvent by the solute to find the concentration of the solution. To learn how to calculate the concentration of a solution as a percentage or parts per million, scroll down!

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