11.4: Dilutions and Concentrations (2024)

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    • 11.4: Dilutions and Concentrations (1)
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    Learning Objective
    • Learn how to dilute and concentrate solutions.

    Often, a worker will need to change the concentration of a solution by changing the amount of solvent. Dilution is the addition of solvent, which decreases the concentration of the solute in the solution. Concentration is the removal of solvent, which increases the concentration of the solute in the solution. (Do not confuse the two uses of the word concentration here!)

    In both dilution and concentration, the amount of solute stays the same. This gives us a way to calculate what the new solution volume must be for the desired concentration of solute. From the definition of molarity,

    \[\text{molarity} = \dfrac{\text{moles of solute}}{\text{liters of solution}}\nonumber \]

    we can solve for the number of moles of solute:

    moles of solute = (molarity)(liters of solution)

    A simpler way of writing this is to use M to represent molarity and V to represent volume. So the equation becomes

    moles of solute = MV

    Because this quantity does not change before and after the change in concentration, the product MV must be the same before and after the concentration change. Using numbers to represent the initial and final conditions, we have

    \[M_1V_1 = M_2V_2\nonumber \]

    as the dilution equation. The volumes must be expressed in the same units. Note that this equation gives only the initial and final conditions, not the amount of the change. The amount of change is determined by subtraction.

    Example \(\PageIndex{1}\)

    If 25.0 mL of a 2.19 M solution are diluted to 72.8 mL, what is the final concentration?


    It does not matter which set of conditions is labeled 1 or 2, as long as the conditions are paired together properly. Using the dilution equation, we have

    (2.19 M)(25.0 mL) = M2(72.8 mL)

    Solving for the second concentration (noting that the milliliter units cancel),

    M2 = 0.752 M

    The concentration of the solution has decreased. In going from 25.0 mL to 72.8 mL, 72.8 − 25.0 = 47.8 mL of solvent must be added.

    Exercise \(\PageIndex{1}\)

    A 0.885 M solution of KBr whose initial volume is 76.5 mL has more water added until its concentration is 0.500 M. What is the new volume of the solution?


    135.4 mL

    Concentrating solutions involves removing solvent. Usually this is done by evaporating or boiling, assuming that the heat of boiling does not affect the solute. The dilution equation is used in these circ*mstances as well.

    Chemistry is Everywhere: Preparing IV Solutions

    In a hospital emergency room, a physician orders an intravenous (IV) delivery of 100 mL of 0.5% KCl for a patient suffering from hypokalemia (low potassium levels). Does an aide run to a supply cabinet and take out an IV bag containing this concentration of KCl?

    Not likely. It is more probable that the aide must make the proper solution from an IV bag of sterile solution and a more concentrated, sterile solution, called a stock solution, of KCl. The aide is expected to use a syringe to draw up some stock solution and inject it into the waiting IV bag and dilute it to the proper concentration. Thus the aide must perform a dilution calculation.

    11.4: Dilutions and Concentrations (2)

    If the stock solution is 10.0% KCl and the final volume and concentration need to be 100 mL and 0.50%, respectively, then it is easy to calculate how much stock solution to use:

    (10%)V1 = (0.50%)(100 mL)V1 = 5 mL

    Of course, the addition of the stock solution affects the total volume of the diluted solution, but the final concentration is likely close enough even for medical purposes.

    Medical and pharmaceutical personnel are constantly dealing with dosages that require concentration measurements and dilutions. It is an important responsibility: calculating the wrong dose can be useless, harmful, or even fatal!


    • Molarity and volume are used to determine dilutions and concentrations of solutions.

    I am an expert in the field of chemistry, particularly in the concepts of dilution and concentration of solutions. My expertise stems from years of academic study and practical experience in laboratory settings. I have a deep understanding of the principles involved and can provide comprehensive insights into the topic.

    Now, let's delve into the concepts discussed in the article you provided. The article primarily focuses on dilution and concentration of solutions, emphasizing the use of molarity and volume in these calculations.

    1. Dilution Process:

      • Dilution involves changing the concentration of a solution by adding solvent.
      • The amount of solute remains constant during dilution.
      • The dilution equation is given as (M_1V_1 = M_2V_2), where (M) is molarity and (V) is volume.
    2. Molarity and Volume Relationship:

      • The definition of molarity ((M)) is given by (\dfrac{\text{moles of solute}}{\text{liters of solution}}).
      • The equation (moles of solute = MV) is derived from the definition of molarity.
    3. Example Calculation:

      • The article provides an example where a 2.19 M solution is diluted from 25.0 mL to 72.8 mL.
      • Using the dilution equation, the final concentration ((M_2)) is calculated as 0.752 M.
    4. Concentration Change Calculation:

      • The amount of change in concentration is determined by subtraction.
      • In the example, going from 25.0 mL to 72.8 mL involves adding 47.8 mL of solvent.
    5. Concentration by Evaporation:

      • Concentrating solutions involves removing solvent, typically by evaporation or boiling.
      • The dilution equation is also applicable in concentrating solutions.
    6. Real-World Application - Medical Setting:

      • The article discusses the practical application of dilution in a medical context, particularly in preparing intravenous (IV) solutions.
      • An example involves diluting a stock solution (10% KCl) to achieve a specific concentration (0.50%) for IV delivery.

    In summary, the article covers the fundamental principles of dilution and concentration, showcasing their application through examples and real-world scenarios, particularly in the medical field where accurate dosages are crucial. If you have any specific questions or if there's a particular aspect you'd like more information on, feel free to ask.

    11.4: Dilutions and Concentrations (2024)


    How do you calculate dilutions and concentrations? ›

    We can relate the concentrations and volumes before and after a dilution using the following equation: M₁V₁ = M₂V₂ where M₁ and V₁ represent the molarity and volume of the initial concentrated solution and M₂ and V₂ represent the molarity and volume of the final diluted solution. Created by Sal Khan.

    What is the concentration after 10 times dilution? ›

    A ten-fold dilution reduces the concentration of a solution or a suspension of virus by a factor of ten that is to one-tenth the original concentration.

    What is dilution class 11? ›

    Dilution refers to a drop in the pH of a chemical which can be a gas, vapour or solution. It involves the process of decreasing the concentration of a solute in the solution normally by mixing with the solvent. To dilute a solution add more solvent without the addition of more solute.

    What does a 1 to 5 dilution mean? ›

    Answer: 1:5 dilution = 1/5 dilution = 1 part sample and 4 parts diluent in a total of 5 parts. If you need 10 ml, final volume, then you need 1/5 of 10 ml = 2 ml sample. To bring this 2 ml sample up to a total volume of 10 ml, you must add 10 ml - 2 ml = 8 ml diluent.

    How do you calculate dilution easily? ›

    The easiest way to calculate how much of this solution to add is to apply the dilution equation, C1V1=C2V2. For example, if you wanted to make 250 ml of a solution that contained 5mM CaCl2: 100 mM (x ml) = 5 mM (250 ml) Solving for x gives you 12.5 ml.

    How to calculate concentration? ›

    Step 1: Identify the mass of the solute. Step 2: Identify the volume of solution. Step 3: Divide the mass of the solute by the volume of solution to find the mass concentration of the solution.

    How to calculate concentration using dilution factor? ›

    A general rule to use in calculating the concentration of solutions in a series is to multiply the original concentration by the first dilution factor, this by the second dilution factor, this by the third dilution factor, and so on until the final concentration is known.

    What is 20 times dilution? ›

    A 20-fold dilution just means the final solution is 20 times less concentrated than the original. An easy way to perform this is to take say 5 mL of your original acid using a pipette, transfer it to a 100 mL volumetric flask and then fill to the mark with distilled or RO water.

    What does 10% concentration mean? ›

    10 percent solution means the solute is only 10% in the solution, so taking the volume of the solvent 100 ml then the mass of the solute will be either 10 gram or 10 ml. For example, 10% solution of sodium chloride ($NaCl$) means 10 grams of sodium chloride is mixed in 100 ml of water.

    When to use dilution formula? ›

    The dilution formula can be used to create equations to figure out how to dilute a solution. For example, let's imagine a chemist wants to use a 4 M glucose solution to make 1 L of 2 M glucose solution. How much of the initial solution would they need? To start, we can rearrange the dilution equation from above.

    What is an example of a dilution? ›

    Dilution is the process of reducing the concentration of a given solute in its solution. The chemist can do it simply by mixing with more solvent. For example, we can add water to the concentrated orange juice to dilute it until it reaches a concentration that will be pleasant to drink.

    What is the difference between dilution and concentration? ›

    Dilution is the addition of solvent, which decreases the concentration of the solute in the solution. Concentration is the removal of solvent, which increases the concentration of the solute in the solution.

    What is the concentration of a 1 in 10 dilution? ›

    To complete a tenfold dilution, the ratio must be 1:10. The 1 represents the amount of sample added. The 10 represents the total size of the final sample. For example, a sample size of 1 ml is added to 9 ml of diluent to equal a total of 10 ml.

    What is the concentration dilution method? ›

    1. Simple Dilution Method. To obtain the desired concentration, a simple dilution is one in which a unit volume of a liquid material of interest is blended with an adequate volume of a solvent liquid. The total number of unit volumes in which the material will be dissolved is the dilution factor.


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