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6.3: Concentration

  • Page ID
    50512
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    Skills to Develop

    • Define the terms "concentrated" and "dilute".
    • Define concentration, and list the common units used to express the concentration of solutions.
    • Calculate concentration in units of molarity or molality.
    • Calculate the amount of solute needed to make a given amount of solution with a given concentration.

    IntroductionCK12 Screenshot 6-3-1.png

    Concentration is the measure of how much of a given substance is mixed with another substance. Solutions can be said to be dilute or concentrated. When we say that vinegar is \(5\%\) acetic acid in water, we are giving the concentration. If we said the mixture was \(10\%\) acetic acid, this would be more concentrated than the vinegar solution.

    A concentrated solution is one in which there is a large amount of solute in a given amount of solvent. A dilute solution is one in which there is a small amount of solute in a given amount of solvent. A dilute solution is a concentrated solution that has been, in essence, watered down. Think of the frozen juice containers you buy in the grocery store. What you have to do is take the frozen juice from inside these containers and usually empty it into 3 or 4 times the container size full of water to mix with the juice concentrate and make your container of juice. Therefore, you are diluting the concentrated juice. When we talk about solute and solvent, the concentrated solution has a lot of solute versus the dilute solution that would have a smaller amount of solute.

    The terms "concentrated" and "dilute" provide qualitative methods of describing concentration. Although qualitative observations are necessary and have their place in every part of science, including chemistry, we have seen throughout our study of science that there is a definite need for quantitative measurements in science. This is particularly true in solution chemistry. In this section, we will explore some quantitative methods of expressing solution concentration.

    Molarity

    Of all the quantitative measures of concentration, molarity is the one used most frequently by chemists. Molarity is defined as the number of moles of solute per liter of solution. The symbol for molarity is \(\text{M}\) or moles/liter. Chemists also use square brackets to indicate a reference to the molarity of a substance. For example, the expression \(\left[ \ce{Ag^+} \right]\) refers to the molarity of the silver ion. Solution concentrations expressed in molarity are the easiest to calculate with but the most difficult to make in the lab.

    \[\text{molarity} \: \left( \text{M} \right) = \frac{\text{mol solute}}{\text{L solution}}\]

    To solve these problems, we will set them using the factor-label method. To review these steps:

    1. Identify the "given" information in the problem. Look for a number with units to start this problem with.

    2. What is the problem asking you to "find"? In other words, what unit will your answer have?

    3. Use ratios and conversion factors to cancel out the units that aren't part of your answer, and leave you with units that are part of your answer.

    4. When your units cancel out correctly, you are ready to do the math. You are multiplying fractions, so you multiply the top numbers and divide by the bottom numbers in the fractions.

    Example 6.3.1

    What is the concentration, in \(\text{mol/L}\), where \(137 \: \text{g}\) of \(\ce{NaCl}\) has been dissolved in enough water to make \(500 \: \text{mL}\) of solution?

    Solution:

    Given: \(137 \: \text{g} \: \ce{NaCl}\), \(500 \: \text{mL}\) solution

    Find: \(\text{molarity} \: \left( \text{M} \right) = \frac{\text{mol solute}}{\text{L solution}}\)

    \[\frac{137 \: \cancel{\text{g} \: \ce{NaCl}}}{500 \: \cancel{\text{mL solution}}} \cdot \frac{1 \: \text{mol} \: \ce{NaCl}}{58.42 \: \cancel{\text{g} \: \ce{NaCl}}} \cdot \frac{1000 \: \cancel{\text{mL solution}}}{1 \: \text{L solution}} = \frac{4.69 \: \text{mol} \: \ce{NaCl}}{1 \: \text{L solution}} = 4.69 \: \text{M} \: \ce{NaCl}\]

    Example 6.3.2

    What mass of potassium sulfate is in \(250 \: \text{mL}\) of \(2.50 \: \text{M}\) potassium sulfate, \(\ce{K_2SO_4}\), solution?

    Solution:

    Given: \(250 \: \text{mL}\) solution

    Find: \(\text{g} \: \ce{K_2SO_4}\)

    Ratios: \(2.50 \: \text{M}\) or \(2.50 \: \text{mol} \: \ce{K_2SO_4}/1 \: \text{L}\) solution

    \[250 \: \cancel{\text{mL solution}} \cdot \frac{1 \: \cancel{\text{L solution}}}{1000 \: \cancel{\text{mL solution}}} \cdot \frac{2.50 \: \cancel{\text{mol} \: \ce{K_2SO_4}}}{1 \: \text{L solution}} \cdot \frac{174.3 \: \text{g} \: \ce{K_2SO_4}}{1 \: \cancel{\text{mol} \: \ce{K_2SO_4}}} = 109 \: \text{g} \: \ce{K_2SO_4}\]

    Molality

    Molality is another way to measure concentration of a solution. It is calculated by dividing the number of moles of solute by the number of kilograms of solvent. Molality has the symbol \(\text{m}\).

    \[\text{molality} \: \left( \text{m} \right) = \frac{\text{mol solute}}{\text{kg solvent}}\]

    Molarity, if you recall, is the number of moles of solute per volume of solution. Volume is temperature dependent. As the temperature rises, the molarity of the solution will actually decrease slightly because the volume will increase slightly. Molality does not involve volume, and mass is not temperature dependent. Thus, there is a slight advantage to using molality over molarity when temperatures move away from standard conditions.

    Example 6.3.3

    Calculate the molality of a solution of hydrochloric acid where \(12.5 \: \text{g}\) of hydrochloric acid, \(\ce{HCl}\), has been dissolved in \(115 \: \text{g}\) of water.

    Solution:

    Given: \(12.5 \: \text{g} \: \ce{HCl}\), \(115 \: \text{g} \: \ce{H_2O}\)

    Find: \(\text{molality} \: \left( \text{m} \right) = \frac{\text{mol} \: \ce{HCl}}{\text{kg} \: \ce{H_2O}}\)

    \[\frac{12.5 \: \cancel{\text{g} \: \ce{HCl}}}{115 \: \cancel{\text{g} \: \ce{H_2O}}} \cdot \frac{1 \: \text{mol} \: \ce{HCl}}{36.46 \: \cancel{\text{g} \: \ce{HCl}}} \cdot \frac{1000 \: \cancel{\text{g} \: \ce{H_2O}}}{1 \: \text{kg} \: \ce{H_2O}} = \frac{ 2.98 \: \text{mol} \: \ce{HCl}}{1 \: \text{kg} \: \ce{H_2O}} = 2.98 \: \text{m} \: \ce{HCl}\]

    Although these units of concentration are those which chemists most frequently use, they are not the ones you are most familiar with. Most commercial items you buy at the grocery store have concentrations reported as percentages. For example, hydrogen peroxide you buy is approximately \(3\%\) hydrogen peroxide in water; a fruit drink may be \(5\%\) real fruit juice. This unit is convenient for these purposes, but not very useful for many chemistry problems. Molarity and molality are preferred because these units involve moles, or how many solute particles there are in a given amount of solution. This comes in handy when performing calculations involving reactions between solutions.

    Another common unit of concentration is parts per million (\(\text{ppm}\)) or parts per billion (\(\text{ppb}\)). If you have ever looked at the annual water quality report for your area, contaminants in water are typically reported in these units. These units are very useful for concentrations that are really low. A concentration of \(1 \: \text{ppm}\) says that there is 1 gram of the solute for every million grams of the mixture. Because we will not deal with concentrations this low throughout most of this course, we will not use this unit in our calculations. However, you should be aware of it and understand it when you see it.

    Lesson Summary

    • Concentration is the measure of how much of a given substance is mixed with another substance.
    • Molarity is the number of moles per liter of solution.
    • Molality is calculated by dividing the number of moles of solute by the kilograms of solvent. It is less common than molarity but more accurate because of its lack of dependence on temperature.

    Vocabulary

    • Concentration: The measure of how much of a given substance is mixed with another substance.
    • Concentrated: A solution in which there is a large amount of solute in a given amount of solvent.
    • Dilute: A solution in which there is a small amount of solute in a given amount of solvent.
    • Molarity: The number of moles of solute per liter of solution.
    • Molality: The number of moles of solute per kilogram of solvent.

    Contributors


    6.3: Concentration is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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