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Composition of Solutions

Solution Composition


Problems and Solutions

Introduction to Solutions

A solution is a homogeneous mixture. That means the components of a solution are so evenly spread throughout the mixture that there are no perceivable differences in composition. Solutions can be formed by mixing two substances together such as sugar and water. If you pour a packet of sugar into a glass of water, initially you have a suspension as the sugar crystals float about in the glass. When you have stirred the sugar and water for long enough, you will eventually get a clear, colorless mixture. Some people, especially young children, can be fooled by such a demonstration into thinking that the sugar has "disappeared". However, as chemists, we know better. The law of conservation of matter states that the sugar can not just disappear, it must have gone somewhere else. That somewhere else is into solution. The sugar has become evenly dispersed. In fact the sugar molecules are so well spread out that we can no longer see a single sugar crystals. However, if you taste the water, you will find it to be sugary--confirming the presence of sugar in the water. The minor component of the solution is called the solute. In the present example, sugar is the solute. The major component of the solution is called the solvent. In this case water is the solvent.

Solutions can also be formed by mixing together many different phases of matter. For instance, air is a solution. The solute gasses oxygen, carbon dioxide, argon, ozone, and others are dissolved in the solvent nitrogen gas. Another example is found in "gold" jewelry. Most of the golden jewelry sold in the world is not 24 karat (i.e. 100% pure gold) but rather it is a solution of other metals, commonly silver and copper, in a gold solvent. Such a solution of metal(s) in another metal is called an amalgam.

The Composition of Solutions

Perhaps the most important property of a solution is its concentration. A dilute acetic acid solution, also called vinegar, is used in cooking while a concentrated solution of acetic acid would kill you if ingested. The only difference between such solutions is the concentration of the solute. In order to quantify the concentrations of solutions, chemists have devised many different units of concentration each of which is useful for different purposes.

Molarity, the number of moles of solute per liter of solution, has the units moles / L which are abbreviated M. This unit is the most commonly used measure of concentration. It is useful when you would like to know the number of moles of solute when you know both the molarity and the volume of a solution. For example, it is easy to calculate the volume of a 1.5 M solution of HCl necessary to completely react with 0.32 moles of NaOH:

Normality, the number of molar equivalents of solute per liter of solution, has the units equivalents / L which are abbreviated N. To illustrate the difference between molarity and normality let's assume that we had used a 1.5 M solution of sulfuric acid, H2SO4, instead of a 1.5 M solution of hydrochloric acid, HCl in the above example. Because sulfuric acid can donate two protons to the NaOH, as noted in the , it will only take half as much sulfuric acid as hydrochloric acid to neutralize the sodium hydroxide.

In the present example, the 1.5 M solution of sulfuric acid reacts like a 3.0 M solution of hydrochloric acid because there are two equivalents of H+ per mole of sulfuric acid. Therefore, that solution of sulfuric acid is 3.0 N.

The number of equivalents per mole of solute depends on the reaction of interest. For acid-base reactions, (discussed in Acids and Bases) the molarity and normality are related by the number of protons an acid can donate. For monoprotic acids, like HCl, HF, and HClO4 the molarity and normality are equal. For diprotic acids like H2SO4 and H2C2O4 the normality is twice the molarity. For triprotic acids like H3PO4 the normality is three times the molarity. In redox reactions (discussed in Electrochemistry) the number of moles of electrons a molecule are ion can donate or accept determines the relationship between normality and molarity. For example, it is common for IO3 - to give up five electrons. Therefore, the normality of a solution of IO3 - is five times its molarity.

Molality is the number of moles of solute per kilogram of solvent and is abbreviated with a lower case m. The major advantage to using molality, m, instead of molarity, M, as a measure of concentration is that molality is temperature independent because it, unlike molarity, includes no volume term. As the temperature increase, the volume of solution generally increases slightly, causing a decrease in molarity but no change in molality. Therefore, if we are interested in the properties of a solution at different temperatures, as we will be when we discuss colligative properties, we should use molality. Due to 1 L of water having a mass of 1 kg (at 4oC), the molality and molarity of dilute aqueous solutions near room temperature are approximately the same value. The difference between molality and molarity becomes important for concentrated solutions or at temperatures much different than room temperature.

Another temperature independent measure of concentration is mass percent. Mass percent is defined as the mass of solute divided by the mass of the solution multiplied by 100%. Mass percents are useful when the molar mass of a compound, like a protein, is unknown.

The fifth and final measure of concentration we will discuss is called mole fraction. Mole fraction is the ratio of the number of moles of solute to the total number of moles of solution. This measure of concentration is particularly useful when talking about gaseous solutions and for some of the colligative properties.

To highlight the differences between those five measures of concentration, calculate the molarity, normality, molality, mass percent, and mole fraction of acetic acid, C2H3O2H, in a solution composed of 14.1 g of acetic acid and 250 g of water with a final solution volume of 260 mL. Compare your answers to the solutions given below:

To calculate the molarity, we find the number of moles of acetic acid, HAc, per liter of solution:

To find the normality, we realize that HAc is a monoprotic acid, so the normality equals the molarity. So the solution is 0.904 M in HAc.

To calculate the molality of the solution, we find the number of moles of acetic acid per kilogram of solvent. Note that we divide by the mass of the solvent and not by the mass of the solution.

To calculate the mass percent of acetic acid in water we divide the mass of acetic acid, 14.1 g, by the total mass of solution, 264.1 g, and multiply by 100%. The solution is 5.34% acetic acid by mass.

The final concentration calculation is to find the mole fraction of acetic acid in the solution. To do so we find the number of moles of acetic acid, then divide that by the total number of moles in solution:


There are two common ways to prepare an aqueous solution. The first is to weigh out a known mass of solute, then add it to a given amount of solvent to achieve the desired concentration. The other method involves the dilution of a concentrated stock solution with more solvent to achieve a solution with a lower concentration than the original solution. To calculate the concentration of the diluted solution we will use the following formula:

Figure %: The Relationship between Concentration and Volume for Dilution Problems

Suppose we wished to make 350 mL of a 0.15 M solution of sodium sulfate by diluting some 1.2 M sodium sulfate stock solution. To calculate the volume of stock solution necessary, we can solve the for v1:

There are several variants on the dilution problem such as asking for the volume of solution at a given concentration produced by diluting a known volume and concentration of a stock solution. All of these problems are readily solved by rearranging the concentration-volume equation then plugging in the known information.

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