Lesson 8:
The Chemistry of Solutions



In this lesson we will answer the following question:
  • What is involved in the chemistry of solutions?
  • How is the concentration of a solution calculated?
  • How are dilutions performed?


Reading Assignment

Along with the online lecture, read chapter 7 in Basic Chemistry for Water and Wastewater Operators.



Solutions are homogenous mixtures with contain two or more substances. A solution has uniform composition. Exampes are sugar and table salt in water. The dissolving medium (water) is the solvent and the dissolved substances (sugar or salt) is the solute. If both components in a solution are 50%, the term solute can be assigned to either component. When gas or solid material dissolves in a liquid, the gas or solid material is called the solute. When two liquids dissolve each other, the major component is called the solvent and the minor component is called the solute.

A Solution


Many chemical reactions are carried out in solutions, and solutions are also closely related to our everyday lives. The air we breathe, the liquids we drink, and the fluids in our body are all solutions. Futhermore, we are surrounded bysolutions such as the air and waters.

A heterogenous mixture of two or more substances is called a suspension. For example, clay in water. In this case, suspended particles of the dispersed substance, clay, are distributed nonuniformly in the medium. The bottom part of the mixture has more particles than the upper. When suspended particles are too small to settle by the force of gravity and too large to dissolve to form a solution, the suspension is known as a colloid. Particle size in a colloidal suspension is 1-100 nm. A nanometer is equal to 1/1,000,000 mm or 10-6 mm. These particles show peculiar dancing movements known as Brownian motions due to their continuous collisions with water molecules. Suspended particles of a colloid cause turbidity, and will be discussed later in the course.

Solutions of ionic compounds and acids in water conduct electricity because they produce ions. These substances are known as electrolytes. Most of the covalent compounds stay as molecules in their solutions and do not conduct electricity. Such substances are known as nonelectrolytes. Sodium chloride and hydrochloric acid are electrolytes, and sugar is an example of a nonelectrolyte.




Types of Solutions

At the molecular level, molecules and ions of a solute are completely mixed with and interact with those of the solvent when a solute dissolves in a solvent. This type of mixing is homogenous because no boundary is visible in the entire solution. In a mixture, differences may exist between regions or parts of the whole system.

Material exists in three states: solid, liquid, and gas. Solutions exist in all of these states:



Forming a Solution

Not every combination of two substances becomes a solution.  When you pour milk on your cereal in the morning, the resulting mixture is not a solution because the cereal does not become dissolved in the milk.  Similarly, when mud in water causes turbidity, the mud is not part of a solution.  We use the term insoluble to describe two substances which do not form a solution when they are mixed together. 

A solution is only formed when two substances mix homogeneously, meaning that any portion of the solution will contain a specific amount of both the solute and the solvent.  In the cases of cereal and milk or of muddy water, the two substances in the mixture will settle apart into two layers over time, so they are not homogeneously mixed.  When you are dealing with a true solution, the two (or more) substances found in the solution will never settle apart.

The homogeneous mixture found in a solution is the result of a chemical interaction between the solute and the solvent.  In a solution, chemical bonds between the solute and solvent hold the solute in the solution and prevent it from settling out.  The chemical bonds found between solute and solvent typically include the weak intermolecular forces introduced in lesson 5 - van der Waal's forces and hydrogen bonds.  For example, when acetone is added to water, hydrogen bonds form between the two substances as shown below:

Acetone and water solution.
Two different views of the interaction between acetone and water.

These bonds keep the acetone dissolved in the solution.  Once the acetone is fully dissolved and mixed into the water, each milliliter of the solution will contain the same amount of acetone and the same amount of water. 

Solutes and Solvents

Although most of the solutions we will deal with in this course are liquids, you should be aware that solutions can be made up of any combination of gases, liquids, and solids.  For example, the air you breathe is an example of a gaseous solution consisting primarily of nitrogen and oxygen while steel is a solid solution in which iron is the solvent and carbon and manganese are the solutes.  

In each solution, the solvent is the substance which determines the state of the finished solution.  For example, when you add salt (a solid) to water (a liquid), you can tell that the water is the solvent since the resulting solution is a liquid.  If both the solute and the solvent have the same state, the solvent is typically the part of the solution which is present in the highest concentration. 

Another distinction between solutes and solvents is that solutes are sometimes changed when they become part of a solution while solvents are typically unchanged.  For example, ionic compounds such as calcium carbonate and table salt break apart into their constituent ions when they become part of a solution. 

Like Dissolves Like

Not every solvent will be able to dissolve every type of solute.  Chemists use the phrase "like dissolves like" to summarize the idea that solvents are best able to dissolve solutes which have a similar chemical composition and which form the same types of bonds. 

Although there are many characteristics which may affect how a solute and solvent relate, the simplest distinction is whether the molecule can form hydrogen bonds.  Molecules such as water, alcohols, and acetone which can form hydrogen bonds tend to be soluble in each other.  On the other hand, molecules such as oil, gasoline, and grease which cannot form hydrogen bonds and instead are attracted to each other only by van der Waal's forces tend to be soluble in each other but are not soluble in water. 

Water and oil don't mix.

When insoluble substances are mixed together, they settle out into two separate layers, as shown above.


Universal Solvents

Water is sometimes called the universal solvent because of its ability to dissolve a diverse array of substances.  Acetone is also occasionally referred to as a universal solvent since it is able to dissolve oils, alcohols, and water.  In truth, however, there is no such thing as a universal solvent because no one substance is capable of dissolving every possible solute. 

Even though there is no true universal solvent, you use one very good solvent every day - soap.  Soap is made up of molecules which act like an oil on one end and like an alcohol on the other, so they are soluble in oils, in water, and in alcohol. 

Soap attracts both oils and water.

When you add soap to your dishwater, the "head" of the soap molecule makes the soap dissolve easily in the water.  The "tail" of the soap molecule attracts oils and grease which are not usually soluble in water and which would not be removed by washing with water alone.  When you rinse the soapy water off your dishes, the oils and greases are washed away with the soap. 



Solubility and Saturation


A variety of units can be used to measure the concentration of solute in a solution.  In general, a concentrated solution is one where the amount of solute in a given volume of solvent is great.  A dilute solution is one where the amount of solute in a given volume of solvent is relatively small.  But can we mix up a solution of any concentration?  For example, can we produce a 90% solution of table salt in water?  How about a 90% solution of table salt in gasoline?

A few substances are infinitely soluble, or miscible, which means that they can be mixed together in any proportion.  Ethyl alcohol and water are an example of miscible substances since they can be mixed together in concentrations ranging from pure alcohol to pure water.  However, most substances are not infinitely soluble. 

Solubility is a term used to describe the amount of solute which can be dissolved in a solvent.  The solubility of two substances will depend on the similarity of the two substances.  As mentioned on the last page, some substances (such as oil and water) have a solubility of close to zero.  Most substances, however, will have a solubility somewhere between complete insolubility and complete miscibility. 



Saturated Solution

Once a solution has reached the limit of the solute's and solvent's solubility, the solution is said to be saturated meaning that it can hold no more solute.  Dissolved particles of the solute are in equilibrium with the undissolved particles. The rate of dissolving is equal to the rate of crystallizing.

If additional solute is added to a saturated solution, the extra solute will settle out, forming a separate layer like the kind you would see when two substances are insoluble. 

Supersaturated salt solution.

A saturated solution of table salt and water.

You can form your own saturated solution of table salt and water as follows.  Add salt to water, stirring constantly until the salt dissolves.  At first, the salt will completely dissolve in the water, discoloring the water slightly but leaving no visible solid residue.  However, once you have added a certain amount of salt to the water, the solution becomes saturated.  When you add more salt past the saturation point, the salt will not dissolve into the water no matter how long you mix the solution.  Instead, the extra salt will settle out in a layer at the bottom of the solution as shown above. 



Unsaturated Solutions

A solutino with any amount of dissolved solute less than the amount required to make a saturated solution is considered to be unsaturated.



Supersaturated Solutions

Whenever a solution contains more solute than it can hold, it is said to be supersaturated. It can be prepared by heating a saturated solution, adding more solute, and then cooling it gently. Excess dissolved solute crystallizes by seeding supersaturated solution with a few crystals of the solute.

Solutions can become supersaturated in a variety of ways, but in every case the supersaturated solution is unstable.  If more of the solute is added or if the conditions change in any way, the extra solute will settle out of the supersaturated solution.  In the water vapor and air solution, dust particles in the air provided the slight change which caused water vapor to settle out, forming clouds and rain. 

If you've ever made sweetened iced tea, you will have taken advantage of the characteristics of a supersaturated solution.  By adding sugar to hot tea, you were able to dissolve much more sugar into the water than you would have been able to dissolve into cold tea.  When the tea cooled, the additional sugar remained dissolved in the tea as a supersaturated solution.  If you tried to add more sugar to the cooled tea, however, the excess solute would drop out of solution and the tea would become less sweet.  A dilute solution contains less solute and a concentrated solution, more.



Standard Solutions

A standard solution is an accurately prepared solution used to determine the concentration of other solutions, which are then known as standardized solutions. In the lab, we can use a standard acid solution to standardize a base solution, and vice versa. The volumetric technique of matching a standard solution and a solution of unknown concentration is known as titration. This process of comparison is known as standardization.


Factors Influencing Solubility

The solubility of two substances depends on several factors in addition to the identity of the substances.  These factors can include characteristics of the environment and the state of the solute and solvent.  In every case, these factors will influence the amount of solute which can be dissolved in a solvent.

Environmental factors which influence solubility include temperature and pressure.  For example, warm air is able to dissolve much more water vapor than cold air can.  You may  have noticed that the air is humid (full of water vapor) only on warm days.  If very humid air cools suddenly, the extra water vapor will fall out of solution and will turn into liquid water.  The liquid water in the air forms clouds or fog.



The solubility of a solute can also depend on its oxidation state, which refers to the amount of electrons found in the substance.   For example, iron and manganese tend to enter water in a low oxidation state, meaning that they have a relatively large number of electrons.  But when these metals are exposed to air, they become oxidized (lose electrons) and are no longer very soluble in water.  So the oxidized metals drop out of solution and cause red or black water complaints as well as stains on sinks and clothes. 

The nature of the solute and solvent play a role as well. Like substances dissolve in like solvents. Inorganic substances dissolve in inorganic solvents and organic substances dissolve in organic solvents. Solubility of a substance depends on two types of forces: attractive forces among the solute particles and attractive forces betwen solute and solvent particles. The former cause lower solubility and the latter, more.


The layering seen in a solution which has passed its saturation point resembles the layering seen when two insoluble substances are mixed.  But, as you can see in the illustration below, these two situations are actually quite different.  One of the layers in the saturated solution contains both solute and solvent while the layers in the insoluble mixture contain only one substance per layer. 

A supersaturated solution and a mixture of two insoluble substances

The extra solute added to a saturated solution may settle either to the top or to the bottom of the solution.  The location of the extra solute depends on its density, a concept we will discuss in a later lesson.



Solutions and Concentration

In lab, we will often deal with solutions.  This lesson introduces two related concepts - the concentration of a solution and the process of diluting a solution. 

parts of a solution
A solution


A solution consists of a liquid (the solvent) with a substance (the solute) dissolved in it.  You are probably familiar with many solutions from your everyday life.  Milk is a solution consisting of water (the solvent) with lactose and salts dissolved in it.  Ocean water is another type of solution.  Both of the examples given above, along with many of the solutions we work with in lab, are known as aqueous solutions because the solvent is water. 

Have you ever mixed up orange juice from concentrate and added too many cans of water?  I'm sure you could taste the difference between the watery orange juice and the properly prepared orange juice.  The amount of solute (orange juice concentrate in the case of this example) in a solution is known as the solution's concentration.  As you will find, solutions with different concentrations act differently in the lab, just as different concentrations of orange juice taste different in your kitchen.  The rest of this page will be devoted to the terminology and math we use to determine the concentration of solutions. 

Up to this point we have used what is called stoichiometry to "count" atoms, molecules and ions by measuring mass of pure substances and using molar masses to calculate the number of chemical entities (moles). Many of the reactions we have studied involve solutions, where we are interested in a solute that is dissolved in a solvent, and we can not measure the mass of the solute independent of the solvent. We also need to realize that many chemical reactions require the reactants to be mobile, where they can bump into each other, and this can occur whenthey are dissolved in a solvent. Sot it is very important that we can count chemical entities when the entity of interest is a solute dissolved in a solvent, and in which case we measure the mass of volume of the solution as a whole (solvent plus all solutes) of which volume is typically the easiest to measure.



Concentration of a Solute

There are two basic ways of reporting the concentration of a solute in a solvent, by reporting the mass of solute in a given volume, or the number of moles of solute in a given volume. These are effectively conversion factors that define the equivalent mass or moles of a solute to the volume of the solution.



Mass Concentration

Mass concentration has typical units of g/L (this can also be mg/L):



1 mg/L = 1 parts per million (ppm). The primary difference is that ppm is a mass/mass calculation, while mg/L is a mass/volume calculation. Due to the special characteristics of water, the concentration of an aqueous solution is the same when calculated in mg/L as it is when calculated in ppm. So, a solution with a concentration of 5.5 mg/L is also 5.5 ppm.



You dissolve 1 mg of salt in water to produce 2 L of solution. What is the concentration of salt in the solution?

You can state the concentration as either 0.5 mg/L or 0.5 ppm.




Mole Concentration (Molarity (M))

Mole concentration has units of mol/L or M:


This means that a 3M solution of sucrose has 3 moles of sucrose per liter.





Molarity (M)

We can measure the concentration of a solute through Molarity (M) because it is the number of moles (gram formula weights of compounds) of the solute per liter of its solution. A molar (M) solution contains 1 mol of the solute per liter, and a 2 molar (2M) solution contains 2 mol of the solute per liter. A molar solution of HCl, for example, contains about 36.5 grams of HCl per liter of solution and is labled M HCl.

There are a few terms you should be familiar with pertaining to molarity, such as Avogadro's number, which states the number of objects in a mole is equal to 6.02 x 1023. A mole is the amount of a substance that contains 6.02 x 1023 particles. A mole of any pure substance has a mass in grams exactly equal to that substance's molar mass. Molarity is a unit of concentration equal to the number of moles of solute in 1L of solution.

This means for CO2, which has a molar mass of 48g (according to the periodic table), that:

6.02 x 1023 molecules of CO2 = 48g

Let's look at the molarity of a NaCl solution. According to the periodic table, the molar mass of NaCl is 58g. This means that a 1M solution of NaCl has 58 grams of NaCl dissolved in 1 liter of water (H2O) or, stated another way:

A 1M solution of NaCl = 58 g/L or 58,000 mg/L (remember from common conversions that 1g is equal to 1,000mg).




What is the molarity when 0.75 mol is dissolved in 2.5L of solution?




Calculate the molarity when 25g of KBr are dissolved in 750mL.

First determine the molar mass of KBr through the periodic table, which is 119 g/mol. Now determine the number of moles before determining the molarity of the solution:


To determine the molarity of the solution, which is defined as moles per liter:


Now let's determine how many grams of solute will need to be added at a certain molarity and volume.




How many grams of table sugar (C12H22O11) would you need to dissolve in water to produce 0.75 liters of a 0.125M aqueous solution of table sugar?

The first step in finding the answer to this question is to calculate the number of moles of table sugar which would be needed:


To get "moles of solute" on one side by itself to solve for it, you will move 0.75 L from the right side to the left side by multiplying. It cancels the "0.75 L" on the right side by doing so, leaving you with:

0.125M  x  0.75 L = moles of solute

0.09375 mol = moles of sugar


Next you have to transform the number of moles of sugar into grams of sugar. We will need to first calculate the molar mass of the table sugar (C12H22O11), which is 342.34 g/mol. To convert this measurement into grams, take the molar mass and multiply it by the number of moles determined.

342.34 g/mol x 0.094 mol = 32.2g


So, to answer the question in the example, 32.2 grams of table sugar would need to be dissolved in enough water to make up 0.75 liters of a 0.125M aqueous solution.


Percent Concentration

The final unit we use to measure concentration is percent.  Percent concentration is calculated using the following formula:

Notice that I have given no units for the amounts of solute and solution.  That is because you can either calculate weight per weight (w/w) percent concentration or volume per volume (v/v) percent concentration.  Since these two methods can give you different answers, you should always note which method you used.



An aqueous solution contains 0.011g of sulfuric acid and 2,000g of water. What is the percent concentration of the solution?

Don't forget that the amount of solution equals the amount of solute plus the amount of solvent (0.011g + 2,000g = 2,000.011g).


Since percent concentration numbers are sometimes hard to understand, we can convert these measurements to ppm (parts per million) very easily because 1 ppm is just 10,000 times bigger than 1%. For example, if you have a 0.02% solution, this is equivalent to 0.02 x 10,000 = 200 ppm, which is a much more convenient figure to use than a tiny percentage.



Parts Per Million (ppm)

The key point about ppm is that it tells you how many "units" of a substance you have for every million units of the whole solution or mixture. In contrast, a percentage tells you how much of something you have "per hundred", and so it's a very similar measurement to ppm. The most important thing to keep in mind when performing a ppm calculation is that the units you choose for the solution and the units for the substance you're interested in, have to be the same. You can't use a mass of the solute and a volume for the whole solution. It must be mass/mass or volume/volume. If the measurement is in mg/L, a conversion to ppm is easy, because 1 mg/L = 1 ppm.

If you want to convert the concentration directly to ppm, bypassing the mg/L step first, you can. Let's look at the previous example for percent concentration, except this time let's determine the ppm.



An aqueous solution contains 0.011g of sulfuric acid and 2,000g of water. What is the ppm of the solution?

Don't forget that the amount of solution equals the amount of solute plus the amount of solvent (0.011g + 2,000g = 2,000.011g).

When reporting concentration, sometimes ppm is easier than a small percentage, such as the case with our examples; 5.5 ppm is much easier than 0.00055%.




In lab, you will often be given a stock solution which you will need to dilute to a given concentration for use in a lab exercise.  Dilution consists of adding more solvent to a solution so that the concentration of the solute becomes lower. Adding a solvent does not change the moles of solute, so Molesinitial = Moles final.


In the picture above, I've shown the solute as yellow dots and the solvent as solid blue.  The 1 L beaker on the left shows the initial concentration, which we might represent as 13 dots/L.  The beaker on the right is the result of dilution of the left beaker.  We added more solvent so that the solution's total volume was 3 L.  As a result, the concentration of the diluted beaker is (13 dots)/(3 L), or 4.3 dots/L. 


Calculating Dilution

Dilution calculations are simplified by using the following equation:

Since Molesinitial = Moles final, concentration can be calaculated from molarity and volume of the solution you have and the solution you want.

M1V1 = M2V2


M1 = molarity concentration of the first solution
V1 = volume of the first solution
M2 = molarity concentration of the second solution
V2 = volume of the second solution

Concentration and volume in the equation above can have any units as long as the units are the same for the two solutions. 

As long as you know three of the four values from the equation above, you can calculate the fourth.  Let's consider a sample problem:




You have 1L of a 0.125M aqueous solution of table sugar. You want to dilute the solution to 0.05M. What do you do?

To solve the problem, you simply plug in the three numbers you know:

M1V1 = M2V2

(0.125M)(1L) = (0.05M)(V2)

(0.125M/L) / 0.05M = V2

2.5L = V2

Using the equation, you determine that the volume of the diluted solution should be 2.5L.  So we simply add enough water to the first solution so that the solution's volume becomes 2.5 L. 


A Few More Notes

Since this lesson is concerned nearly exclusively with math, I'll give you a few more hints to make sure you solve your math problems correctly:



You have 4 L of an 90% aqueous stock solution of hydrochloric acid.  You want 1 L of a 25% solution.  How much of the stock solution do you need to use?

M1V1 = M2V2


4 L and 90% are solution 1 and 25% and 1 L are solution 2. The 4L isn't really important, you just have that much of the stock solution. You need to determine how much of that 4 L you need to create 1 L of a 25% solution. Plug in the values:

M1V1 = M2V2

(90%)( V1) = (25%)(1 L)       (the % needs to be represented in decimal form)

(0.90)(V1) = (0.25)(1 L)         (divide both sides by 0.90 to get V1 on one side by itself to solve for it)

V1 = (0.25) / (0.90)

V1 = 0.27 L

We can use dilution calculations to determine other forms of measurements, such as ppm. Let's look at one more problem:



Water from your well contains 4 ppm iron. you take a 5 mL sample of the well water and dilute it with distilled water until it reaches a volume of 10 mL. What is the iron concentration of the diluted solution?

Think of the solutions as the "before" solution and the "after" solution. The "before solution" is the 5 mL sample, which contains 4ppm iron. The "after" solution will be the solution you make after dilution. You know the volume (10 mL), you need to know the ppm concentration. Plug in the values:

M1V1 = M2V2

(4 ppm)(5 mL) = (M2)(10 mL)                    (divide both sides by 10 mL to get M2 on one side by itself to solve for it)

(20 ppm/mL) / (10 mL) = M2

2 ppm = M2


So the iron concentration will be 2 ppm at a 10 mL volume.




A solution consists of a homogeneous mixture of two or more substances.  Intermolecular forces such as van der Waal's forces or hydrogen bonds hold the solute and solvent together.  The similarities of structure and bonding between the solute and solvent determine the degree of solubility of the pair. 

A few substances are completely miscible, so they can be mixed in any proportion.  In contrast, most solutions will become saturated once the solubility of the solute in the solvent has been reached.  Solutions can become supersaturated when environmental or physical characteristics change. 

Concentration is the amount of solute in a solution, measured as molarity, ppm, mg/L, or percent.  Dilution is a process used to lower the concentration of a solution by increasing its volume. 

New Formulas Used

  M1V1 = M2V2

Conversions between types of concentration:

1 mg/L = 1 ppm

1,000,000 ppm = 100%

1,000,000 mg/L = 100%





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