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CONCENTRATION AND DILUTION - convert concentration to molarity

Physiology 1, Las Positas College Name:

In science, concentration is a measure of the number of particles (solutes) in a given volume. If one room has 100 people in it, and a room of equal size has 50 people, one can say that the concentration of people in one room is twice that of the other. Quite simple, isn’t it?

On a molecular level, consider whether you put one lump or two of sugar, or no sugar at all, in your coffee. If you use two lumps, you prefer twice as many molecules of sucrose per cup than a person who uses one lump. If you prefer no sugar, the concentration of sucrose molecules is 0 molecules/cup.

If your coffee is too strong or too sweet, you might add a little water. Scientifically speaking, you are diluting your coffee. Dilution reduces the concentration of a solution. If the coffee is still too strong, and you dilute it again, you are performing a serial dilution – that is, you are reducing the concentration in successive steps until the result is satisfactory.

In medicine, the satisfactory result is often that a medicine is strong enough to have its desired effect but weak enough to avoid killing the patient. Thus, it is important to have a firm enough grasp of the concept of concentration to understand it instinctively and be able to manipulate commonly used units of concentration.

What Happens When Something Dissolves

When you add a teaspoon of sugar (sucrose) to your coffee or tea, you are adding and dispersing more than eight septillion (8 x 1024) individual sucrose molecules. These molecules are too small to see, but you can taste them.

While table sugar is made up of sucrose molecules (remember covalent compounds from chemistry?), table salt (sodium chloride) is a very different kind of chemical compound, an ionic compound. It is made up of two smaller particles, a sodium ion and a chlorine ion. Sodium chloride can be made in the laboratory (don’t try this at home!) by exposing a quantity of sodium atoms to a quantity of chlorine atoms. These two elements react explosively, and when they do, each chlorine atom appropriates one electron belonging to a sodium atom. The result is a negatively charged chlorine particle, properly called a chloride ion. Each sodium atom has lost an electron, making it a positively charged sodium ion. Since oppositely charged particles attract each other, the two ions combine to form an ionic compound.

Na + Cl ( Na+ + Cl– ( NaCl

When ionic compounds are added to water, the polarity of the water molecules is often strong enough to “ionize” or “dissociate” the particles of the ionic compound. In the case of NaCl, this means, that the particles of the ionic compound are once again converted into ions, Na+ and Cl–, which likewise are too small to see. The salt is still there; you can’t see it, but you can taste it.

NaCl Na+ + Cl–

Thus, a solution of sucrose is made up of sucrose molecules dispersed in a solvent, in this case, water. A solution of sodium chloride is made up of ions dispersed in the solvent. The substance, which is dispersed in a solvent, is called the solute.

Vocabulary Review
SOLUTION: a homogeneous mixture of a solute dissolved in a solvent.

SOLUTE: can be thought of as the “particulate” part of the solution. It is generally the smaller quantity and is “enveloped” by the solvent. It may be solid, liquid, or gaseous.

SOLVENT: generally the greater quantity in the solution. It is the “suspending” or “carrying” medium, and is generally liquid, although it may be gaseous. For now, we will deal only with liquid solvents. For physiology, the only liquid solvent we will be concerned with is water. Therefore, unless stated otherwise, the solvent is understood to be water.

Not all ionic compounds dissolve in water as easily as sodium chloride. Calcium carbonate (“chalk”) is an ionic compound, which dissolves just slightly in water, but enough to cause tap water to be “hard". Some covalent compounds, such as sucrose and glucose, disperse easily in water,. Other covalent compounds, especially fats and oils, strongly resist dispersal by water, which is why oils usually form a separate layer when mixed with water.

Methods of Expressing Concentration

While concentration is a way of measuring how much of a solute is dissolved in a solvent, there is more than one way of combining these components.

If you weigh both the solute and the solvent before combining them, you have a solution expressed as weight per weight, or w/w. If you weigh the solute, but add just enough solvent to produce a certain volume of solution, the solution is expressed as weight per volume, or w/v. If both the solute and the solvent are liquids, it is usually convenient to measure volumes of each, rather than weighing them, so that your solution is expressed as volume per volume, or v/v.

The choice of method usually depends on convenience or convention. Solids can be measured accurately only by weight. Liquids are more conveniently measured by volume, but also can be measured easily by weight. Thus, when the solute is a solid (which is usually the case, but not always) it is massed out on a balance. When the solvent is a liquid (which is usually the case), it is measured in a graduated cylinder. Since the finished product, the solution, is also a liquid, it is conveniently measured by its volume. A normal saline solution (0.9% sodium chloride in water) would usually be made by massing out a quantity of sodium chloride and dissolving it in the correct volume of water (w/v). On the other hand, rubbing alcohol is a 70% solution of 2-propanol in water; since both of these substances are liquids, you would simply combine 70 volumes of 2-propanol and 30 volumes of water to make rubbing alcohol (v/v).

Units of Concentration: Percentage and Molarity

The simplest way to express concentration is by means of percentage. A certain percent, or hundredths, of the solution is composed of solute, and the remainder is solvent.
When expressing the percentage concentration of a solid solute in a solution, it is generally considered to be the amount of the solute (in mass units) in the finished total volume of the solution. For example:

2% NaCl solution = 2 g NaCl / 100 mL finished solution

This means: 2 g NaCl dissolved in enough water to make a total volume of 100 mL (recall that percent means per hundred).

4% NaCl solution = 4 g NaCl / 100 mL (finished solution)

Normal or physiological saline solution is 0.9% sodium chloride in water. If you intend to make a 100 mL saline solution, how much NaCl do you have to weigh out and dissolve it in how many g of water (w/w)? ____________________________
Since 1 gram of water equals 1 milliliter of water (this is not true of most other liquids!), it would be more convenient to measure out 99.1 mL of water (w/v). However, most convenient is to dissolve the NaCl in a little water and then bring the volume up to a final volume of 100 mL (also w/v). Or, since the amount of solute in the solution is so small, a more casual technician might satisfactorily just combine the NaCl with 100 mL of water and be done with it.

If you need 500 mL (half a liter) of physiological saline, how much NaCl do you have to dissolve in a final water volume of 500 mL?

A common clinical expression of concentration is milligrams per 100 mL solution (mg/100mL). For example, normal fasting levels of glucose in the blood are 80 to 90 mg of glucose per 100 mL of whole blood volume. This is most often expressed as 80-90 mg/dl, since 1 dl = 100 mL. Sometimes this is also expressed as mg%.

Molarity is an important unit of concentration, routinely used by chemists and biologists. It is defined as

I.e., a 1 M NaCl solution = 1 mole of NaCl / liter of solution
Can you remember what a mole is?
A mole of a compound is the amount of the compound in grams equal to its molecular weight. To compute the molecular weight of anything, one simply adds the atomic weights of the components of the compound (molecule).
For the following calculations use the periodic table provided in the lab or see in your textbook p.15.
The molecular wt. of NaCl is the atomic wt. (a.w.) of Na _________
plus the atomic wt. (a.w.) of Cl _________

Total ______________.
In other words: ____________ grams of NaCl is a mole of NaCl.

Of great interest to chemists and (believe it or not) physiologists as well, is the fact that one mole of any molecule has exactly the same number of molecules as does one mole of any other molecule. A smart fellow named Avogadro figured this out and told us that a mole of anything contains 6.02 x 1023 molecules. This is called Avogadro’s number.

So, ___________ grams of NaCl is 1 mole of NaCl and contains 6.02 x 1023 molecules of NaCl.

Based on the periodic table of elements compute the molecular weight of potassium permanganate, KMnO4 .
K (a.w.) ____________
Mn (a.w.) ____________
O (a.w.) ____________

A mole of KMnO4 weighs ____________ grams.

How many molecules are in a mole of KMnO4 ? ____________

Compute the molecular wt. of glucose (C6H12O6):

The use of molarity has a distinct advantage over percentage, because it tells us how many particles of a molecule or ion are present in the solution, and therefore is a true expression of concentration. A 2 M solution is twice as concentrated as a 1 M solution. (Meaning it has twice the amount of solute or number of molecules per finished liter of solution). A 0.5 M solution is 1/2 as concentrated as a 1 M solution, etc.

If we know the moles of a solute per liter of solution, we can easily compute the grams of the solute per liter. Suppose we have a hypothetical solute with a molecular wt. of 40.2 grams.
A 1 M solution of this would contain _______g/ L.

A 0.5 M solution would contain _________ g / L.
(remember, 1 M is twice as concentrated as a 0.5 M solution)

One half liter of a 1 M solution would contain ______ g of hypothetical solute.

At risk of overstating the obvious, it is helpful to remind oneself that molarity, like any concentration can be thought of as a ratio. I.e., a 1 M solution is 1 mole / liter; a 0.5 M solution is 0.5 moles / liter.

If you are given a grams per liter concentration, you can convert it into a molarity concentration. For example, what is the molarity of 4 g of NaCl dissolved in a total volume of one liter? Using the unit factor method, you set up the problem like this:

4 g 1 mole = moles liter x 58.5 g _________ liter

Exercises: You must use the unit factor method and show all your work.
1) You have to measure out 43.9 g of NaCl and dissolve it in a total volume of one liter. What will the molarity of your solution be?

2) What is the molarity of a 0.9% sodium chloride solution? (also known as physiological or normal saline)

Lab Exercise: A Simple Chemical Test for Chloride Ions

As you will recall, sodium chloride is an ionic substance, which dissolves in water to form sodium ions and chlorine ions:
NaCl Na+ + Cl–

Silver nitrate is also an ionic compound, which dissolves in water to form silver ions and nitrate ions:
AgNO3 Ag+ + NO3–

When these four ions are mixed together, the silver ions react with the chloride ions to form a new ionic compound, silver chloride. Even though this compound is ionic, water molecules are not strong enough to ionize it. Thus silver chloride appears in the mixture as cloudy, white particles which eventually settle out (in high concentrations, the particles may appear pale yellow).
Na+ + Cl– + Ag+ + NO3– ( AgCl + Na+ + NO3–

Another new compound, sodium nitrate, also forms, but this compound is very soluble in water and remains ionized.

Perform this test for silver ions by obtaining two test tubes and a rack. Put on gloves for this exercise and the one that follows. Put a dropper full of 0.1 M sodium chloride solution in one tube, and a dropper full of demineralized water in the second tube. Then add one drop of 0.1 M silver nitrate solution to each tube and swirl a bit to mix. Observe the cloudy appearance in the tube, which contains chloride ions (if both tubes are cloudy, you messed up or the tubes were not clean).

Add 4-5 additional droppers full of demineralized water to the tube containing the silver chloride. Observe how the cloudiness persists even when the mixture is diluted. This is a relatively sensitive test, which can be used to detect both chloride ions and silver ions.

Silver ions are toxic heavy metals, therefore, dispose of the contents of both test tubes in the bottle designated for waste containing silver. Rinse the test tubes first with tap water, then with demineralized water.


Many times it is convenient to measure concentrations by first making one or more dilutions of a sample being tested. The diluted sample is then tested for concentration of solute and “back figuring” is done to arrive at the concentration of the solute in the original, undiluted sample. Suppose you have a sample and dilute it by placing one part sample in 9 parts water. What will be the concentration of the diluted sample relative to the original sample? Think of it this way: If you put 1 mL of original solution of [unknown] in 9 mL of water, the solute that had been in 1 mL is now spread (diluted) into a total volume of 10 mL. It is therefore 10 times less (or 0.1 times) as concentrated as the original. To put it simply, the lower concentration is always equal to the higher concentration divided by the dilution factor. For example, if you diluted a 6% solution by a factor of 10, the diluted solution would have a 0.6% concentration. If you diluted an 8 M solution by a factor of 2, the diluted solution would have a 4 M concentration.

If you diluted a solution 1 to 10, and the diluted solution’s concentration was 0.125 M, what was the molarity of the original solution? __________

A serial dilution is a series of dilutions where a first dilution is diluted again. This second dilution is in turn diluted itself, etc. Suppose you make a 1 in 10 dilution (as in the above example) three times. You then test the last diluted mixture and determine that it is 0.00125 M. What is the molarity of the original? ______________

After five 1:10 serial dilutions of a 35M NaOH solution the molarity would be _______

Lab Exercise: Using Serial Dilution to Determine Chloride Concentration

Serial dilution is a process of reducing the concentration of a mixture, in a gradual, methodical way, until the desired concentration is obtained. In this experiment you will serially dilute a solution containing chlorine ions and test each dilution to learn at which concentration the ions are no longer detectable by the test you will use. Serial dilution is a technique frequently used in biology, especially in microbiology to reduce the population of bacteria in a culture to an easily countable number.

In this experiment, you will use three kinds of pipettes: a simple plastic transfer pipette (the one you had calibrated during the last lab) to test for chlorine ions; a traditional serological pipette as well as a micropipette for performing the dilutions.

Preparing a 10% NaCl Solution
Fill a clean 250-mL beaker with demineralized water. Label it and set aside for use during this experiment.

Obtain a clean 150-mL beaker. Set it on a centigram balance. Zero the balance. Add exactly 10.00 g of sodium chloride to the beaker.

At your workstation, use a graduated cylinder to add about 80 mL of demineralized water to the sodium chloride. Use a clean stirring rod to stir the mixture until the compound is completely dissolved, that is, until no crystals remain visible on the bottom when you stop stirring.

Pour the solution back into the cylinder. Add just enough demineralized water to bring the level to 100.0 mL – you may use your calibrated transfer pipette to help you. Make sure the bottom of the meniscus rests exactly on the 100-mL calibration line.

Now pour all the solution back into the beaker. Label the beaker with the correct concentration of the sodium chloride solution in %. Also decide whether this solution is w/w, w/v, or v/v, (circle the right one) and include that information on the label.

Use your calibrated plastic transfer pipette to move exactly 3 mL of the solution to a clean test tube. Label the tube with the concentration of the solution. .

Making a Serial Dilution

Obtain five clean 50-mL beakers, and eight clean test tubes and a rack.

a) Use a serological pipette fitted with a manual pipettor to measure out, as accurately as you can 9 mL of demineralized water into one of the beakers.

In the next step, you will perform a transfer using a micropipette. The micropipette is an expensive and delicate instrument. Before you proceed any further call your instructor over for a quick lesson in proper use of the micropipette.

b) When you have received instruction on use of the micropipette, use it to transfer 1.000 ml of your starting NaCl solution into the beaker containing the 9 mL of water. Be sure to use the blowout feature on the micropipette.

Label the beaker with the correct concentration of the diluted sodium chloride solution (Hint: The solution in this beaker is a 1 to 10 dilution of the NaCl solution you took one ml out of). Again, use your calibrated plastic transfer pipette to move exactly 3 mL of the diluted solution to a clean test tube. Label the tube with the concentration of the solution it contains.

Rinse your 3-mL transfer pipette with demineralized water and discard the rinsings in the sink, then dry the outside with a tissue.

c) Repeat step (b), except use the diluted solution in the 50 ml beaker as your starting solution. In other words, make a 1 to 10 dilution of the dilution you just made in the 5 ml beaker. Again prepare a test tube with exactly 3 mL of this new dilution.

d) Repeat this serial dilution technique three more times; Each time use the latest made solution (always in a 50 ml beaker) as the solution you take 1 ml out of. If you have done this correctly, your final beaker will have a 0.0001% NaCl solution. Make sure all 6 test tubes are labeled.
Into the 7th test tube, after thoroughly cleaning your calibrated transfer pipette, put 3 mL of demineralized to use as a negative control. Into the 8th test tube, put 3 mL of regular tap water.

Test the dilutions in the test tubes for the presence of chloride ions by adding one drop of 0.1 M silver nitrate solution. Start with the 10% solution. Swirl to mix, and observe the positive reaction indicating the presence of chloride ions. Continue with the lower NaCl concentrations until the test for chloride ions is no longer positive -- that is, until you no longer visually detect any cloudiness. Then do the same with the negative control (demineralized water) and with the tap water.

You should have a series of dilutions having decreasingly lower concentrations of a white, cloudy precipitate, the silver chloride. Your negative control should have no precipitate and should be completely clear. Get your instructor to inspect your test tubes before going on.

Estimating the Concentration of Chloride Ions in Tap Water

Compare the appearance of the test tube containing tap water with your serial dilutions to estimate the concentration of chloride ions in the sample of tap water.
NaCl concentration in tap water = __________________________

What is the sensitivity limit of this test? (The sensitivity limit of a test is the smallest concentration that gives a response (cloudiness in this test).)

Cleaning Up

Dispose of all solutions containing silver ions in the bottle designated for waste containing silver. Rinse the glassware first with tap water, then with demineralized water, before returning it to the supply location. Your gloves can go into the regular trash.


Liter of finished solution


Molarity (M) =



What does molarity measure the concentration of? Use molarity as a conversion factor in calculations. Another way of expressing concentration is to give the number of moles of solute per unit volume of solution. 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.