IX. STOCK SOLUTIONS AND DILUTIONS Consider your 10% w/v sucrose and 1M NaCl, prepared as part of module VIII and stored in the refrigerator, as stock solutions from which other solutions can be made.

EXAMPLE:  MAKING 1% w/v SUCROSE FROM 10% w/v STOCK:

A 1% sucrose solution can be prepared from the 10% stock by 1:10 dilution, that is, one volume of 10% sucrose is diluted to ten times that volume, using water.  Note that "to" ten times that volume is not the same as with ten times that volume.  The "dilution factor" in this case is 1/10 (= desired concentration/original concentration = c2/c1), which can also be described as a "one volume plus nine volumes" dilution.  To make 100 ml of 1% sucrose, one would pipette 10 ml of stock 10% sucrose into a 100 ml volumetric flask, and bring the total volume to 100 ml with water.

Dilution of stock solutions is simply a more convenient may of making up variations of solution concentrations than weighing out the chemical each time.  The amount of chemical involved is exactly the same.  If you were making 100 ml of a 1% sucrose solution "from scratch" rather than from a stock, you would dissolve 1 g of sucrose in 100 ml total.  When making 100 ml of it by dilution, you use 10 ml of 10% stock.  This stock contains 10 g sucrose per 100 ml, = 1 g sucrose per 10 ml.  Thus, the use of 10 ml of 10% stock is equivalent to the use of 1 g solid sucrose.

EXAMPLE:  MAKING 0.1M NaCl (one-tenth Molar) FROM 1.0M STOCK:

0.1M NaCl can be made from your 1M stock using essentially the same procedure as for the 1% sucrose above.  In this case the dilution factor (desired conc./stock conc.= c2/c1) is 0.1M/1M = 1/10.  To make 100 ml of 0.1M NaCl, one would pipette 10 ml of stock 1M NaCl into a 100 ml volumetric flask, and bring the total volume to 100 ml with water.

What is the weight of sodium chloride contained in 10 ml of stock 1M NaCl?  One liter (1000 ml) of this stock contains 58.4 g NaCl; therefore 100 ml of stock contains one-tenth this amount, or 5.84 g, and 10 ml of stock contains 0.584 g.  Thus, in making 100 ml of 0.1M NaCl (previous example), when we pipetted 10 ml stock 1M NaCl into the volumetric flask, we were actually putting 0.584 g NaCl into the flask.

What is the Molarity of a solution containing 0.584 g NaCl per 100 ml?  Multiplying by 10, the solution has a concentration of 5.84 g NaCl per 1000 ml, i.e., 5.84 g/l.  Since 1 Molar NaCl is 58.4 g/l, 5.84 g/l = 0.1M.  Another way to look at it is that 0.584 g NaCl is 1/100th of a Mole, and 100 ml is 1/10th of a liter.  Thus, we have 0.01Mole/0.1 liter = 0.1Mole/l = 0.1 Molar NaCl.

EXAMPLE: PREPARING 100 ml of 0.1M NaCl FROM 1.0M STOCK:

As noted above, the dilution factor = c2/c1 = 1/10.  The dilution factor X the desired volume (v2) = the required volume of stock solution (v1), or, in brief notation,

c2/c1 X v2 = v1.  Dividing each side by v2, we obtain

c2/c1 = v1/v2, and thus

v1 X c1 = v2 X c2.

In words, this means that the volume of stock solution multiplied by its concentration always equals the volume of diluted solution multiplied by its concentration.

In the above example, v1 = 10 ml, c1 = 1.0 M, v2 = 100 ml, c2 = 0.1M.  Checking whether v1 X c1 = v2 X c2, we have 10 X 1 = 100 X 0.1, i.e., 10 = 10, meaning that the dilution calculation is correct.

EXERCISE #1: Prepare 5% sucrose from the 10% stock.  Prepare a total volume of 10 ml (using pipettes and test tube).  Store this solution in the refrigerator.  You will use it later on.

Before proceeding, write down anticipated procedure in your Tech Facility lab notebook.  Be methodical about this, to avoid mistakes.  What is the dilution factor?  What total volume of solution is desired?  What is the stock solution concentration?  What volume of stock will be needed?  What volume of water will be needed?

Your notebook should look something like this:

Solution desired: 5% sucrose; Stock: 10% sucrose

Dilution factor: 5%/10% = 1/2; Volume desired: 10ml

Vol. stock needed, = dilution factor X Vol. solution desired: 5ml

Vol. water needed, = Vol. desired - Vol. stock = 5ml.

Does the relation v1 X c1 = v2 X c2 hold for percent solutions?  Test this using your calculations; record answer in Tech Facility lab notebook.

LISTING INGREDIENTS OF SOLUTIONS IN TABULAR FORM:

Another good way to record information for making solutions is in the form of an ingredient Table:

Ingredient   Final Conc.   Dil. Factor     Amount

10% sucrose      5%           1/2           5 ml

water             -            -            5 ml

total vol.  =  10 ml

EXERCISE #2:

Proceed to make the solution (5% sucrose from the 10% stock).  Prepare a total volume of 10 ml (using pipettes and test tube).

EXERCISE #3:

Prepare 10ml of 1% sucrose from the 5% sucrose.  Again, write down anticipated procedure in Notebook before starting.  Here, and for all other exercises below, check whether your calculations agree with v1 X c1 = v2 X c2.

EXERCISE #4:

Prepare 50ml of 0.1M NaCl from your 1M NaCl stock (write procedure in notebook).  Store this solution in the refrigerator.  You will use it later on.

EXAMPLE: (STOCK SOLUTION CONCENTRATION IN UNITS OF ACTIVITY):

MAKE 100 ml OF HEPARIN SOLUTION AT 50 U/ML, USING A 2,000 U/ML STOCK.

Ingredient Table:

Ingredient      Final Conc.  Dil. Factor       Amount

2,000U/ml heparin  50U/ml   1/40 (50/2000)   2.5 ml (1/40 X 100 ml = 2.5ml)

water                                       97.5 ml

Total vol.  =  100 ml

EXERCISE #5:

IN YOUR TECH FACILITY NOTEBOOK, PREPARE AN INGREDIENT TABLE SHOWING HOW TO MAKE 50 ml OF HEPARIN SOLUTION AT 10 U/ml, USING A 1,000 U/ml STOCK. <<to check: see answer "a" in answer section at end>>   Does the relation v1 X c1 = v2 X c2  hold for calculations using units of activity as well?

DILUTIONS OF PERCENT SOLUTIONS:

Suppose that you had available a stock solution of 95% v/v ethyl alcohol (ethanol), a concentration that is, in fact, a standard one at which ethanol is obtained.  Suppose, also, that your lab protocol calls for 50% ethanol.  The dilution factor is 50/95, and thus if you decide to prepare 100 ml of 50% ethanol the volume of 95% ethanol needed will be 50/95 X 100 = 52.63 ml.  This is certainly an awkward volume to measure out.

Fortunately, there is a different, more convenient way to make the dilution.  Note that, if we elect to make 95ml total volume instead of 100ml, the dilution factor X volume desired

= 50/95 X 95 = 50 ml!  In practice, we need only to take a 100ml graduated cylinder, fill it to 50ml with 95% ethanol, and bring it to 95ml with water (then mix!).  The only conditions are that 95ml total volume is enough, and that the error involved in using a graduated cylinder instead of a volumetric flask can be tolerated.  The latter is usually true for solutions that have concentration specified in percent (as opposed to molarity).

The general rule here is that the total volume to be made is a number of ml equivalent to the number designating the percent concentration of the stock (here, = 95)  Of course, some fraction or some multiple of this number could also be used if more or less total volume is required.

Ingredient table:

Ingredient                     Final Conc.  Dil. Factor   Amount

95% v/v ethyl alcohol (ethanol)   50% v/v    50/95         50 ml

water                                                      45 ml                                               total vol.  =  95 ml

EXERCISE #6: Write out an ingredient table showing how you would prepare 30% v/v ethanol from 95% v/v ethanol.

EXERCISE #7:

Write out an ingredient table showing how you would prepare 30% v/v ethanol from 70% v/v ethanol.

EXERCISE #8:

Write out an ingredient table showing how you would prepare 20% v/v glycerol solution from 75% v/v glycerol solution.

SOLUTIONS CONTAINING MIXTURES OF INGREDIENTS:

Thus far, you have prepared solutions containing a single chemical.  Frequently, however, experiments require the use of complex mixtures of chemicals.

EXAMPLE:  1 liter of 1M sucrose, 1M NaCl.

Make "from scratch", meaning that you will not use stock solutions for this.  For 1 liter, 342.3 g sucrose and 58.4 g NaCl are dissolved in total of 1 liter.  It is usually preferable to add the dry chemicals slowly to water that is stirring continuously (magnetically).

Table in Notebook:

Ingredient   Final Conc.   Dil. Factor     Amount

sucrose         1M             -           342.3 g

NaCl            1M             -            58.4 g

water            -             -        to 1000 ml

total vol.  =  1000 ml

EXAMPLE:  1 liter of 0.1M sucrose, 0.1M NaCl.

Make from stocks; for 1 liter, 100 ml 1M sucrose, 100 ml 1M NaCl, water to 1 liter total.  Should you measure the volumes using graduated cylinders or volumetric flasks?  You must decide in advance on degree of accuracy required.  In many cases, the grad. cylinders are "good enough", but this should be decided by consultation with the research sponsor or other experienced workers in your research lab.  CAUTION: In either case, a large error is possible if you do not get all of the 100 ml stock solution out of either the vol flask or the cylinder.  So - remember to rinse flask or cylinder with water and decant the rinse into the 1 liter volumetric flask before filling to the 1 l mark.

Table in Notebook:

Ingredient   Final Conc.   Dil. Factor     Amount

1M sucrose     0.1M           1/10          100 ml

1M NaCl        0.1M           1/10          100 ml

water            -              -           800 ml

total vol. =  1000 ml

EXAMPLE:  100 ml of 0.1M sucrose, 0.5M NaCl.

Table in Notebook:

Ingredient   Final Conc.   Dil. Factor     Amount

1M sucrose     0.1M           1/10          10 ml

1M NaCl        0.5M           1/2           50 ml

water            -              -           40 ml

total vol.  =  100 ml

EXAMPLE:  100 ml of 0.14M sucrose, 0.58M NaCl.

Table in Notebook:

Ingredient   Final Conc.   Dil. Factor                 Amount

1M sucrose     0.14M      0.14/1 = 0.14 (=14/100)       14 ml

1M NaCl        0.58M      0.58/1 = 0.58 (=58/100)       58 ml

water            -              -                       28 ml

total vol.  =  100 ml

EXAMPLE:  100 ml of 0.64M sucrose, 0.58M NaCl.

Table in Notebook:

Ingredient   Final Conc.   Dil. Factor                 Amount

1M sucrose     0.64M      0.64/1 = 0.64 (=64/100)       64 ml

1M NaCl        0.58M      0.58/1 = 0.58 (=58/100)       58 ml

water            -              -                       ?????

total vol. = 122ml before adding water!!!

Since the volume exceeds 100 ml., this solution cannot be made from the stocks listed!

EXAMPLE:  SAME SOLUTION USING HIGHER CONCENTRATION STOCKS:

100 ml of 0.64M sucrose, 0.58M NaCl, from new 2M stocks.

Table in Notebook:

Ingredient   Final Conc.   Dil. Factor                 Amount

2M sucrose     0.64M      0.64/2 = 0.32 (=32/100)       32 ml

2M NaCl        0.58M      0.58/2 = 0.29 (=29/100)       29 ml

water            -              -                       39 ml

total vol. =  100 ml

The solution can now be made!

EXERCISES #9 - #12:

For each of the following exercises, write an ingredient table in your Techniques Facility Notebook, then prepare the solution.

EXERCISE #9:

100 ml of 0.1M sucrose, 0.1M NaCl.

You already have 1M NaCl stock; prepare 100 ml of 1M sucrose stock before making the mixed solution.  Store the sucrose stock in refrig.

EXERCISE #10:

100 ml of 1% w/v sucrose, 0.1M NaCl.

EXERCISE #11:

100 ml of 0.1% w/v sucrose, 0.05M NaCl

EXERCISE #12:

100 ml of 0.25M sucrose, 0.9% w/v NaCl

You already have 1M sucrose stock; prepare 100 ml of 10% (w/v) NaCl stock before making the mixed solution.

EXAMPLE, SERIAL DILUTION:

100 ml OF 0.0001M sucrose, 0.0001M NaCl (= 0.1mM sucrose, 0.1mM NaCl;  = 100μM sucrose, 100μM NaCl)

Table in Notebook:

Ingredient   Final Conc.   Dil. Factor     Amount

1M sucrose     0.0001M      1/10,000       0.01 ml

1M NaCl        0.0001M      1/10,000       0.01 ml

water            -              -         99.98 ml

total vol.  =  100.00 ml

Although the solution could be made this way, there is a chance for considerable error when very small volumes such as 0.01ml (10μl) must be pipetted.  Therefore, it is preferable in this instance to do "serial dilutions" of the stock 1M sucrose and 1M NaCl solutions, in effect producing more dilute starting stock solutions.

EXERCISE #13:

Prepare the same solution as in previous example, except by serial dilution.  First prepare 100ml each of 0.01M sucrose and 0.01M NaCl using 1ml pipettes and 100ml volumetric flasks.  Then dilute these stocks a second time in preparing the solution.

New Table in Notebook (fill in; check: ans. b):

Ingredient     Final Conc.   Dil. Factor     Amount

0.01M sucrose     ?              ?              ?

0.01M NaCl        ?              ?              ?

water             -              -           98 ml

total vol.  =  100 ml

EXAMPLE:

PREPARE A SET OF SOLUTION TUBES, 10ml EACH, CONTAINING 0.1M SUCROSE AND FIVE CONCENTRATIONS OF NaCl RANGING FROM  0.1M-0.5M IN 0.1M INCREMENTS.  INCLUDE A ZERO NaCl TUBE.

Volumes in ml, tube #

Ingredient      1      2      3      4      5      6

1M sucrose      1      1      1      1      1      1

1M NaCl         -      1      2      3      4      5

water to 10ml   9      8      7      6      5      4

Final conc.

sucrose      0.1M   0.1M   0.1M   0.1M   0.1M   0.1M

NaCl           0    0.1M   0.2M   0.3M   0.4M   0.5M

Note that the 1 ml sucrose can be added to all tubes using the same pipette (or pipette tip), and the varying volumes of NaCl can be added using a single 5 ml pipette.  The water can be added to all tubes using a single 10 ml pipette.

EXERCISE #14:

PREPARE A SET OF SOLUTION TUBES, 10ml EACH, CONTAINING 0.5M NaCl AND FIVE CONCENTRATIONS OF SUCROSE RANGING FROM 0.1M-0.5M IN 0.1M INCREMENTS.  INCLUDE A ZERO SUCROSE TUBE.

First, prepare an ingredients Table as above, then proceed.

(to check: see ans. c).

EXERCISE #15:

PREPARE A SET OF SOLUTION TUBES, 10ml EACH, CONTAINING 0.3M NaCl AND FIVE CONCENTRATIONS OF SUCROSE RANGING FROM 0.05M-0.25M IN 0.05M INCREMENTS.  INCLUDE A ZERO SUCROSE TUBE.

First, work out an ingredients Table by yourself, then check it against answer d.  As you add a given ingredient to a tube, check it off in the Table in your notebook.  That way, if you are interrupted while preparing these solutions, you will know what you have already done when you resume.  It is surprisingly easy to forget where you are in making up a solution, so that the habit of checking off ingredients should be developed.

EXAMPLE:  USE OF ONE SOLUTION TO DILUTE ANOTHER

There is actually another highly efficient way to prepare this same set of solutions.  Since all of them contain 0.3M NaCl, initially only mixtures #1 and #6 are prepared, and in excess volume (say, 40 ml of each).

#1 = 0.3M NaCl

#6 = 0.3M NaCl, 0.25M sucrose

These are then used to prepare all of the other solutions, without adding water, as follows:

Volumes in ml, tube #

Ingredient                  1      2      3      4      5      6  0.3M NaCl                  10      8      6      4      2      -

0.3M NaCl, 0.25M sucrose    -      2      4      6      8     10  Final conc.

sucrose                   0     0.05M  0.1M   0.15M  0.2M  0.25M

NaCl                     0.3M   0.3M   0.3M   0.3M   0.3M  0.3M

The general principle here: if you dilute one solution containing a certain concentration of a chemical (e.g., 0.3M NaCl) with another solution containing the same concentration of that chemical, the concentration of that chemical remains constant.  The dilution affects only ingredients that differ in concentration.

EXERCISE #16:

You have two solutions; one is 1M NaCl, 1M sucrose.  The other is 1M sucrose.  Fill in the ingredient table below to make 50 ml of each solution. (answer e)

Volumes in ml, tube #

Ingredient                   1      2      3      4      5      6  1M sucrose                  50      ?      ?      ?      ?      ?

1M NaCl, 1M sucrose          -      ?      ?      ?      ?      ?  Final conc.

sucrose                    1M     1M     1M     1M     1M     1M

NaCl                        0    0.1M   0.3M   0.4M   0.8M    1M

STOCK SOLUTIONS, ANOTHER LOOK:

Suppose that you need a relatively large volume of a multi-ingredient solution frequently for experiments.  You could prepare it all at once, in very large volume, and store it for future use.  However, this would take up a great deal of refrigerator or freezer space.  You could also prepare it freshly each time by using individual stocks of each ingredient, as in examples above.  However, there is a more efficient way: as a concentrated solution.  Here, the complete solution is made in advance, in concentrated form.

EXAMPLE: Ten experiments are planned, each one requiring one liter of 0.1M sucrose, 0.2M NaCl as an "incubation medium".  Instead of preparing 10 liters of the solution, we prepare one liter at ten times the desired final concentration, store it, and dilute 100ml of it to 1 liter each time it is needed.  This is known in laboratory "lingo" as a ten times or "10 X" solution, and the final solution as "1 X".

In Notebook:

Final concentration and volume of solution desired: 10 liters of 0.1M sucrose, 0.2M NaCl.

For 10X stock, prepare 1M sucrose, 2M NaCl.

Ingredient Table:

Ingredient   Final Conc.   Amount

sucrose        1M          342.3 g

NaCl           2M          116.8 g

water   to 1 liter.

In addition to the usual information, the storage bottle would be labeled "10X incubation medium", and/or "dilute 1:10 before use".

EXERCISE #17:

Experiments are planned, each requiring 1 liter of 0.01M sucrose, 1% NaCl as an "wash medium".  In your notebook, write an ingredient table showing how you would prepare a 10X solution. <see ans. f>

EXERCISE #18:

A FEW PROBLEMS INVOLVING SOLUTIONS ACTUALLY PREPARED IN BIOLOGICAL SCIENCES RESEARCH LABS AT HUNTER COLLEGE:

In Tech Facility notebook, write down how you would do each of the following.  Use ingredient tables.

1. Prepare 10ml of a stock solution containing 20mg/ml streptomycin. 2. Using the above stock solution, what volume of it would you add to 500 ml of a growth medium so that the final concentration of streptomycin is 25 micrograms/ml? (ignore the slight dilution of the 500 ml)

3. Given a 2X stock of phosphate buffer (pH 7.4) plus 10 ml of a stock solution of 16% v/v formaldehyde, prepare as large a volume as you can of 4% v/v formaldehyde in 1X phosphate buffer.

4. Given 1 liter of a stock solution of 1M Na-acetate buffer, pH 5.5, plus 10 ml of a stock solution of cycloheximide containing 10 mg/ml cycloheximide in water, prepare 1 liter of 0.1M Na-acetate, pH 5.5, containing 10 micrograms/ml cycloheximide. EXTRA EXERCISE IN MAKING SOLUTIONS

From the stock solution listed in the following table (columns A & B) make a medium with the final or desired concentrations shown in column C.

 COLUMN A COLUMN B COLUMN C SOLUTION STOCK CONCENTRATION DESIRED CONCENTRATION Formamide 100% 50% SSC 20X 3X Denhardt's 50X 1X Dextran Sulfate 50% 10% EDTA 0.5M, pH 8 1mM Heparin 10mg/ml 1μg/ml tRNA 50mg/ml 0.4mg/ml DTT 1M 10mM SSDNA 2mg/ml 0.1mg/ml Deionized Distilled H2O Final Volume to 100ml

─────────────────────────────────────────────────────────────────

Ingredient      Final Conc.  Dil. Factor       Amount

1,000U/ml heparin  10U/ml 1/100 (10/1000) 0.5 ml (1/100 X 50 ml)

water                                    49.5 ml

Total vol.  =   50 ml

Ingredient     Final Conc.   Dil. Factor     Amount

0.01M sucrose   0.0001M        1/100          1 ml

0.01M NaCl      0.0001M        1/100          1 ml

water             -              -           98 ml

total vol.  =  100 ml

Volumes in ml, tube #

Ingredient      1      2      3      4      5      6

1M sucrose      0      1      2      3      4      5

1M NaCl         5      5      5      5      5      5

water to 10ml   5      4      3      2      1      0

Final conc.

sucrose      0      0.1M   0.2M   0.3M   0.4M   0.5M

NaCl         0.5    0.5M   0.5M   0.5M   0.5M   0.5M

<<Answer d>>            Volumes in ml, tube #

Ingredient      1      2      3      4      5      6

1M sucrose      -      0.5    1      1.5    2      2.5

1M NaCl         3      3      3      3      3      3

water to 10ml   7      6.5    6      5.5    5      4.5

Final conc.

sucrose        0     0.05M  0.1M   0.15M  0.2M   0.25M

NaCl          0.3M   0.3M   0.3M   0.3M   0.3M   0.3M

<<Answer e>>                          Volumes in ml, tube #

Ingredient                   1      2      3      4      5      6

1M sucrose                  50     45     35     30     10      0

1M NaCl, 1M sucrose          0      5     15     20     40     50  Final conc.

sucrose                    1M     1M     1M     1M     1M     1M

NaCl                        0    0.1M   0.3M   0.4M   0.8M    1M

─────────────────────────────────────────────────────────────────

In Notebook:

Final concentration and volume of solution desired: 10 liters of 0.01M sucrose, 1% NaCl.

For 10X stock, prepare 0.1M sucrose, 10% NaCl.

Ingredient Table (for 1 liter):

Ingredient   Final Conc.   Amount

sucrose       0.1M          34.2 g

NaCl          10%          100 g

water   to 1 liter.