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Laboratory Calculations

Laboratory calculations and making proper solutions are some of the most important procedures in a research or industry laboratory.  If solutions are not prepared accurately, experiments may fail, and this is a waste of time and money.  Biological experiments are particularly sensitive to alterations in chemical composition of solutions.   For example, enzymatic reactions are extremely sensitive to alterations in pH, and salt concentrations; incorrectly prepared media may inhibit bacterial growth; DNA migration in agarose gels can be altered by inexact calculation. 

 Solution components are almost always expressed as concentrations – the amount of solute per volume of solution.   There are many ways to describe solution concentration, but all of them must express the quantity of solute present in a given quantity of solvent. Concentration can be expressed in several different format solutions in the lab, however the two most common are concentrations based on molarity and concentration based on % (weight/volume) and %(volume/volume). 

 Concentrations based on Molarity

Mole = 6.02 X 10²³ atoms
A mole of substance is the amount of that substance that contains 6.02 X 10²³ atoms.  

Molecular weight (MW) = g/mole
The molecular weight of a particular molecule is the sum of the atomic weights of all of its constituent atoms.  For nearly any laboratory reagent, the molecular weight does not need to be calculated, but is provided on the chemical bottle or jar that the reagent comes in, or can be found in reference material. 

 Molarity (M) = moles of solute/liters of solution = moles/L
Molarity is a measure of concentration of a solution, and can be calculated if the molecular weight of a substance is known. 

Example:
You want to prepare exactly 0.5 L (500mL) of a 0.250M Na₂SO₄ solution in water.  How many grams of do you need to measure out for the solution? [MW of Na₂SO₄ is 142]

I am going to present three ways of doing this calculation, as different people think about these things differently. 

Method 1 has as its first step rearranging the equation for M to solve for the number of moles of solute

Then the number of grams of solute is computed. 

Method 2 uses solution molarity as a conversion factor between volume of solution and number of moles of solute.  That is, for the solution here, 0.250 mol Na₂SO_4/1.0 L of solution   

You can remember a general formula for this approach: volume wanted (L) x M x MW = g, remembering that you have to always put in your volume wanted in liters.  So if you want to make 50 mLs of a solution, you would have to put .05L into this equation.  

Method 3, which may be a bit unusual, but sometimes easier depending how your brain works:

Formula to remember:

M x MW = g/L

 M (moles/L) x MW (g/mole) = g/L

 So for the example above:

 0.250M x 142 g Na₂SO₄/ 1 mol Na₂SO₄ = 35.5 g/L

 we only want to make 500 mLs, so 35.5/2 = 17.8g/500mLs

 ** Remember if you are making 500 mls of solution, you are not adding solute to 500 mls of water, but you are putting solute into a final volume of 500mls**

 Concentration based on %

 Solution concentrations expressed as percents have no theoretical significance, but they are commonly encountered and it is necessary to be familiar with them.  Calculation of concentration based on % is actually more straightforward then molarity, but often the most confused.  Weight/volume (w/v) or volume/volume (v/v) can determine these percentages.   [Note: other fields such as industrial chemistry use w/w solutions, however since I have never encountered this in biotech, I am leaving it out]

 10%(w/v) solution  = 10g/100mls.  

10g of solute would be dissolved in water and then the volume adjusted with a volumetric flask or graduated cylinder to 100mL (this might require the addition of anywhere from 70 to 99 mls of water depending on the solute).  ** Again, remember you are not adding 10g to 100 mls of water, but you are putting 10g into a final volume of 100mls** 

5%(v/v) solution  = 5mls/100mls.

When a liquid solute is used it is often convenient to prepare a solution on a volume basis such as dissolving 5.0 ml of ethanol in a sufficient volume of water to produce 100 ml of solution.   This ethanol-water solution is 5% ethanol by volume. 

 To calculate % concentrations, just multiply the percentage x the volume you want to make.

 mg/ml Concentration

Solutions are sometimes expressed in mg/ml.  For example, DNA concentrations are almost always expressed in this manner, even though it is not the most precise way of denoting concentration.  Other laboratory reagents are also sometimes made in this way.

 This type of solution is expressed as how many mg of solute are in 1ml of solution. 

 So to make 100 mls of a 5mg/ml solution of a solute you would need 500mg (5g x 100) of solute, put into a final volume of 100mls. 

Dilutions from stocks

Most of the time in a laboratory setting, you are not weighing out powders every time you want to make a particular solution, for two reasons:

1.        inconvenience

2.       Sometimes it would be nearly impossible to weigh out small enough amounts to make a particular solution (mM concentrations). 

 Certain commonly used reagents are made up in high concentrations, and then diluted as necessary to male other solutions. 

 So for example, 5M NaCl is a common lab stock.  If you need to make a 1M solution of salt, you do not need to weigh out grams of salt, but can just dilute the 5M salt into the desired volume. 

 The Master equation for doing this type of calculation is as follows:

What you want  = the final concentration do you want – this can be expressed in %, M, or mg/ml
What you have = the concentration of the stock solution you have on hand – this can be expressed in %, M, or mg/ml

 **what you want and what you have must be expressed in the same units!!**

Final volume means how much of the solution you want to make.  If you use liters as your units, your answer will be in liters.  If you use mls as units, your final answer will be in mls. 

Ex. 1: If you want to make 100mls of 1M salt from a 5M stock, you can solve as follows:

Ex. 2: If you want to make 1L of 100mM Tris from a 1M stock, you can solve as follows:

  **Notice that I expressed 1M stock as 1000mM because you have to keep the units the same.  I could have converted the 100mM to 0.1M, and the answer would come out the same.**

 Ex. 3: You want to make 40 mls of a 0.5%glucose solution from a 20% stock:

 Mixed solutions

 In a laboratory setting you often have to prepare a solution that is a mixture of many components.   Some of these components may have stock solutions, others may have to be weighed out, etc.  You can again use the “master equation to determine how to make this type of solution. 

Example:

0.5M(what you want)  x 500 mls = 50mls of 5M salt into a final volume of 500mls water

5M (what you have)

0.8%(what you want)  x 500 mls = 40mls of 10% glucose into a final volume of 500mls water

10% (what you have)

1mM (what you want)  x 500 mls = 1mls of 0.5M EDTA into a final volume of 500mls water

500mM (what you have)

0.05 mg/ml (what you want)  x 500 mls = 5mls of 10mg/ml proteinase K into a final volume of 500mls water

5 mg/ml (what you have)

For the MgCl₂

Method 2: (L) x M x MW = g                  0.5L x 0.1M x 203g/mole = 10.15 g MgCl₂ into a final volume of 500mls. 

Method 3: M x MW = g/L                       0.1M x 203g/mole = 20.3g/L =10.15g MgCl₂ into a final volume of 500mls.

So to make you Practice Buffer, you would mix the following in a 500mL graduated cylinder:

50mls of 5M salt

40mls of 10% glucose

1mls of 0.5M EDTA

5mls of 10mg/ml proteinase K

10.15g MgCl₂

You would mix by inversion, and then add water to a final volume of 500mls. 

2X, 10X, solutions

One last way that concentration can be represented in a laboratory setting.  As I said before, concentrated stock solutions are often made for convenience.  Sometimes a concentrated buffer (which is usually a mixture of different reagents) is also made as a concentrated stock.  These stock are generally made in concentrations which make dilution to a “working concentration” convenient. 

For example, if there is a common buffer that is used frequently in large volumes in the lab, concentrated stock that is 10 times more concentrated can be made.  This is referred to as a 10X stock.  The working concentration is referred to as 1X. 

So if you want to make 600 mls of 1X buffer:

1X (what you want)  x 600 mls = 60mls of 10X stock into a final volume of 600mls water

10X (what you have)

Sample Calculation:

You need to make DNA binding buffer for your experiment on protein interactions with DNA.  Below are listed the recipe for this buffer and some reagents that you have at your disposal.  How would you make this solution?