Making Solutions and Dilutions

Making solutions and dilutions is standard practice in biological science laboratories. You need to be able to follow a set of specifications to make solutions and dilutions after calculating the quantities needed for the components of the final solution. You probably learned this in your previous biology or chemistry classes. The following sample questions will help refresh your memory. You should be able to quickly perform similar calculations for other solutions at the end of this laboratory. Also, there may be more than one way to calculate the amounts of solute and solvent for each solution stated in the questions. Please read the overview at the beginning of each section before doing the calculations.

I. Percentages

Overview:

In many cases, the concentration of a substance is expressed as a percentage. Most of the time, this does not imply high precision. However, if you are unsure whether a precise value is necessary, strive to be as exact as possible, as it may make the difference between the success and failure of an experiment.

Caution: Most of your calculations use the metric system, where you typically convert by multiplying by 1000 factors, while percentages are based on 100. It is worth a final check on any percentage calculation to ensure you deal with parts per hundred, not per thousand.

Percentage (weight to final volume)

This percentage is most frequently used for aqueous solutions containing solid solutes. It is presented as 5% (weight/volume) or 5% by the ratio of grams of solute per 100 milliliters (ml) of the final solution.

To calculate the amount of solute and solvent, do the following:

1. Change the percent to its decimal equivalent (5% = 0.05)
2. Determine the volume of solution needed (usually in ml)
3. Use the following equation to determine the weight of solute needed:

percent desired (as decimal equivalent) = weight (g)/volume required (ml)

Percentage (weight to final weight)

It is the same calculation as above, except that the concentration is expressed as the weight of solute to the weight of the final solution/mixture. Remember 1ml of water = 1 g

This calculation is indistinguishable from the one above for dilute aqueous solutions. However, if the resultant solution has a different specific gravity, this percentage will differ.

Question 1: (a) How do you make 25 ml of 3% (w/v) glycine solution if glycine is provided in powder form? Ensure your answer is comprehensive, including the steps involved in creating the solution. (b) How do you make 30 g of 60% (w/w) sucrose with flour?

Percentage (volume to volume)

Mixtures of liquids are often expressed as volume-to-volume. Figure out exactly as above, except using (ml) rather than grams.

Question 2: Instead of glycine powder, you use the same weight of 100% glycine solution that you calculated in Q1a. What is the % (v/v) of the solution if glycine’s specific gravity is 1.6 g/ cm³(ml)?

II. Molarity (Molar and mMolar Solutions)

Overview:

Many important solutions are made as molar solutions, measured in M or mol/L. A 1 M solution contains a mole of solute (grams equivalent weight = the molecular weight of the solute) in one liter of solvent. Although a 1 M solution is a good stock solution, it is too concentrated to be used directly in the laboratory exercises without diluting, as concentrations in the protocols are usually given as mM (= 0.001 M)

1. To make 1 liter of a 1 M solution, you can add up the atomic/molecular weight of the chemical or find the formula weight directly (it is often listed on the label). Weigh this solute and dissolve it in less than 1 liter of water. After the solute is completely dissolved, add water to the 1-liter level.
2. To make other quantities and concentrations, you can use formulas to determine how much solute to add to a particular volume and molarity solution. You can find such formulas in almost any introductory chemistry book. For one liter of a 1 M NaCl solution, weigh 58.44 g of NaCl, dissolve it in a small amount of water, and then bring the final volume to 1 liter. However, you can also use ratios to determine how much solute and water would be needed if the final volume is less than or more than 1 liter.

Question 3: How can you make 34 ml of a 10 mM NaCl solution if the molecular weight of NaCl is 58.44 g/mol?

III. Normality

Overview:

Normality is a specialized case of molarity that refers to the molarity of strongly acidic or basic ions, measured in N or Eq/L. If a substance has only one acidic or basic ion per molecule (i.e., NaOH, HCl), its normality is equal to its molarity. However, if a molecule has more than one acidic or basic group, its normality is greater than its molarity. For example, H₂SO₄ ionizes into two H⁺ ions and one SO₄^2- ion; therefore, it has a normality twice that of its molarity. Because normality represents the concentration of acid or base groups, it is a better measure of the strength of an acid or base than its molarity.

IV. Osmolarity

Overview:

Osmolarity measures the total concentration of dissolved particles in a solution in units of Osm/L. For non-ionizable substances, their osmolarity is equal to their molarity. However, for an ionizable substance, its osmolarity is higher than its molarity. For example, approximately 95% of NaCl molecules dissociate into their constituent ions in water. Therefore, a 1 M solution of NaCl is a 1.9 osmolar solution. Because many substances are partially ionized and the degree of ionization usually depends on concentration, the osmolarity of complex mixtures is more often measured than calculated.

V. Dilutions

Overview:

Many of the solutions you make above are not used directly but are further diluted to be working solutions.

Dilution calculations:

The previously made-up or purchased solutions are often further diluted to make the working solutions. They can be expressed as percentages, N, or as molar concentrations (M, mM). The desired dilutions can be determined by using ratios or the formula: Ci × Vi = cf × vf, where Ci = initial concentration, Vi = initial volume, cf = final concentration, and vf =final volume.

Question 4: You have a 15% solution of red blood cells in PBS. How do you use it to prepare 20 ml of a 2% solution of red blood cells in PBS when the PBS solution is provided?

VI. Mixtures

Overview:

Many of the solutions you use are complex mixtures of substances. The key to understanding these calculations is remembering that all substances must be present at their proper concentrations in the final solution.

To determine final concentrations in complex mixtures, use the formula Ci x Vi = cf × vf for each component of the mixture. Ci: stock concentration, Vi: stock volume, cf: final concentration of the mixture, vf: final volume of the mixture.

Question 5: Your laboratory partner attempts to prepare 145 ml of solution X by adding 45 ml of 100 mM KCl to 100 ml of 100 mM sucrose. What are the final concentrations of (a) KCl and (b) sucrose in solution X?

Steps to make a complex solution:

1. First, write down all the substances in the final mixture and the components’ concentrations or formula weights.
2. Then, determine how much each component should be added to the mixture to give the proper final concentration. You can add and mix all the components.
3. Lastly, bring the solution up to the final volume.

Question 6: How do you make up 10 ml of 100 mM sucrose and 20 mM KCl solution (Solution X) if you have a stock solution of 100 mM KCl and the molecular weight of sucrose is 380 g/mol?

VII. Bacterial Colony Count and Concentration

Overview:

It is often necessary to determine the concentration of a bacterial culture by plating a series of diluted bacterial culture on agar plates and then counting the colonies that grow on the plates. The following is a practice question to help you determine the concentration of the bacterial culture.

Steps to determine concentration of a bacterial culture:

1. First, know the dilution factor and volume plated on the agar plate.
2. Count the number of colonies.
3. Use the following equation to calculate the original bacterial concentration of the culture:

(dilution factor) x (# of colonies on the agar plate / volume of diluted bacterial in ml)

Question 7: You have a bacterial culture that contains an unknown number of bacteria. You prepare a 10⁵ dilution of the culture in a buffer and then place 0.1 ml of this dilution on a Petri dish, spreading it evenly over the surface of an agar plate. After overnight incubation, you observe 30 bacterial colonies growing on the plate. If each colony is formed from a single bacterium, how many bacteria per ml were in the original culture? Show all your calculation steps.