Example of calculating the molarity of ions in an aqueous solution

Dissolving electrolytes in water separates them into oppositely charged ions, which allow the resulting solution to conduct electricity. Some examples of common electrolytes are different types of salts, such as sodium chloride and potassium nitrate, acids such as sulfuric and nitric acids, and some bases such as sodium hydroxide, among others.

In the following sections it is explained in detail by means of examples, how to calculate the molar concentration of ions in solution for different types of electrolytes, including both strong and weak electrolytes.

Why is it important to be able to calculate the molar concentration of ions in solution?

For various reasons, it is necessary to determine or calculate the molar concentration of these ions when preparing a solution. On the one hand, the total concentration of ions allows us to have an idea of ​​their ability to conduct electricity. On the other hand, the total concentration of ions also influences the ionic strength of a solution, which affects the chemical equilibria of different real systems such as weak acids and weak bases.

Finally, the concentration of different ions is very important in the field of biology and biochemistry. This is because the concentrations of ions such as sodium and potassium, as well as chloride and other anions, are important factors in determining membrane potential, the tendency for an ion to pass spontaneously across one side of the membrane. to the other, and a multitude of other transport phenomena of great importance for the proper functioning of the cell.

Calculation of ion concentration in strong electrolyte solutions

A strong electrolyte is an ionic substance that, when dissolved in water, becomes completely ionized. This means that the dissociation reaction is irreversible, and all the formula units of the compound separate to give rise to the maximum possible number of ions in solution.

For this reason, in the cases of strong electrolytes, the calculation of the ion concentration consists of a simple stoichiometric calculation, depending on the balanced or balanced chemical reaction. Take the following case as an example.

Example of calculating the concentration of ions for a strong electrolyte.

Statement:

Calculate the molar concentration of phosphate ions and the molar concentration of potassium ions in a solution prepared by dissolving 10.00 grams of potassium phosphate in 500.0 mL of solution.

Solution:

These types of problems can be solved by following a series of ordered steps. Some steps will be unnecessary depending on the data provided by the statement, but generally speaking, you can always use:

Step #1: Extract the data and unknowns, determine the relevant molecular weights, and perform the necessary unit transformations.

This is almost always the first step in solving any type of problem. In this case, the statement indicates that the solution is prepared by dissolving 10.00 g of potassium phosphate (K ₃ PO ₄ ) , which corresponds to the mass of the solute.

Since the molarity of the ions is requested, we will need at some point the molar mass of the salt which is:

The statement also indicates that 500.00 mL of solution will be prepared, which corresponds to the volume of the solution. Since they ask for molarity, this volume must be transformed to liters.

Step #2: Calculate the molar concentration of the electrolyte. This is also often referred to as the analytical concentration.

In general, it is easier to calculate the concentration of ions in a salt from the molar concentration of the salt itself. We do this using the molarity formula and the data presented above.

Where C _K3PO4 refers to the molar concentration of the salt.

AUTHOR’S NOTE: In general, it is customary to use C to represent any analytical concentration in any concentration unit. By analytical concentration we mean concentrations calculated from the measured amounts of solutes, solvents, and solutions. This is to distinguish them from the concentrations of the different species after a chemical reaction or when establishing chemical equilibria.

Step #3: Write the balanced dissociation equation

In this case, it is a strong electrolyte, so the reaction is irreversible (an equilibrium is not established):

Step #4: Use the stoichiometric relationships obtained from the balanced equation to determine the concentration of the ions of interest.

Once the equation is written, all that is required is to use stoichiometry to determine the concentrations of the ions. We can do the stoichiometric calculations directly using the molar concentration instead of the moles, since all the calculations we are carrying out refer to a single solution in which the volume is not changing, so the concentration is directly proportional to the moles of each species.

This means that the concentrations of the two ions are determined by:

Calculation of ion concentration in weak electrolyte solutions

In the case of weak electrolytes, the fundamental difference is that the dissociation reaction is reversible, and only a small fraction of the solute molecules dissociate to form free ions. For this reason, to calculate the ion concentration in these cases, the chemical equilibrium must be solved.

Example of calculating the ion concentration for a weak electrolyte.

Statement:

Calculate the molar concentration of acetate ions and hydronium ions in a solution prepared by dissolving 10.00 grams of acetic acid in 500.0 mL of solution, knowing that the acid has an acidity constant of 1.75 .10 ^-5 .

Solution:

Since this case deals with a solution of acetic acid, which is a weak electrolyte, we must proceed to solve the ionic equilibrium that is established by dissolving this solute in water. The first steps are the same as above, but from step 4 onwards the procedure changes. Here’s how:

Step #1: Extract the data and unknowns, determine the relevant molecular weights, and perform the necessary unit transformations.

The mass of the solute is again 10.00g and the volume of the solution is also 500.0 mL, which is equivalent to 0.5000 L as we saw earlier. The molecular weight of acetic acid (CH ₃ COOH) is 60.052 g/mol.

Step #2: Calculate the molar concentration of the electrolyte.

Using the data presented above, the initial or analytical molar concentration of acetic acid is:

Step #3: Write the balanced dissociation equation

Unlike the previous case, because it is a weak electrolyte, the reaction is reversible, so an equilibrium is established:

Step #4: Solve the chemical equilibrium to determine the concentrations of all species.

This part of the process is completely different from the previous ones, since the final concentrations of the ions cannot be determined directly from the initial concentration of the acid by stoichiometry, since these concentrations must also satisfy the equilibrium condition given by the law of mass action.

In this particular case, the equilibrium condition is determined by the expression of the equilibrium constant:

The following ICE table relates the initial concentrations to the final ones. In this case, since we do not know in advance how much acid actually dissociates, then the change in its concentration must be expressed as an unknown (X). Then, by stoichiometry, it is established that X must also be formed from acetate ions and from protons:

To find the unknown, X, it is enough to use the equation of the acidity constant:

This equation can be rewritten as:

which is a second degree equation whose solution, after substituting the value of the acidity constant, is:

As we can see in the ICE table, the concentration of both ions is, in this case, equal to X, so we can write

The concentration of both ions is equal to 2.41.10 ^-3 molar.

References

Bolívar, G. (2020, July 9). Weak electrolytes: concept, characteristics, examples. Recovered from https://www.lifeder.com/electrolitos-debiles/

Brown, T. (2021). Chemistry: The Central Science (11th ed.). London, England: Pearson Education.

Chang, R., Manzo, Á. R., Lopez, PS, & Herranz, ZR (2020). Chemistry (10th ed.). New York City, NY: MCGRAW-HILL.

Garcia, J. (2002). Concentrations in clinical solutions: theory and interconversions. Rev. costarric. science. med. , 23 , 81–88. Retrieved from https://www.scielo.sa.cr/scielo.php?script=sci_arttext&pid=S0253-29482002000100008

Sarica, S. (nd). Ion concentration with examples. Retrieved from https://www.chemistrytutorials.org/ct/es/44-Concentraci%C3%B3n_de_iones_con_ejemplos