Chemical Calculations for Solutions | General Chemistry 2

Chemical calculations for solutions are studied in this chapter: solubility and mole fraction, electrolytes, ionic strength, precipitation reactions, net ionic equation, molarity vs. molality, dilution, acid-base titrations

Solutions and Solubility


A homogeneous mixture consisting of a solvent (usually present in greater quantity) and one or more dissolved species called solute. A saturated solution is an homogeneous mixture that contains as much solute as possible ⇒ additional solute will remain undissolved

An aqueous solution of NaCl is a homogeneous mixture composed of NaCl (the solute) dissolved in water (the solvent)



The maximum of solute that can be dissolved in a specified amount of a solvent at a particular temperature. A solid is more soluble at higher temperatures and in a solvent with similar types of intermolecular forces

The solubility of NaCl in water at 25°C is 360 g per kg of water ⇒ 360 g of NaCl can be dissolved in 1 kg (1 L) of water. If more NaCl is added, it will remain undissolved


Mole fraction x:

The number of moles of a component divided by the total number of moles in a mixture. The mole fraction of a solute is calculated as follows:

xsolute = nsolutensolution = nsolutensolute + nsolvent




A substance that produces ions when dissolved in solution. Electrolytic solutions conduct electricity: mobile ions move and conduct an electric current

  • Strong electrolytes are completely dissociated into ions (ex: NaCl)
  • Weak electrolytes are partially dissociated into ions (ex: HF)
  • Non-electrolytes dissolve to give non-conducting solution ⇒ they do not dissociate into ions (ex: CCl4)


Ionic strength I (in mol.L-1):

A measure of the electrical intensity of a solution containing ions

I = 12 i = 1n ci zi2

ci = concentration of ion i (in mol.L-1)
zi = charge of ion i

Precipitation Reactions

Precipitation reaction:

A chemical reaction in which a precipitate is formed. A solid forms if ions of an insoluble salt are present

Ni2+ (aq) + S2- (aq) → NiS (s)
Aqueous solution of Ni2+ and S2- results in the formation of a precipitate: NiS

AgNO3 (aq) + NaCl (aq) → AgCl (s) + NaNO3 (aq)
Homogeneous mixture of AgNOand NaCl results in the formation of a precipitate: AgCl


Types of equations:

  • Molecular equation: compounds are represented as if none of the reactants or products has dissociated
  • Ionic equation: strong electrolytes are represented as ions
  • Net ionic equation: an ionic equation from which spectator ions have been eliminated ⇒ only ions involved in the reaction are shown


AgNO3 (aq) + NaCl (aq) → AgCl (s) + NaNO3 (aq)   [molecular equation]
Ag+ (aq) + NO3- (aq) + Na+ (aq) + Cl- (aq) → AgCl (s) + Na+ (aq) + NO3- (aq)   [ionic equation]
Ag+ (aq) + Cl- (aq) → AgCl (s)   [net ionic equation]


How to determine the net ionic equation for a precipitation reaction:

  1. Write and balance the molecular equation
  2. Write the ionic equation by representing strong electrolytes into their constituent ions
  3. Identify the ions that appear on both sides of the equation: these are the spectator ions
  4. Write the net ionic equation removing spectator ions

Molarity vs. Molality

Molarity M (in mol.L-1):

The number of moles of solute per liter of solution

M = nsoluteVsolution

nsolute = moles of solute (in mol)
Vsolution = volume of solution (in L)


Molality m (in

The number of moles of solute dissolved in 1 kg of solvent

m = nsolutemsolution

nsolute = moles of solute (in mol)
msolution = masse of solution (in kg)

Dilution of a Solution

Mole-volume relationship:

n = M x V

n = number of moles (in mol)
M = molarity (in mol.L-1)
V = volume (in L)


The process of preparing a less concentrated solution from a more concentrated one. The principle of a dilution is to decrease the concentration (molarity) of a solute in a solution by adding more solvent without changing the total number of moles of solute present in solution: moles of solute before dilution = moles of solute after dilution

Volume of solvent required to dilute a solution 10 times:

Solution 1: concentrated solution; solution 2: dilute solution

Diluting a solution 10 times means: M2 = M110
The total number of moles of solute present in the solution does not change during dilution ⇒ moles of solute before dilution = moles of solute after dilution: n1 = n2
 ⇒ M1 x V1 = M2 x VM1 x V1 = M110 x V2 ⇒ V2 = 10 V1

To dilute a solution 10 times, add 10 times the volume of solvent

Acid-Base Titrations


A laboratory technique used to determine the unknown concentration of an acid or base using a neutralization reaction. A neutralization reaction is a reaction between an acid and a base resulting in the formation of water and a salt.

Titration principle

A solution of known concentration (the titrant) is gradually added to a solution of unknown concentration (the analyte) in order to determe the unknown concentration. Indicators, substances which change color with pH, are used to identify the endpoint of the titration. At the endpoint of the titration, the number of moles of acid is equal to the number of moles of base.

How to determine the concentration of an acid solution:

  1. Add a strong base solution with known concentration to the acid solution
  2. Stop adding the base exactly when all the acid has been neutralized: indicator should change color. This is called the endpoint of the titration
  3. Determine the volume of base added
  4. Determine the concentration of the acid solution
    At the endpoint of the titration, moles of acid = moles of base
    MaVa = MbVb with M = molarity (mol.L-1) and V = volume (L)

Check your knowledge about this Chapter

The solubility of a solute in a solvent is primarily determined by the nature of the solute and solvent, temperature, and pressure:

  • The "like dissolves like" principle suggests that polar solutes tend to dissolve in polar solvents, while nonpolar solutes are more soluble in nonpolar solvents.
  • Temperature usually increases solubility for solids and liquids but may decrease it for gases
  • Pressure has a significant impact on the solubility of gases, with higher pressures generally leading to higher solubility according to Henry's law.
  • Additionally, the presence of other solutes can affect solubility through a common ion effect or by altering the dielectric constant of the solvent.

The mole fraction of a component in a solution is calculated by dividing the moles of that component by the total moles of all components in the solution. It provides a measure of the proportion of moles contributed by a specific component.

An electrolyte is a substance that, when dissolved in a solvent, produces ions and conducts electricity. It differs from a non-electrolyte, which does not ionize in solution and does not conduct electricity.

A strong electrolyte is a compound that completely dissociates into ions when dissolved in water, resulting in a solution that conducts electricity very well due to the high concentration of ions. A weak electrolyte, on the other hand, only partially dissociates into ions in solution, making it a poor conductor of electricity compared to strong electrolytes.

Ionic strength is a measure of the concentration of ions in a solution, considering both the number of ions and their charges. It is crucial because it accounts for the overall effect of ions on solution properties and reactions.

A precipitation reaction is defined as a chemical reaction in which two soluble ionic compounds in solution react to form an insoluble solid substance, known as a precipitate.

We recognize a precipitation reaction by observing the formation of a cloudy or milky appearance in the solution or the settling of a solid at the bottom. This visual change indicates the removal of ions from the solution in the form of an insoluble compound, signaling the occurrence of a precipitation reaction. Additionally, solubility rules can be applied to predict whether a given combination of ions will result in the formation of a precipitate based on their inherent solubilities.

A net ionic equation focuses only on the species directly involved in the reaction, excluding spectator ions. It simplifies the representation of the chemical change, highlighting the essential components.

Molarity is the concentration of a solute in a solution expressed as moles of solute per liter of solution, whereas molality is the concentration expressed as moles of solute per kilogram of solvent. Molarity is more suitable for reactions occurring in a solution volume, while molality is preferred in situations where temperature changes may affect the solution volume.

Molarity is calculated by dividing the moles of solute by the volume of the solution in liters, while molality is calculated by dividing the moles of solute by the mass of the solvent in kilograms. Molarity is in moles per liter (mol/L), and molality is in moles per kilogram (mol/kg).

The relationship between moles and the volume of a solution can be expressed using the formula for molarity:

n = M x V

n = number of moles (in mol)
M = molarity (in mol.L-1)
V = volume (in L)

The formula for dilution is M1 V1 = M2 V2​, where and M1 and V1​ are the initial concentration and volume, and M2 and V2 are the final concentration and volume. This formula ensures the conservation of moles of solute before and after dilution. It is commonly used to calculate the volume or concentration needed when diluting a solution to achieve a desired concentration.

An acid-base titration is performed to determine the concentration of an unknown solution by reacting it with a known solution of opposite acidity. The titration involves incremental addition of the titrant (known solution) until the reaction reaches completion, as indicated by a noticeable change in the pH of the solution.

An equivalence point in a titration is the moment at which the amount of titrant added is stoichiometrically equivalent to the amount of substance present in the sample. This means the reactants have reacted in their exact proportions according to the balanced chemical equation, with no excess of either reactant.

It is typically determined by using an indicator that changes color at a specific pH or by using a pH meter to detect a sudden change in the pH of the solution, which corresponds to the completion of the reaction.

The role of indicators in acid-base titrations is to provide a visual signal, usually a color change, to identify the endpoint of the titration. Indicators are chosen based on their pH transition range, which should coincide with the pH at which the reaction between the acid and base is stoichiometrically equal. The correct choice of an indicator ensures that the color change will happen at the equivalence point, thus allowing the experimenter to accurately determine when the titration is complete.

To calculate the concentration of an unknown solution in an acid-base titration:

  1. Write the balanced equation.
  2. Determine the mole ratio between the acid and base.
  3. Record the volume and concentration of the titrant (the solution of known concentration).
  4. Identify the equivalence point volume.
  5. Calculate moles of titrant.
  6. Use the mole ratio to find moles of the unknown.
  7. Divide the moles of the unknown by the volume of the solution to get the concentration.