Chemical Calculations for Solutions | General Chemistry 2

Chemical calculations for solutions are studied in this chapter: the definition of a solution, molarity versus molality, electrolytes, dilution of a solution, precipitation reactions, acid-base titrations


Solution: homogeneous mixture composed of a solute and a solvent
Solute: material dissolved
Solvent: material into which the solute is dissolved (usually present in greater quantity)

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


Saturated Solution: homogeneous mixture that contains the maximum amount of solute possible ⇒ additional solute remains undissolved
Solubility: maximum quantity of solute dissolvable in 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: 

xsolute = nsolutensolution = nsolutensolute + nsolvent



Molarity versus Molality

Molarity M (in mol.L-1):

M = nsoluteVsolution

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



Molality m (in

m = nsolutemsolution

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



Electrolytes: substances that produce ions when dissolved in solution

Strong electrolytes ⇒ completely dissociate into ions (ex: NaCl)
Weak electrolytes ⇒ partially dissociate into ions (ex: HF)
Nonelectrolytes ⇒ do not dissociate into ions (ex: CCl4)

Electrolyte solutions conduct electricity: mobile ions move and conduct an electric current


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


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)


Dilution Principle: decreasing the concentration (molarity) of a solute in a solution by adding more solvent

Solution 1 = concentrated solution; Solution 2 = diluted solution
The amount of solute does not change, only the amount of solvent:
n1 = n2M1 x V1 = M2 x V2


Diluting a solution 10 times means we want: M2 = M110

The amount of solute does not change:
n1 = n2 ⇒ M1 x V1 = M2 x V2M1 x V1 = M110 x V2 ⇒ V2 = 10 V1

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

Precipitation Reactions

When solutions of salts are mixed, a solid can form if ions of an insoluble salt are present. This is a precipitation reaction and the solid is called a precipitate. Molarity is usually used to calculate quantities in precipitation reactions.


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

Acid-Base Titrations

Titration: lab technique used to determine the unknown concentration of an acid or base using a neutralization reaction

Chemical equation of neutralization reaction:
strong acid (pH < 7) + strong base (pH > 7) → salt + H2O

Titration principle:

  • Titrant: acid/base with a known concentration
  • Analyte: acid/base solution being analyzed
  • Indicators: substances which change color with pH

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