# Chemical Calculations for Solutions | General Chemistry 2

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

## Solutions

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

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

The solubility of NaCl in water at 25°C is 360 g per 1 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 = $\frac{{\mathrm{n}}_{\mathrm{solute}}}{{\mathrm{n}}_{\mathrm{solution}}}$ =

## Molarity versus Molality

Molarity M (in mol.L-1):

M = $\frac{{\mathrm{n}}_{\mathrm{solute}}}{{\mathrm{V}}_{\mathrm{solution}}}$

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

Molality m (in mol.kg-1):

m = $\frac{{\mathrm{n}}_{\mathrm{solute}}}{{\mathrm{m}}_{\mathrm{solution}}}$

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

## Electrolytes

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 = $\frac{1}{2}$

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

## Diluting 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

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

Diluting a solution 10 times means we want: M2 = $\frac{{M}_{1}}{10}$
The amount of solute does not change:
n1 = n2 ⇒ M1 x V1 = M2 x V2M1 x V1 = $\frac{{M}_{1}}{10}$ x V2 ⇒ V2 = 10 V1

To dilute a solution 10 times, 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
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)