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Amphoteric Nature of Water:
Amphoterism: The ability to react as either an acid or a base.
Water molecules occasionally self-ionizes into hydroxide (OH⁻) and hydrogen ions (H⁺, aka protons).
The hydroxide ion is a strong (conjugate) base and readily accepts protons.
The proton reacts with a base to form conjugate acids.
H⁺ doesn't exist freely in solutions: Protons are very reactive due to their high charge density. In aqueous solutions, protons instantaneously bind to water molecules to form hydronium ions (H₃O⁺).
Hydronium will continuously dissociate into H₂O and H⁺, protonating other compounds. In a system at equilibrium, [H₃O⁺] will appear constant as the dissociation of a hydronium molecule would just protonate another water molecule.
For simplicity, H₃O⁺ and H⁺ symbols can be used interchangeably.
Equation for the self-ionization of water:
2H₂O (l) ⇌ H₃O⁺ (aq) + OH⁻ (aq)
Equilibrium Expression for the Self-Ionization Constant of Water:
Kw = [OH⁻][H₃O⁺]
At 25°C, this constant always equals 1.0×10⁻¹⁴.
In this case, both [OH⁻] and [H₃O⁺] equal 1.0×10⁻⁷ M.
Because the dissociation of water is endothermic, raising the temperature of a solution will simultaneously increase [H₃O⁺] and [OH⁻], while lowering the temperature of a solution will simultaneously decrease those concentrations. Regardless of the temperature changes, the acidity/basicity remains unchanged.
An acidic solution would mean that [H₃O⁺] > [OH⁻]
A neutral solution would mean that [H₃O⁺] = [OH⁻]
A basic solution would mean that [H₃O⁺] < [OH⁻]
Power of Hydrogen (pH):
The pH scale measures the concentration of hydronium ions (H₃O⁺) in an aqueous solution. It is logarithmic (base of 10), which means that every integer on the scale represent a difference of hydronium concentration by tenfold.
The pH of a solution determines how acidic or basic it is. Acids release protons when dissociated, so when mixed with water, these protons merge with water molecules to increase the hydronium content. On the other hand, bases readily accept protons, so when mixed with water, these compounds collect the H+, reducing the hydronium content.
Formula for Calculating pH:
pH = -log[H₃O⁺]
(Originates from the exponent of the concentration in scientific notation: [H₃O⁺] = 10⁻ᵖᴴ)
Lower pH means that the solution is more acidic, and higher pH means that the solution is more basic.
Formulas for Calculating pOH:
pOH = 14 - pH
pOH = -log[OH⁻]
Evidently, the power of hydroxide is inversely related to pH.
Higher pOH means that the solution is more acidic, and lower pOH means that the solution is more basic.
Deriving from the fact Kw = 1.0×10⁻¹⁴ at 25°C, pH + pOH = 14 at that temperature.
Solving pH using Strong Acid/Base Examples:
NOTE: When given the molarity of acids or bases for calculating pH or pOH, you are solving for the concentration of how much H⁺/H₃O⁺ or OH⁻ they produce.
Example #1: What is the pH of 0.50 M HCl?
HCl is an acid, so we use the pH formula: pH = -log[H₃O⁺]
HCl dissociates into H⁺ and Cl⁻, so there must be 0.50 M H⁺/H₃O⁺: pH = -log[0.50]
The answer is pH = 0.30
Example #2: What is the pH of 0.020 M HNO₃?
HNO₃ is an acid, so we use the pH formula: pH = -log[H₃O⁺]
HNO₃ dissociates into H⁺ and NO₃⁻, so there must be 0.020 M H⁺/H₃O⁺: pH = -log[0.020]
The answer is pH = 1.70
Example #3: What is the pH of 0.040 M Ca(OH)₂?
Ca(OH)₂ is a base, so we use the pOH formula: pOH = -log[OH⁻]
Ca(OH)₂ dissociates into Ca²⁺ and 2OH⁻, so there must be 0.080 M OH⁻: pOH = -log[0.080]
The answer for pOH is 1.10. Then, we subtract it by 14: pH = 14 - 1.10
The answer is pH = 12.90
Why is pH important?
A proton has a high charge density and is highly electrophilic. Therefore, pH influences many aspects of chemistry, such as altering the solubility of compounds, affecting equilibrium, and observing acid/base strength on a macroscopic level. It also has numerous applications in other fields, such as its role in biological processes and indicating environmental health.
EXTRA: Can pH go beyond the 0-14 scale?
pH can be measured as a negative or >14 value, but the calculation progressively becomes inaccurate the further it deviates from the normal 0-14 range.
The International Union of Pure and Applied Chemistry (IUPAC) actually defines pH as: pH = -log[a(H⁺)]
pH = -log[H₃O⁺] is a simplified equation, but it is an accurate approximation for most cases.
a(H⁺) stands for activity of hydrogen, measuring its "effective" concentration or its availability to react. This is influenced by the electrostatic interactions of ions in the solution.
Most of everyday, biological, and environmental processes take place in "dilute" solutions that fall within the 0-14 range. In dilute solutions, the ions are dispersed further apart from each other, so they don't interact with each other as often.
It takes a very concentrated solution to have a pH beyond the scale, so the ions are closer together and therefore interact with each other. All the ionic activity would affect simple pH calculations.
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