pH Calculator

pH is a scale used to measure how acidic or basic (alkaline) a solution is. The pH scale typically ranges from 0 to 14 in aqueous solutions, with:

• pH values less than 7 indicating acidic solutions
• pH equal to 7 indicating a neutral solution
• pH values greater than 7 indicating basic (alkaline) solutions

Technically, pH is the negative logarithm (base 10) of the hydrogen ion concentration [H⁺] in moles per liter: pH = -log₁₀[H⁺]

The pH scale is logarithmic (based on powers of 10) for several important reasons:

• It compresses a wide range of hydrogen ion concentrations into a manageable scale from 0 to 14
• Hydrogen ion concentrations in solutions can vary by a factor of 10¹⁴, which would be unwieldy to express directly
• Using a logarithmic scale makes it easier to express and compare these vast differences in concentration

Because of this logarithmic nature, each whole number change in pH represents a tenfold change in hydrogen ion concentration. For example, a solution with pH 3 is ten times more acidic than a solution with pH 4 and one hundred times more acidic than a solution with pH 5.

pH and pOH are complementary measurements in aqueous solutions at 25°C:

• pH measures the concentration of hydrogen ions [H⁺]
• pOH measures the concentration of hydroxide ions [OH⁻]
• They are related by the equation: pH + pOH = 14

This relationship exists because of water's self-ionization equilibrium: H₂O ⇌ H⁺ + OH⁻, with an equilibrium constant (Kw) of 1.0 × 10⁻¹⁴ at 25°C.

Therefore, if you know the pH, you can calculate the pOH by subtracting the pH from 14, and vice versa.

To calculate pH from hydrogen ion [H⁺] concentration:

Where [H⁺] is the molar concentration of hydrogen ions in mol/L.

For example, if the hydrogen ion concentration is 1.0 × 10⁻³ mol/L:

pH = -log₁₀(1.0 × 10⁻³) = -(-3) = 3

Conversely, to calculate hydrogen ion concentration from pH:

[H⁺] = 10⁻ᵖᴴ

For example, if the pH is 5:

[H⁺] = 10⁻⁵ = 0.00001 mol/L = 1.0 × 10⁻⁵ mol/L

Pure water has a pH of 7 at 25°C because of its self-ionization equilibrium:

H₂O ⇌ H⁺ + OH⁻

In pure water, the concentrations of H⁺ and OH⁻ ions are equal. The equilibrium constant for this reaction (Kw) is 1.0 × 10⁻¹⁴ at 25°C:

Kw = [H⁺][OH⁻] = 1.0 × 10⁻¹⁴

Since [H⁺] = [OH⁻] in pure water, we can write:

[H⁺]² = 1.0 × 10⁻¹⁴

[H⁺] = 1.0 × 10⁻⁷ mol/L

Using the pH formula:

pH = -log₁₀(1.0 × 10⁻⁷) = 7

It's important to note that the pH of pure water can vary with temperature because Kw changes with temperature. At higher temperatures, Kw increases, resulting in a pH slightly lower than 7 for pure water.

Buffers are solutions that resist changes in pH when small amounts of acid or base are added. They typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid.

Buffers maintain pH through two main mechanisms:

• When acid is added: The conjugate base in the buffer reacts with the added H⁺ ions, neutralizing them. For example, in an acetate buffer (CH₃COOH/CH₃COO⁻):

  CH₃COO⁻ + H⁺ → CH₃COOH

• When base is added: The weak acid in the buffer donates H⁺ ions to neutralize the added OH⁻ ions:

  CH₃COOH + OH⁻ → CH₃COO⁻ + H₂O

The pH of a buffer solution is determined by the Henderson-Hasselbalch equation:

pH = pKa + log₁₀([conjugate base]/[weak acid])

Where pKa is the negative logarithm of the acid dissociation constant.

Buffers are most effective when the ratio of conjugate base to weak acid is between 0.1 and 10, which corresponds to a pH within ±1 unit of the pKa.

pH plays a crucial role in living organisms for several reasons:

• Enzyme activity: Enzymes function optimally within specific pH ranges. Changes in pH can alter enzyme shape and activity, affecting metabolic processes.
• Protein structure: pH affects protein folding and function, as proteins have groups that can gain or lose protons depending on pH.
• Cell membrane integrity: Extreme pH values can damage cell membranes and disrupt cellular processes.
• Blood pH regulation: Human blood must maintain a pH between 7.35-7.45. Even small deviations can lead to serious conditions like acidosis or alkalosis.
• Digestive system: Different regions of the digestive tract operate at different pH values, optimized for specific digestive enzymes:
  • Stomach: Highly acidic (pH 1.5-3.5) for protein digestion
  • Small intestine: Slightly alkaline (pH 7-8.5) for fat and carbohydrate digestion
• Plant nutrient uptake: Soil pH affects the availability of nutrients to plants. Most plants prefer slightly acidic soils (pH 6-7).
• Aquatic organisms: Fish and other aquatic life are sensitive to pH changes in their environment. Most freshwater organisms thrive in waters with pH 6.5-8.5.

Living organisms have developed various buffer systems to maintain appropriate pH levels in different body compartments and tissues, highlighting the critical importance of pH homeostasis for life.