pH Calculator
Calculate pH, pOH, and ion concentrations for acids, bases, and buffers.
Understanding pH and Acid-Base Chemistry
pH is a logarithmic measure of the hydrogen ion concentration in a solution. Introduced by Danish chemist S.P.L. Sorensen in 1909, the pH scale provides a convenient way to express acidity and basicity on a scale from 0 (strongly acidic) to 14 (strongly basic), with 7 being neutral at 25°C.
The Mathematics of pH
pH is defined as the negative base-10 logarithm of the hydrogen ion activity, which for dilute solutions approximates to:
pH = -log₁₀[H⁺]
Because this is a logarithmic scale, each unit change in pH represents a tenfold change in hydrogen ion concentration. A solution at pH 2 has 100 times more H⁺ ions than a solution at pH 4. This is why even small pH changes can have significant chemical and biological effects.
Calculating pH for Different Solution Types
Strong acids and bases dissociate completely in water. For a strong monoprotic acid like HCl at concentration C: pH = -log(C). For a strong base like NaOH: pOH = -log(C), then pH = 14 - pOH.
Weak acids and bases establish an equilibrium. For a weak acid HA with dissociation constant Ka at concentration C, the hydrogen ion concentration is found by solving: Ka = x²/(C - x), where x = [H⁺]. When Ka is much smaller than C, this simplifies to x ≈ √(Ka × C).
Buffer solutions contain a weak acid and its conjugate base (or a weak base and its conjugate acid). Their pH is calculated using the Henderson-Hasselbalch equation: pH = pKa + log([A⁻]/[HA]). Buffers resist pH changes when small amounts of acid or base are added, making them essential in biological and industrial systems.
Key Relationships
- pH + pOH = 14 at 25°C (from the water autoionization constant Kw = 10⁻¹⁴)
- [H⁺] × [OH⁻] = 10⁻¹⁴ M² in any aqueous solution at 25°C
- pKa + pKb = 14 for a conjugate acid-base pair
- Ka × Kb = Kw for a conjugate pair
pH in Practice
Blood pH is maintained between 7.35 and 7.45 by the bicarbonate buffer system — deviations beyond this range (acidosis or alkalosis) are medical emergencies. Soil pH affects nutrient availability for plants; most crops grow best at pH 6.0-7.0. Swimming pool water is kept at pH 7.2-7.8 to balance chlorine effectiveness with swimmer comfort. In industrial chemistry, pH control is critical for reaction rates, product yields, and equipment corrosion prevention.
For reactions involving acids and bases, the equation balancer can help you write correct balanced equations, and the stoichiometry calculator can determine the quantities involved.
Frequently Asked Questions
What is pH and what does the pH scale measure?
pH stands for "potential of hydrogen" and measures the concentration of hydrogen ions (H+) in a solution. It is defined mathematically as pH = -log10[H+], where [H+] is the molar concentration of hydrogen ions.
The pH scale runs from 0 to 14 at 25 degrees C:
- pH 0-6.9 — Acidic solutions. Lower pH means higher acidity. Stomach acid has a pH around 1-2, lemon juice around 2, and coffee around 5.
- pH 7.0 — Neutral. Pure water at 25 degrees C has equal concentrations of H+ and OH- ions (1 x 10^-7 M each).
- pH 7.1-14 — Basic (alkaline) solutions. Higher pH means stronger basicity. Baking soda has a pH around 8.3, ammonia around 11, and drain cleaner around 14.
Because pH is a logarithmic scale, each whole number change represents a tenfold difference in H+ concentration. A solution at pH 3 is ten times more acidic than one at pH 4, and one hundred times more acidic than pH 5.
What is the difference between a strong acid and a weak acid?
The key difference is the degree of dissociation in water:
- Strong acids dissociate completely — every molecule releases its H+ ions into solution. There are only seven common strong acids: HCl (hydrochloric), HBr (hydrobromic), HI (hydroiodic), HNO3 (nitric), H2SO4 (sulfuric), HClO3 (chloric), and HClO4 (perchloric).
- Weak acids dissociate partially — an equilibrium exists between the undissociated acid (HA) and its ions (H+ and A-). The equilibrium constant Ka quantifies this: a larger Ka means stronger dissociation.
For strong acids, calculating pH is straightforward: pH = -log(concentration). For weak acids, you must solve the equilibrium expression Ka = [H+][A-]/[HA], which typically requires the quadratic formula or an approximation.
The same distinction applies to bases: strong bases (like NaOH) dissociate completely, while weak bases (like NH3) establish an equilibrium characterized by Kb.
How does the Henderson-Hasselbalch equation work for buffers?
The Henderson-Hasselbalch equation provides a convenient way to calculate the pH of a buffer solution:
pH = pKa + log([A-]/[HA])
Where pKa = -log(Ka), [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.
Key insights from this equation:
- When [A-] = [HA] — The log term becomes zero, and pH = pKa. This is the point of maximum buffer capacity.
- When [A-] > [HA] — The log term is positive, and pH > pKa (more basic).
- When [A-] < [HA] — The log term is negative, and pH < pKa (more acidic).
Buffers resist pH changes because adding acid converts A- to HA (absorbing H+), while adding base converts HA to A- (absorbing OH-). Buffers work effectively within about 1 pH unit of the pKa value.
What are common applications of pH in real life?
pH measurement and control is critical across many fields:
- Biology and medicine — Blood pH is tightly regulated between 7.35 and 7.45. Even small deviations (acidosis or alkalosis) can be life-threatening. Enzymes function optimally within narrow pH ranges.
- Agriculture — Soil pH affects nutrient availability. Most crops prefer slightly acidic soil (pH 6.0-7.0). Acidic soils may need lime, while alkaline soils may need sulfur amendments.
- Water treatment — Drinking water pH is maintained between 6.5 and 8.5. pH affects disinfection efficiency, corrosion of pipes, and taste.
- Food science — pH controls microbial growth, flavor, and preservation. Pickling uses acidic solutions (pH below 4.6) to prevent botulism.
- Swimming pools — Pool water is maintained at pH 7.2-7.8 for effective chlorine disinfection and swimmer comfort.
What is the relationship between pH, pOH, and Kw?
In any aqueous solution at 25 degrees C, three quantities are linked by the autoionization of water:
Water naturally dissociates into H+ and OH- ions: H2O <-> H+ + OH-. The equilibrium constant for this process is Kw = [H+][OH-] = 1.0 x 10^-14 at 25 degrees C.
Taking the negative logarithm of both sides gives the fundamental relationship:
pH + pOH = 14
- If you know pH — Calculate pOH = 14 - pH, then [OH-] = 10^(-pOH).
- If you know [H+] — Calculate pH = -log[H+], then pOH and [OH-] follow.
- If you know [OH-] — Calculate pOH = -log[OH-], then pH = 14 - pOH.
This relationship only holds at 25 degrees C. At higher temperatures, Kw increases (water dissociates more), making neutral pH slightly below 7. At 37 degrees C (body temperature), Kw = 2.4 x 10^-14 and neutral pH is about 6.8.