pH and pOH Relationship Equation, Derivation & Rearrangements

Core idea

Overview

This equation defines the logarithmic relationship between hydronium and hydroxide ion concentrations in aqueous solutions at 25°C. It is derived from the water autoionization constant, Kw, which establishes that the sum of the negative logarithms of these concentrations remains constant in water.

When to use: This relationship is applicable to any aqueous solution at standard temperature (25°C). It is specifically used to convert between the acidity scale (pH) and the basicity scale (pOH) when the concentration of one ion species is known.

Why it matters: It allows chemists to quickly characterize the chemical nature of a solution using a single scale regardless of whether it is acidic or basic. This is essential for maintaining proper conditions in biological systems, industrial processes, and environmental water testing.

Symbols

Variables

pH = pH Value, pOH = pOH

p H

pH Value

V a r iab l e

pO H

pOH

V a r iab l e

Walkthrough

Derivation

Understanding pH and pOH Relationship

Relates pH and pOH through Kw (or pKw) in aqueous solutions.

Applies at a fixed temperature (commonly 298 K in exams).

1

Start with Kw:

Take -log10 of both sides to convert to p-scales.

[H^{+}] [O H^{-}] = K_{w}

2

Derive the p-Relationship:

At 298 K, pKw $\approx$ 14 so pH + pOH = 14.

pH + pOH = p K_{w}

Result

pH + pOH = p K_{w}

Source: OCR A-Level Chemistry A — pH and Buffers

Free formulas

Rearrangements

Solve for $p H$

Make pH the subject

p H = 14 - pO H

Start from the relationship between pH and pOH. To make pH the subject, subtract pOH from both sides of the equation.

Difficulty: 2/5

Solve for $pO H$

pH and pOH Relationship

pO H = 14 - p H

To rearrange the relationship between pH and pOH to solve for pOH, subtract pH from both sides of the equation.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a straight line with a negative slope of -1, crossing both the pH and pOH axes at 14. This linear relationship means that for every unit increase in pOH, the pH decreases by exactly one unit, reflecting the inverse balance between these two values. In chemistry, this shape shows that as pOH values become larger, the corresponding pH values become smaller, illustrating the constant sum of the two variables. The most important feature is the constant negative slope, which confirms that the sum of pH and

Graph type: linear

Why it behaves this way

Intuition

The equation illustrates a seesaw-like balance in aqueous solutions at 25°C, where an increase in acidity (lower pH) is always compensated by a decrease in basicity (higher pOH) to maintain a constant sum.

pH

A measure of the acidity or basicity of an aqueous solution, defined as the negative base-10 logarithm of the molar concentration of hydronium ions, [H₃O⁺].

A lower pH value indicates a higher concentration of hydronium ions, meaning the solution is more acidic.

pOH

A measure of the basicity or acidity of an aqueous solution, defined as the negative base-10 logarithm of the molar concentration of hydroxide ions, [OH⁻].

A lower pOH value indicates a higher concentration of hydroxide ions, meaning the solution is more basic.

14

The value of the negative base-10 logarithm of the ion product of water (pKw) at 25°C. It represents the equilibrium constant for the autoionization of water, Kw = [H₃O⁺][OH⁻] =

This constant signifies that in any aqueous solution at 25°C, the product of the hydronium and hydroxide ion concentrations is fixed, meaning as one increases, the other must decrease proportionally to maintain this

Signs and relationships

-log: The negative logarithm transforms very small, inconvenient concentrations (e.g., 10⁻⁷ M) into more manageable, positive whole numbers (e.g., 7). It also ensures that a higher concentration of H₃O⁺ (more acidic)

Free study cues

Insight

Canonical usage

pH and pOH are dimensionless logarithmic values used to characterize the acidity and basicity of aqueous solutions based on ion activities.

Common confusion

Applying the constant 14 to solutions at temperatures other than 25°C; pKw is temperature-dependent and decreases as temperature increases.

Dimension note

pH and pOH are logarithmic ratios. The log function requires a dimensionless argument, which is achieved by dividing the ion concentration by the standard state concentration (1 M).

Unit systems

$p H$ dimensionless · Defined as the negative decadic logarithm of the activity of hydrogen ions. In dilute solutions, activity is approximated by molar concentration relative to a standard state of 1 mol/dm3.

$pO H$ dimensionless · Defined as the negative decadic logarithm of the activity of hydroxide ions.

$14$ dimensionless · This constant represents the pKw (negative log of the water autoionization constant) specifically at 25°C (298.15 K).

One free problem

Practice Problem

An industrial cleaning solution is found to have a pOH of 3.65. Calculate the pH of the solution at room temperature.

pOH3.65

Solve for: $p H$

Hint: Subtract the given pOH from the constant value of 14.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

Finding pH of a solution when only pOH is known.

Study smarter

Tips

Verify the solution temperature is 25°C, as the sum shifts slightly as temperature changes.
Remember that a low pH implies a high pOH, and vice versa.
The equation is a simplified form of pKw = 14.

Avoid these traps

Common Mistakes

Assuming sum is always 14 at any temperature.
Forgetting the relationship.

Keep going

Related Formulas

Common questions

Frequently Asked Questions

Relates pH and pOH through Kw (or pKw) in aqueous solutions.

This relationship is applicable to any aqueous solution at standard temperature (25°C). It is specifically used to convert between the acidity scale (pH) and the basicity scale (pOH) when the concentration of one ion species is known.

It allows chemists to quickly characterize the chemical nature of a solution using a single scale regardless of whether it is acidic or basic. This is essential for maintaining proper conditions in biological systems, industrial processes, and environmental water testing.

Assuming sum is always 14 at any temperature. Forgetting the relationship.