How do you find the pH of a solution of water?

You find the pH of a solution of water by calculating the negative logarithm of its hydronium ion concentration.

Understanding pH and Hydronium Ions

The pH scale is a numerical scale (typically from 0 to 14) used to specify the acidity or basicity of an aqueous solution. A pH of 7 is neutral, a pH less than 7 is acidic, and a pH greater than 7 is basic. This scale is fundamentally linked to the concentration of hydrogen ions (H⁺) or, more accurately, hydronium ions (H₃O⁺) in the solution.

Hydronium ions (H₃O⁺) are formed when a hydrogen ion (which is essentially just a proton) attaches to a water molecule (H₂O). The concentration of these hydronium ions, denoted as [H₃O⁺], is a key factor in determining acidity. The higher the [H₃O⁺], the more acidic the solution, and the lower the pH.

The Formula for Calculating pH

The fundamental way to find the pH of an aqueous solution, including pure water or a solution dissolved in water, is through a specific mathematical formula that directly uses the hydronium ion concentration.

As stated by the reference, we can calculate the pH of a solution by taking the negative logarithm of the hydronium ion concentration, or pH = -log[H₃O⁺].

• pH: This is the value you want to find.
• -log: This stands for the negative logarithm (base 10). The logarithmic scale compresses a wide range of [H₃O⁺] values into a smaller, more manageable pH scale. The negative sign ensures that pH values are typically positive.
• [H₃O⁺]: This is the molar concentration of hydronium ions in the solution, measured in moles per liter (M).

This formula provides a precise method to quantify the acidity or basicity based on the actual concentration of hydronium ions present.

Applying the Formula

The process of finding pH using the formula involves determining or knowing the [H₃O⁺] and then applying the negative logarithm calculation.

The Case of Pure Water

Pure water is a special case because it undergoes a process called autoionization. A small number of water molecules react with each other to form hydronium ions (H₃O⁺) and hydroxide ions (OH⁻):

2H₂O ⇌ H₃O⁺ + OH⁻

In pure water at 25°C, the concentration of hydronium ions produced by this autoionization is a constant:

[H₃O⁺] = 1.0 x 10⁻⁷ M

Using the formula pH = -log[H₃O⁺]:

• pH = -log(1.0 x 10⁻⁷)
• pH = -(-7)
• pH = 7.0

This calculation confirms that pure water at 25°C is neutral, with a pH of 7.0.

For Other Aqueous Solutions

When substances like acids or bases are dissolved in water, they change the balance of H₃O⁺ and OH⁻ ions, thereby altering the [H₃O⁺] from the pure water value.

• Acids increase the [H₃O⁺], making the solution acidic (pH < 7).
• Bases decrease the [H₃O⁺] (often by increasing [OH⁻], which then reacts with H₃O⁺), making the solution basic (pH > 7).

To find the pH of such solutions using the formula, you need to know the actual [H₃O⁺] of that specific solution. For simple strong acids or bases, this concentration can sometimes be calculated directly from the solution's molarity. For weak acids/bases or more complex mixtures, determining the exact [H₃O⁺] requires considering equilibrium reactions (like Ka or Kb values) or using approximations. However, regardless of how [H₃O⁺] is determined, the method to find pH remains the same: apply the pH = -log[H₃O⁺] formula.

Here are a few examples showing the relationship between [H₃O⁺] and pH:

In summary, finding the pH of a solution of water, whether pure or with dissolved substances, relies on determining the hydronium ion concentration and then applying the fundamental formula: pH = -log[H₃O⁺].