The pH scale quantifies the acidity or basicity of an aqueous solution, a measurement fundamental to chemistry and biology. The term pH stands for the “potential of hydrogen” and provides a convenient scale for expressing the wide range of hydrogen ion concentrations found in solutions. This scale runs from 0 to 14. A value less than 7 indicates an acidic solution, a value greater than 7 indicates a basic (or alkaline) solution, and a value of 7 is neutral, like pure water.
The scale is logarithmic, meaning that each whole number change in pH represents a tenfold difference in the concentration of hydrogen ions ([H+]). For instance, a solution with a pH of 3 is ten times more acidic than a solution with a pH of 4. This logarithmic nature allows scientists to manage the concentration numbers that would otherwise be cumbersome to write and compare.
Calculating the Initial Hydrogen Ion Concentration
To calculate the pH of a solution, the first step is to determine the concentration of hydrogen ions, represented as [H+], which is measured in Molarity (M) or moles per liter (mol/L). For simple calculations, we focus on strong acids, which are defined as substances that completely break apart, or dissociate, when dissolved in water. Hydrochloric acid (HCl), a common strong acid, releases all of its hydrogen ions into the solution.
For a strong acid that releases one hydrogen ion per molecule, the concentration of the acid is directly equal to the concentration of the hydrogen ions. For example, if you have a \(0.01\) M solution of HCl, the [H+] is also \(0.01\) M.
Strong bases, like sodium hydroxide (NaOH), fully dissociate to release hydroxide ions ([OH-]) instead of hydrogen ions. Calculating the [H+] for a basic solution requires an extra step, which involves using a different but related calculation called pOH.
Applying the pH Formula and Interpreting the Result
Once the hydrogen ion concentration, [H+], is known, the pH can be calculated using the formula: \(\text{pH} = -\log[\text{H}^+]\). The “log” represents the base-10 logarithm, a mathematical function that compresses the wide range of concentration values into the concise 0 to 14 scale. The negative sign is included because the hydrogen ion concentrations are very small numbers, which would otherwise result in negative pH values.
Using the example of a \(0.01\) M [H+] solution, you would first enter \(0.01\), then press the “log” button, and finally, multiply the result by \(-1\). The logarithm of \(0.01\) is \(-2.0\), and multiplying by \(-1\) yields a pH of \(2.0\). This result confirms the solution is acidic since the pH is below \(7\).
Finding the [H+] when the pH is known is achieved using the inverse logarithm function: \([\text{H}^+] = 10^{-\text{pH}}\). If a substance has a pH of \(5.5\), the hydrogen ion concentration is calculated as \(10^{-5.5}\), which equals approximately \(3.2 \times 10^{-6}\) M. This inverse relationship allows conversion between the pH value and the actual chemical concentration.
Understanding the Related pOH Calculation
The concept of pOH is complementary to pH and is used to measure the basicity of a solution, focusing on the concentration of hydroxide ions, [OH-]. The formula for pOH is analogous to the pH formula: \(\text{pOH} = -\log[\text{OH}^-]\). For strong bases, the concentration of the base is equal to the [OH-], which allows for a direct calculation of pOH.
In any aqueous solution, pH and pOH are linked by a constant relationship: \(\text{pH} + \text{pOH} = 14\). This relationship is based on the ionic product of water (K_w), which at 25°C is \(1.0 \times 10^{-14}\). The sum of the two logarithmic scales must equal \(14\) because of this fixed product of [H+] and [OH-] concentrations.
This relationship is particularly useful for finding the pH of a basic solution. For example, a \(0.001\) M solution of the strong base NaOH has an [OH-] of \(0.001\) M, resulting in a pOH of \(3.0\). To find the pH, you simply subtract the pOH from \(14\), yielding a pH of \(11.0\), which correctly indicates a basic solution.