Question

At \(25^{\circ} \mathrm{C}\), how are the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of a solution related to each other?

Short answer

At 25 degrees Celsius, the sum of pH and pOH of a solution is always 14. This means if you know the pH, you can calculate the pOH by subtracting the pH from 14, and vice versa.

Step-by-step solution

Understand the relationship between pH, pOH, and Kw

At any temperature, the pH and pOH of a solution are related through the water ionization constant, Kw. At room temperature, which is approximately 25 degrees Celsius, the ionization constant of water, Kw, is always 1.0 x 10^(-14). The relationship is given by the formula pH + pOH = 14 at 25 degrees Celsius.

Express the relationship at 25 degrees Celsius

Because we are focusing on the temperature of 25 degrees Celsius, we use the standard value of Kw at this temperature. The formula simplifies the connection between pH and pOH to the equation pH + pOH = 14.

Key concepts

The Water Ionization Constant (Kw)

Understanding the water ionization constant, often denoted as Kw, is essential in acid-base chemistry. It represents the equilibrium constant for the self-ionization of water, a process where water molecules dissociate into hydrogen ions (\text{H}^+)\text{ or protons and hydroxide ions (\text{OH}^-)}. At any temperature, the product of the concentrations of these ions in pure water is a constant.For a balanced equation of water dissociation, \[\text{2H}_2\text{O} \rightleftharpoons \text{H}_3\text{O}^+ + \text{OH}^-\text{,}\] where \(\text{H}_3\text{O}^+\) represents the hydronium ion, which is simply a hydrogen ion attached to a water molecule. The water ionization constant is mathematical evidence of the chemical equilibrium between water and its ions.

Kw at 25 Degrees Celsius

At a standard temperature of 25 degrees Celsius, \(K_w\), the water ionization constant, has a value of \(1.0 \times 10^{-14}\). This value is critical in analyzing the properties of aqueous solutions and in calculating the pH and pOH, which are measures of acidity and basicity, respectively. A neutral solution at this temperature has equal concentrations of hydrogen ions and hydroxide ions, meaning both pH and pOH will be 7 (as \(\text{pH} = -\text{log} [\text{H}^+]\) and \(\text{pOH} = -\text{log} [\text{OH}^-]\)). When calculating the pH or pOH of a solution, using the known value of \(K_w\) at 25 degrees Celsius simplifies the process and allows for a clear understanding of the solution's acidic or basic nature.

Acid-Base Chemistry

Acid-base chemistry revolves around the substances that donate or accept protons. Acids are proton donors that increase the concentration of hydrogen ions in a solution, while bases are proton acceptors that increase the concentration of hydroxide ions. pH is the measure of acidity, whereas pOH measures the level of basicity in a solution.The pH scale usually ranges from 0 to 14, with 7 being neutral. A pH less than 7 indicates an acidic solution, whereas a pH greater than 7 points to a basic one. By mastering the concepts of pH and pOH, and their relationship through Kw, students can predict the behavior of substances in different chemical reactions, a skill that is fundamental in numerous scientific endeavors.

Chemical Equilibrium

Chemical equilibrium is the state of a chemical reaction in which the rate of the forward reaction equals the rate of the reverse reaction, resulting in no overall net change in the concentrations of reactants and products. This concept is visible in the ionization of water, which is a reversible process, and exemplified by the constant value of Kw.Understanding equilibrium is crucial in acid-base chemistry. In the context of the water ionization constant, once equilibrium is reached, even though water molecules continue to dissociate and recombine, the ratio of the product of concentrations of the ions to the concentration of the un-ionized water remains constant. Thus, being adept at calculating and understanding equilibrium will provide a solid foundation for comprehending complex reactions in chemistry.