Question

The \(\mathrm{pH}\) at which water is maximum dissociated at \(25^{\circ} \mathrm{C}\), is (a) 2 (b) 7 (c) 10 (d) 14

Short answer

The pH at which water is maximally dissociated at 25 degrees Celsius is (b) 7.

Step-by-step solution

Understand the concept of pH

The pH scale is used to quantify the acidity or basicity of an aqueous solution. The pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration, which can be written as pH = -log[H+]. In pure water at 25 degrees Celsius, the concentration of hydrogen ions (H+) is equal to the concentration of hydroxide ions (OH-), and water is considered to be neutral.

Determine the pH of neutral water

At 25 degrees Celsius, pure water dissociates to a very small extent to form equal concentrations of H+ and OH- ions. The concentration of H+ ions in pure water is 1 x 10^-7 M, which results from the self-ionization constant of water, Kw = [H+][OH-] = 1.0 x 10^-14. The pH of a solution where [H+] is 1 x 10^-7 M can be calculated using pH = -log[H+] = -log(1 x 10^-7) = 7.

Identify the correct answer

Since pure water at 25 degrees Celsius has a hydrogen ion concentration of 1 x 10^-7 M, resulting in a pH of 7, option (b) is the correct answer. Water is maximally dissociated at this pH, meaning that it is neither acidic nor basic, but neutral.

Key concepts

pH Scale

The pH scale is a numeric scale used to specify the acidity or basicity (also known as alkalinity) of an aqueous solution. It ranges from 0 to 14, with 7 being neutral. Solutions with a pH less than 7 are considered acidic, and those with a pH greater than 7 are considered basic. The scale is logarithmic, meaning each whole pH value below 7 is ten times more acidic than the next higher value and each whole pH value above 7 is ten times less acidic (or more basic) than the one below it.

This logarithmic nature allows us to work with the extremely wide range of hydrogen ion concentrations found in water-based solutions more easily. It's crucial to note that a pH of 7 is considered neutral only at 25 degrees Celsius, the temperature mentioned in the exercise, as pH can slightly change with temperature.

Hydrogen Ion Concentration

Hydrogen ion concentration in a solution is a measure of the solution's acidity. It refers to the molarity (M), which is the moles of hydrogen ions per liter of solution. The higher the hydrogen ion concentration, the more acidic the solution, and the lower the pH. Conversely, a lower hydrogen ion concentration indicates a less acidic (or more basic) solution and a higher pH.

Understanding the relationship between hydrogen ion concentration and pH is vital. Since pH is defined as the negative logarithm of the hydrogen ion concentration (\( \text{pH} = -\text{log}[H^+] \)), small changes in hydrogen ion concentration can result in significant changes in pH. For instance, a solution with a hydrogen ion concentration of 1 x 10^(-7) M has a pH of 7, as calculated in the exercise solution. Any decrease in concentration will increase the pH and thereby make the solution more basic, while an increase in concentration will decrease the pH, making the solution more acidic.

Self-Ionization of Water

Water's self-ionization is an example of autoionization, where molecules of water, a neutral substance, undergo a chemical reaction with each other to form hydronium ions (H3O+) and hydroxide ions (OH-). In this process, one water molecule donates a hydrogen ion to another water molecule, resulting in the formation of these ions.

The equilibrium constant for this process is known as the self-ionization constant of water, Kw, and at 25 degrees Celsius, it has a value of 1.0 x 10^(-14). This value represents the product of the concentrations of the hydrogen ions and hydroxide ions in pure water. Because pure water is neutral, the concentrations of hydrogen ions and hydroxide ions are equal, which is why the hydrogen ion concentration is 1 x 10^(-7) M, leading to a pH of 7. The self-ionization of water is an important concept because it implies that even pure water contains a small, but not negligible, concentration of ions, which is essential for conduction of electricity and many chemical reactions.