Ionic product of water at \(310 \mathrm{~K}\) is \(2.7 \times 10^{-14} .\) What is the \(\mathrm{pH}\) of neutral water at this temperature?

Understanding the ionic product of water, often symbolized as \(K_w\), is essential for grasping the pH calculation in aqueous solutions. It represents the equilibrium constant for the self-ionization of water. At 25 degrees Celsius, the value of \(K_w\) is \(1 \times 10^{-14}\), but this value changes with temperature. As seen in the exercise, at 310 K, \(K_w = 2.7 \times 10^{-14}\). This means that the concentration of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) in pure water multiply together to give us this product. Thanks to this relationship, if we know the ionic product of water at a certain temperature, we can determine the pH of neutral water by calculating the concentration of hydrogen ions.

It's also interesting to note that when water is neutral, \([H^+]\) is equal to \([OH^-]\); therefore, by taking the square root of \(K_w\), one can find these concentrations easily. This is crucial because knowing \([H^+]\) allows us to calculate the pH, a measure of how acidic or basic the water is.

The concentration of hydrogen ions, denoted by \([H^+]\), is a key parameter in determining the acidity of an aqueous solution. In pH calculations, it's the cornerstone value. For neutral water, which is neither acidic nor basic, \([H^+]\) equals the square root of the ionic product of water, \(K_w\), as the exercise demonstrates. This principle reflects the balanced dissociation of water into hydrogen and hydroxide ions. In our exercise example, for a temperature of 310 K, the \([H^+]\) is calculated as \(\sqrt{2.7 \times 10^{-14}}\), illustrating that even slight variations in temperature can affect this balance. Making sense of these calculations, and understanding that a pH less than 7 is acidic while greater than 7 is basic, helps students predict the nature of other aqueous solutions beyond just pure water.

The terms 'acidic' and 'basic' (or 'alkaline') describe the nature of aqueous solutions and are quantified by the pH scale, which ranges from 0 to 14. A neutral solution, like pure water at 25 degrees Celsius, has a pH of 7. Solutions with a pH below 7 are acidic, which means they have a higher concentration of hydrogen ions \([H^+]\) than hydroxide ions \([OH^-]\). Conversely, if the pH is above 7, the solution is basic, indicating a higher concentration of hydroxide ions. The exercise provided exemplifies how to compute the pH of water at a different temperature, confirming that neutrality can shift with temperature changes. The broader understanding of acidity and basicity is fundamental in various areas, including chemistry, biology, and environmental science, where pH plays a crucial role in reactions and living conditions.

Water is considered a stable molecule, yet it undergoes a natural process of dissociation, albeit to a very small extent. Dissociation of water refers to the separation of water molecules into hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\). At equilibrium, the concentrations of these ions are exceedingly low, yet crucially important. This dissociation is given by the equation \(H_2O(l) \rightleftharpoons H^+(aq) + OH^- (aq)\). The equilibrium constant for this reaction is the ionic product of water, \(K_w\), and it allows us to determine the concentrations of these ions in neutral water.

The understanding of water dissociation is critical not only for calculating pH but also for understanding chemical equilibrium concepts, reaction mechanisms involving acids and bases, and the overall behavior of solutions in chemical processes.