Consider two beakers of pure water at different temperatures. How do their \(\mathrm{pH}\) values compare? Which is more acidic? More basic? Explain.

Pure water naturally undergoes a process called self-ionization or autoionization, where water molecules break down into hydronium ions (H₃O⁺) and hydroxide ions (OH⁻). This reaction can be represented as follows: \[2 H_2O \rightleftharpoons H_3O^+ + OH^-\] The ion product constant for water is given by: \[K_w = [H_3O^+][OH^-]\] At 25°C, the value of \(K_w\) is 1.0 x 10⁻¹⁴. In pure water, the concentration of hydronium ions is equal to the concentration of hydroxide ions ([H₃O⁺] = [OH⁻]). Therefore, at 25°C, the pH of pure water is 7. However, the value of \(K_w\) is temperature-dependent. As the temperature increases, \(K_w\) increases as well, indicating that the concentrations of H₃O⁺ and OH⁻ ions are greater.

As the temperature of the water increases, the ion product constant (\(K_w\)) also increases. This means that the concentrations of both H₃O⁺ and OH⁻ ions are increasing. Since the pH scale is defined as: \[pH = -\log_{10} [H_3O^+]\] An increase in the concentration of H₃O⁺ ions would result in a decrease in pH value, making the water more acidic. On the other hand, an increase in the concentration of OH⁻ ions would result in a decrease in the pOH value, making the water more basic. However, it's essential to note that the increase in both H₃O⁺ and OH⁻ ions' concentrations occurs simultaneously, maintaining an overall neutral charge in the water even at different temperatures. So, although the pH and pOH values might not be equal to 7, the water is still considered neutral because [H₃O⁺] = [OH⁻] at any given temperature.

As stated earlier, as the temperature increases, the concentration of both H₃O⁺ and OH⁻ ions increases. This means that the pH value of water will decrease as the temperature increases. Therefore, the sample of water with a higher temperature will have a lower pH value but will still be neutral due to the equal concentrations of H₃O⁺ and OH⁻ ions. In summary, the water at a higher temperature will have a lower pH but will still maintain its neutral property, as the concentrations of both H₃O⁺ and OH⁻ ions increase equally with temperature. Neither sample of water at different temperatures is considered more acidic or more basic than the other, as they both remain neutral, even with a pH that deviates from 7.