At \(100^{\circ} \mathrm{C}\) the \(\mathrm{H}^{+}\)concentration in water is about \(1 \times 10^{-6} \mathrm{~mol} / \mathrm{L}\), about 10 times that of water at \(25^{\circ} \mathrm{C}\). At which of these temperatures is (a) the \(\mathrm{pH}\) of water the greater? (b) the hydrogen ion (hydronium ion) concentration the higher? (c) the water neutral?

The pH of a solution is a measure of its acidity or basicity, and is calculated using the formula: \( \text{pH} = -\text{log}[\text{H}^{+}] \). This formula tells us that pH is a logarithmic function of the hydrogen ion concentration \( [\text{H}^{+}] \).
So, if the hydrogen ion concentration increases, the pH decreases, making the solution more acidic. Conversely, if the hydrogen ion concentration decreases, the pH increases, making the solution more basic.
In the given problem, calculating the pH for water at two temperatures involved substituting the hydrogen ion concentrations into the formula.
At 100°C, the concentration \( [\text{H}^{+}] \) is \(1 \times 10^{-6} \text{ mol/L} \), resulting in a pH of 6. At 25°C, the concentration \( [\text{H}^{+}] \) is \(1 \times 10^{-7} \text{ mol/L} \), resulting in a pH of 7.
This reveals that the pH at 25°C is higher than at 100°C because of the lower hydrogen ion concentration at the lower temperature.

Hydrogen ion concentration is crucial in determining the acidity of a solution. It is denoted as \( [\text{H}^{+}] \) and plays a direct role in the calculation of pH.
In the context of water, at 100°C, the \( [\text{H}^{+}] \) is \(1 \times 10^{-6} \text{ mol/L} \), meaning there are more hydrogen ions in the water compared to at 25°C, where the \( [\text{H}^{+}] \) is \(1 \times 10^{-7} \text{ mol/L} \).
This higher concentration of hydrogen ions at higher temperatures makes the water more acidic, which reduces its pH value. So, in simple terms, the hotter the water, the more acidic it becomes due to the increased presence of hydrogen ions.
Understanding hydrogen ion concentration helps us see why the pH value changes with temperature variations, explaining why water at 100°C is more acidic (lower pH) than at 25°C.

Water neutrality refers to the state where the concentrations of hydrogen ions \( [\text{H}^{+}] \) and hydroxide ions \( [\text{OH}^{-}] \) are equal.
For water, this means pH equals pOH, and their product remains constant, a value known as the ion product of water \( K_w \). The relationship is given by:
\[ K_w = [\text{H}^{+}] \times [\text{OH}^{-}] \]
At 25°C, \( K_w = 1 \times 10^{-14} \), resulting in equal concentrations of hydrogen and hydroxide ions, leading to a neutral pH of 7. Even when the temperature changes, the product \( K_w \) adjusts, but hydrogen and hydroxide ion concentrations remain balanced.
In the given problem, even though pH changes with temperature, water remains neutral at both 100°C and 25°C because the relationship \( pH = pOH \) holds true, ensuring neutrality is maintained.