Question

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

Short answer

The pH values of the two beakers of pure water at different temperatures differ because the ion product of water, \(K_w\), changes with temperature. In beaker A (higher temperature), the pH value is higher due to increased self-ionization, while in beaker B (lower temperature), the pH value is lower. However, neither beaker is more acidic or more basic than the other, as the water in both beakers remains neutral, with equal concentrations of \(H^+\) and \(OH^-\) ions. The only difference is their temperatures, which affect the ion product of water and the pH values.

Step-by-step solution

Understanding the pH of pure water

First, let us recap the concept of pH. The pH of a solution is defined as the negative logarithm of the concentration of hydrogen ions \([H^+]\) in the solution: \[pH = -\log_{10} [H^+]\] For pure water, it undergoes a self-ionization process, forming equal amounts of hydrogen ions (\(H^+\)) and hydroxide ions (\(OH^-\)): \[2H_2O \rightleftharpoons H_3O^+ + OH^-\] Since pure water is neutral and not acidic or basic, the concentration of hydrogen ions \([H^+]\) equals the concentration of hydroxide ions \([OH^-]\).

Ion product of water

The ion product of water (\(K_w\)) is the product of the concentrations of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) in water at equilibrium: \[K_w = [H^+][OH^-]\] At 25°C, the value of \(K_w\) is \(1.0\times10^{-14}\), which means the concentration of hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) are equal, and each has a concentration of \(1.0\times10^{-7}\) M. Thus, the pH of pure water at 25°C is: \[pH = -\log_{10} [H^+] = -\log_{10}(1.0\times10^{-7}) = 7\]

The effect of temperature on pH of pure water

The ion product of water, \(K_w\), increases with the increase in temperature due to an increase in the self-ionization process. It means that, at temperatures higher than 25°C, the concentrations of \(H^+\) and \(OH^-\) will be higher than \(1.0\times10^{-7}\) M but still equal to each other. When the temperature goes down, on the other hand, the ion product of water decreases. This means that the concentrations of \(H^+\) and \(OH^-\) will be lower than \(1.0\times10^{-7}\) M, but still equal to each other.

Comparing the pH values

Now we have two beakers of pure water at different temperatures. Let's denote them as beaker A (higher temperature) and beaker B (lower temperature). Since the ion product of water is higher in beaker A, the concentrations of \(H^+\) and \(OH^-\) are higher too, and so is the pH value. In beaker B, all those values are lower due to lower ion self-ionization, which results in a lower pH value.

Determining which is more acidic or more basic

As we mentioned before, in both beakers, the concentration of hydrogen ions (\(H^+\)) is equal to the concentration of hydroxide ions (\(OH^-\)); hence, both beakers contain neutral water. Even though beaker A has a higher pH value than beaker B, neither beaker is more acidic or more basic than the other. In both cases, the water is neutral, with the only difference being their temperatures, which affect the ion product of water and the pH values.

Key concepts

Self-ionization of Water

Water is a unique substance because it can act as both an acid and a base. This dual role allows water to undergo a process known as self-ionization. In this process, water molecules interact with each other to form ions. Specifically, two water molecules react, resulting in the formation of a hydronium ion (\(H_3O^+\)) and a hydroxide ion (\(OH^-\)). The chemical equation representing this equilibrium process is:
\[2H_2O \rightleftharpoons H_3O^+ + OH^-\]

• This reaction is in equilibrium, meaning that while some water molecules dissociate into ions, others recombine back into neutral water.
• The concentrations of hydronium and hydroxide ions are equal in pure water, leading to a neutral pH.

Self-ionization is a crucial concept because it helps explain why pure water has a pH of 7 at 25°C. Even though ions are being formed, they are in equal concentration, so their effects neutralize each other. This self-ionization is also temperature-dependent, a point we'll explore further in another section.

Ion Product of Water

The ion product of water, denoted as \(K_w\), is a constant that represents the product of the concentrations of hydronium and hydroxide ions in water at equilibrium. At 25°C, the value of \(K_w\) is specifically defined as:
\[K_w = [H^+][OH^-] = 1.0 \times 10^{-14}\]

• This equation shows that the concentrations of \([H^+]\) and \([OH^-]\) are both \(1.0 \times 10^{-7}\) M under standard conditions.
• The value of \(K_w\) is temperature-dependent, changing as the temperature rises or falls.

The concept of the ion product is significant because it is the basis for determining pH. From \(K_w\), one can derive that the pH of pure water at 25°C is 7, indicating neutrality. It also provides a benchmark for understanding how changes in temperature affect water's acidity and basicity, a concept that relates directly to our next point concerning temperature effects.

Effect of Temperature on pH

The temperature of water can significantly impact its pH, altering how neutral, acidic, or basic the water appears to be. As temperature rises, the self-ionization of water increases due to more energy being available to drive the reaction:
\[2H_2O \rightleftharpoons H_3O^+ + OH^-\]This increased ionization raises the concentrations of both hydronium and hydroxide ions. Consequently, the value of \(K_w\) increases at higher temperatures. Here’s a closer look at how temperature affects pH:

• At higher temperatures, since \(K_w\) increases, so do the concentrations of \([H^+]\) and \([OH^-]\). The pH decreases slightly because even though more \([H^+]\) are present, \([OH^-]\) are as well, maintaining neutrality but at a lower pH value.
• Conversely, at lower temperatures, \(K_w\) decreases, resulting in lower concentrations of both ions which leads to a higher pH.

Even with varying temperatures, pure water remains neutral because the ratio of hydronium to hydroxide ions is always 1:1. However, a higher temperature leads to a slightly lower pH than 7, and a lower temperature has the opposite effect, slightly raising the pH.