Question

Consider two beakers of pure water at different temperatures. How do their pH values compare? Which is more acidic? more basic? Explain.

Short answer

In two beakers of pure water at different temperatures, the beaker with the higher temperature will have a lower pH value, making it more acidic. However, it is essential to note that both solutions remain neutral since the concentrations of hydrogen ions and hydroxide ions are equal despite the temperature changes. The pH decreases due to the increased auto-ionization of water at higher temperatures, leading to a higher equilibrium constant and increased concentrations of both hydrogen and hydroxide ions.

Step-by-step solution

Understand the auto-ionization of water

Auto-ionization is a process in which pure water molecules split into hydrogen ions (H+) and hydroxide ions (OH-). In pure water, the concentration of hydrogen ions and hydroxide ions will be equal. We will use the following equation to express the equilibrium constant of this process: \(K_w = [H^+][OH^-]\)

Calculate the equilibrium constant at room temperature

At room temperature (25°C or 298 K), the equilibrium constant for water is approximately \(1.0 × 10^{-14}\). This means that the product of the concentrations of hydrogen ions and hydroxide ions is constant in pure water at this temperature: \(K_w = [H^+][OH^-] = 1.0 × 10^{-14}\)

Determine the pH of pure water at room temperature

The pH of a solution is defined as: \(pH = -\log[H^+]\) Since the concentration of hydrogen ions and hydroxide ions in pure water is equal, the pH at room temperature can be calculated as: \(-\log[H^+] = -\log[OH^-]\) Using the known value of the equilibrium constant, we can determine the concentration of hydrogen ions in pure water at room temperature: \([H^+] = \sqrt{K_w} = \sqrt{1.0 × 10^{-14}} = 1.0 × 10^{-7}\) Now, we can calculate the pH of pure water at room temperature: \(pH = -\log(1.0 × 10^{-7}) = 7\)

Discuss the effect of temperature on the pH of pure water

As the temperature increases, the auto-ionization of water increases, meaning that the equilibrium constant, \(K_w\), increases as well. This results in a higher concentration of hydrogen ions and hydroxide ions in the water. Therefore, at higher temperatures, the pH of pure water decreases (becomes more acidic) while the pOH (negative logarithm of hydroxide ion concentration) also decreases (becomes more basic), since both hydrogen and hydroxide ions are increasing in concentration.

Compare the pH values of water at different temperatures

Given two beakers of pure water at different temperatures, the one at a higher temperature will have a lower pH value, meaning it is more acidic. While the hydroxide ion concentration also increases, the pOH value decreases, indicating that the solution is becoming more basic. However, it is important to note that it is still a neutral solution as the concentrations of hydrogen ions and hydroxide ions remain equal.

Key concepts

Auto-Ionization of Water

Auto-ionization is a fascinating and important process underlying the chemistry of water. In this process, two water molecules interact, resulting in one molecule donating a proton (H+) to another, forming a hydronium ion (H3O+) and a hydroxide ion (OH-). This is usually simplified to show the formation of H+ and OH- in equations.

• This splitting results in equal concentrations of H+ and OH- in pure water.
• The equilibrium of this reaction is a hallmark of water's unique properties.

Understanding this dynamic allows us to explore fundamental concepts like pH and its variation at different temperatures. The concentration of H+ and OH- are always in balance in pure water, which reflects the neutral characteristic of water at a given temperature.

Effect of Temperature on pH

Temperature has a notable impact on the pH level of water, affecting its acidity and basicity. As the temperature rises, the molecules in water have more energy, which facilitates the auto-ionization process. This speeds up the separation of water molecules into ions:

• Higher temperatures increase the concentrations of both hydrogen ions (H+) and hydroxide ions (OH-).
• The increase in hydrogen ion concentration results in a lower pH, indicating that the water becomes more acidic.
• Conversely, while the pH decreases, the condition is still regarded as neutral because the concentrations of H+ and OH- remain equal.

Therefore, even though higher temperatures cause a decrease in pH, it doesn't mean the water becomes non-neutral; it simply illustrates a shift due to temperature's effect on kinetic energy.

Equilibrium Constant of Water

The equilibrium constant of water, denoted by \(K_w\), is a vital component in understanding the pH scale and water's neutral state at a given temperature. At room temperature (25°C), \(K_w\) is approximately \(1.0 × 10^{-14}\). This relationship can be expressed as:\[ K_w = [H^+][OH^-] \]

• This constant value ensures that the product of the acid (H+) and base (OH-) concentrations in water remains fixed at a specific temperature.
• As temperatures vary, so does \(K_w\), which further influences the levels of H+ and OH- ions.

Ultimately, knowing \(K_w\) enables one to calculate important values like the pH and pOH of water. These calculations inform us about the ionic balance in water's auto-ionization and are essential for comparing water at different temperatures.