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Chapter 14: Problem 1

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

Short Answer

Expert verified
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

01

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: \(K_w = [H^+][OH^-]\)
02

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: \(K_w = [H^+][OH^-] = 1.0 × 10^{-14}\)
03

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: \(pH = -\log(1.0 × 10^{-7}) = 7\)
04

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.
05

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.

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