Problem 85 - Chemistry: The Central Science in SI Units, Global Edition

Question

An unknown salt is either \(\mathrm{NaF}, \mathrm{NaCl}\), or \(\mathrm{NaOCl}\). When 0.050 mol of the salt is dissolved in water to form 0.500 L of solution, the pH of the solution is 8.08 . What is the identity of the salt?

Step-by-Step Solution

Answer

The identity of the unknown salt is \(\mathrm{NaOCl}\), based on the given pH of 8.08, the calculated concentration of hydroxide ions, and the reasonable concentration of \(\mathrm{OCl}^-\) in the solution.

Step 1: Calculate the hydrogen ion concentration from the given pH

Given the pH of the solution is 8.08, we can calculate the concentration of hydrogen ions ([\(\mathrm{H}^+\)]), using the formula: \[\mathrm{pH} = -\log_{10} [\mathrm{H}^+]\] The concentration of hydrogen ions is: \[[\mathrm{H}^+] = 10^{-\mathrm{pH}}\] Plugging in the given pH value: \[[\mathrm{H}^+] = 10^{-8.08} \approx 8.3 \times 10^{-9} \, \mathrm{M}\]

Step 2: Determine the hydroxide ion concentration

Now, let's find the concentration of hydroxide ions ([\(\mathrm{OH}^-\)]). We'll use the ion product of water, \(K_w\), which is: \[K_w = [\mathrm{H}^+] [\mathrm{OH}^-] = 1.0 \times 10^{-14}\] We can solve for [\(\mathrm{OH}^-\)]: \[[\mathrm{OH}^-] = \frac{K_w}{[\mathrm{H}^+]} = \frac{1.0 \times 10^{-14}}{8.3 \times 10^{-9}} \approx 1.2 \times 10^{-6}\, \mathrm{M}\]

Step 3: Calculate the concentration of the anions

Now we move on to calculating the concentration of the anions. We'll look at the salts one by one: 1. For \(\mathrm{NaF}\): Dissociation: \(\mathrm{NaF} \rightarrow \mathrm{Na}^+ + \mathrm{F}^-\) Here, the anion is \(\mathrm{F}^-\), so: \[[\mathrm{F}^-] = \frac{[\mathrm{OH}^-]}{[\mathrm{H}^+]} = \frac{1.2 \times 10^{-6}}{8.3 \times 10^{-9}} \approx 144\] 2. For \(\mathrm{NaCl}\): Dissociation: \(\mathrm{NaCl} \rightarrow \mathrm{Na}^+ + \mathrm{Cl}^-\) In this case, the chloride ion does not affect the pH of the solution, so we cannot determine the anion concentration for this salt based on the pH. 3. For \(\mathrm{NaOCl}\): Dissociation: \(\mathrm{NaOCl} \rightarrow \mathrm{Na}^+ + \mathrm{OCl}^-\) In this case, the anion is \(\mathrm{OCl}^-\), so: \[[\mathrm{OCl}^-] = \frac{[\mathrm{OH}^-]}{[\mathrm{H}^+]} = \frac{1.2 \times 10^{-6}}{8.3 \times 10^{-9}} \approx 144\]

Step 4: Identify the salt

Based on the calculations, we can make the following observations: 1. For \(\mathrm{NaF}\), the concentration of \(\mathrm{F}^-\) is very high, which means it would have a much lower pH. So, this salt is not the one we are looking for. 2. For \(\mathrm{NaCl}\), the solution would be neutral, with a pH close to 7, as chloride ions do not affect the pH. Therefore, this salt is also not the one we are looking for. 3. For \(\mathrm{NaOCl}\), the calculated concentration of \(\mathrm{OCl}^-\) seems reasonable as it stabilized at a pH of 8.08. Thus, considering these observations, we can conclude that the identity of the unknown salt is \(\mathrm{NaOCl}\).

Key Concepts

Hydrogen Ion Concentration

The concentration of hydrogen ions, denoted as \([H^+]\), is crucial in determining the acidic or basic nature of a solution. It is represented on a logarithmic scale known as pH. The pH of a solution intersects with hydrogen ion concentration in a direct mathematical relationship. This relationship is expressed as:

• \( \text{pH} = -\log_{10} [\mathrm{H}^+] \)

Given this formula, knowing the pH allows us to compute the concentration of hydrogen ions using the equation:

• \([H^+] = 10^{-\text{pH}} \)

By plugging in specific pH values, like 8.08 in this context, we can calculate \([H^+] \) as approximately \(8.3 \times 10^{-9} \, \text{M}\). This small concentration reflects a low presence of hydrogen ions, indicating a basic solution.

pH Calculations

The process of calculating pH involves using the hydrogen ion concentration in a solution. Since the pH scale ranges from 0 to 14, a neutral solution has a pH close to 7. A pH less than 7 signifies acidity, while a pH greater than 7 indicates basicity. In terms of calculation:

• Given a hydrogen ion concentration, the pH can be calculated with: \( \text{pH} = -\log_{10} [\mathrm{H}^+] \)

Reversely, knowing the pH, we calculate the hydrogen ion concentration using:

• \([H^+] = 10^{-\text{pH}} \)

This conversion is pivotal in identifying the nature of solutions, such as distinguishing between a neutral, acidic, or basic salt based on its effect on pH when dissolved.

Ion Product of Water

The ion product of water, denoted as \(K_w\), is the basis for understanding the balance between hydrogen ions \([H^+]\) and hydroxide ions \([OH^-]\) in an aqueous solution. This constant is defined as:

• \(K_w = [\mathrm{H}^+] [\mathrm{OH}^-] = 1.0 \times 10^{-14} \)

This equation implies that in pure water, or any neutral solution, the concentrations of \([H^+]\) and \([OH^-]\) must multiply to \(1.0 \times 10^{-14}\). Knowing one of these ion concentrations allows us to deduce the other. For example, if the hydrogen ion concentration is known, the hydroxide ion concentration can be calculated as follows:

• \([OH^-] = \frac{K_w}{[H^+]} \)

Understanding this product is essential for assessing changes in pH, especially when salts are dissolved in water.

Solution Chemistry

Solution chemistry involves understanding how different substances dissolve and interact in a solvent. Here, the focus is on salts and their effects on pH when dissolved in water. Salts dissociate into their constituent ions:

• For \(NaF\): Dissociates into \(\mathrm{Na}^+\) and \(\mathrm{F}^-\)
• For \(NaCl\): Dissociates into \(\mathrm{Na}^+\) and \(\mathrm{Cl}^-\)
• For \(NaOCl\): Dissociates into \(\mathrm{Na}^+\) and \(\mathrm{OCl}^-\)

These ions can influence the pH of the solution when they interact with water's ions. In the case where the pH becomes elevated, like a pH of 8.08, this suggests the presence of a basic anion like \(\mathrm{OCl}^-\). The interaction of this anion with water forms a basic solution, thereby affecting the pH level, which helps identify the dissolved salt.