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?

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: \[[\mathrm{H}^+] = 10^{-8.08} \approx 8.3 \times 10^{-9} \, \mathrm{M}\]

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 [\(\mathrm{OH}^-\)]: \[[\mathrm{OH}^-] = \frac{K_w}{[\mathrm{H}^+]} = \frac{1.0 \times 10^{-14}}{8.3 \times 10^{-9}} \approx 1.2 \times 10^{-6}\, \mathrm{M}\]

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: \[[\mathrm{OCl}^-] = \frac{[\mathrm{OH}^-]}{[\mathrm{H}^+]} = \frac{1.2 \times 10^{-6}}{8.3 \times 10^{-9}} \approx 144\]

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 \(\mathrm{NaOCl}\).