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

Short Answer

Expert verified
The unknown salt is NaF. We determined that NaF and NaOCl are basic salts, resulting in basic solutions when dissolved in water. We calculated the pH for NaF and NaOCl solutions as 8.24 and 9.12, respectively. Since the given pH of the unknown salt's solution is 8.08, which is closer to the pH of the NaF solution, we concluded that the identity of the unknown salt is NaF.

Step by step solution

01

Determine if the salts are acidic, basic, or neutral when dissolved in water

In this step, we will determine if the resulting solution is acidic, basic, or neutral for each of the salts - NaF, NaCl, and NaOCl. For NaCl: When NaCl dissolves in water, it dissociates completely into Na鈦 and Cl鈦 ions. Neither the Na鈦 nor the Cl鈦 ions react with water to produce H鈦 or OH鈦 ions. Hence, the resulting solution is neutral. For NaF: When NaF dissolves in water, it dissociates completely into Na鈦 and F鈦 ions. Fluoride ions (F鈦) react with water to form Hydrofluoric acid (HF) and Hydroxide ions (OH鈦), causing the solution to be basic. For NaOCl: When NaOCl dissolves in water, it dissociates completely into Na鈦 and OCl鈦 ions. Hypochlorite ions (OCl鈦) react with water to form Hypochlorous acid (HOCl) and Hydroxide ions (OH鈦), causing the solution to be basic. From the step 1 result, NaF and NaOCl are potential candidates for the unknown salt since their resulting solutions are basic.
02

Calculate the pH for NaF and NaOCl

Let's calculate the pH value for the resulting solutions of NaF and NaOCl separately. For NaF: The reaction of F鈦 in water is given by: \[F鈦(aq) + H鈧侽(l) \rightleftharpoons HF(aq) + OH鈦(aq)\] Let's assume 'x' moles of F鈦 reacts with water to form 'x' moles of HF and 'x' moles of OH鈦. Now, the equilibrium concentration of F鈦 is given by: \[[F鈦籡 = \frac{(0.050鈭抶)~\text{mol}}{0.5~\text{L}}\] The concentration of OH鈦 at equilibrium is given by: \[[OH鈦籡 = \frac{x~\text{mol}}{0.5~\text{L}}\] Since we are dealing with basic solution, we know that: \[K_b = \frac{[HF][OH鈦籡}{[F鈦籡} = K_w/K_a\] Where, K_b is the base ionization constant, K_w is the ion product of water (\(1.0 脳 10鈦宦光伌\) at 25掳C) and K_a is the acid ionization constant of HF (\(6.8 脳 10鈦烩伌\)). Calculate K_b: \[K_b = \frac{K_w}{K_a} = \frac{1.0 脳 10鈦宦光伌}{6.8 脳 10鈦烩伌} = 1.47 脳 10鈦宦孤筡] We'll assume that x is very small compared to 0.050, hence (0.050 - x) 鈮 0.050. Plug the concentrations into the K_b expression: \[1.47 脳 10鈦宦孤 = \frac{(x)(x)}{(0.050)}\] Solve for x: \[x = [OH鈦籡 = 1.72 脳 10鈦烩伓\] Now, we'll calculate the corresponding pOH: \[pOH = -log_{10} [OH鈦籡 = -log_{10}(1.72 脳 10鈦烩伓) = 5.76\] And finally, we'll calculate the pH of the NaF solution: \[pH = 14 - pOH = 14 - 5.76 = 8.24\] For NaOCl: Let's follow the same process as we did for NaF, using the reaction of OCl鈦 in water: \[OCl鈦(aq) + H鈧侽(l) \rightleftharpoons HOCl(aq) + OH鈦(aq)\] K_a of HOCl is \(2.9 脳 10鈦烩伕\). Calculate K_b: \[K_b = \frac{K_w}{K_a} = \frac{1.0 脳10鈦宦光伌}{2.9 脳 10鈦烩伕} = 3.45 脳 10鈦烩伔\] We'll assume that x is very small compared to 0.050, hence (0.050 - x) 鈮 0.050. Plug the concentrations into the K_b expression: \[3.45 脳 10鈦烩伔 = \frac{(x)(x)}{(0.050)}\] Solve for x: \[x = [OH鈦籡 = 1.31 脳 10鈦烩伒\] Now, we'll calculate the corresponding pOH: \[pOH = -log_{10} [OH鈦籡 = -log_{10}(1.31 脳 10鈦烩伒) = 4.88\] And finally, we'll calculate the pH of the NaOCl solution: \[pH = 14 - pOH = 14 - 4.88 = 9.12\]
03

Identify the unknown salt based on calculated pH values

We found that the pH of NaF solution is 8.24, and the pH of NaOCl solution is 9.12. The given pH of the unknown salt's solution is 8.08. The pH value of 8.08 is closer to the pH of the NaF solution (8.24) than to the pH of the NaOCl solution (9.12). Therefore, the identity of the unknown salt is NaF.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Acid-Base Chemistry
Acid-base chemistry is all about understanding how acids and bases behave in solution. When a substance dissolves in water, it can affect the pH level depending on whether it is an acid, a base, or neutral. In basic solutions, like those formed when salts like NaF or NaOCl dissolve in water, there are more hydroxide ions (OH鈦) than hydrogen ions (H鈦). This results in a pH greater than 7.
When NaF is dissolved, the fluoride ions (F鈦) interact with water in an equilibrium reaction: \( F鈦 + H_2O \rightleftharpoons HF + OH鈦 \). This produces hydroxide ions, making the solution basic. Similarly, NaOCl forms a basic solution through the reaction \( OCl鈦 + H_2O \rightleftharpoons HOCl + OH鈦 \).
The pH value tells us about the solution's acidity or basicity. A pH of 8.08, as observed in the exercise, is slightly basic, indicating the presence of such ions.
Chemical Equilibrium
Chemical equilibrium is a state in which the rates of the forward and reverse reactions are equal, meaning that the concentrations of reactants and products remain constant over time. In this context, the reaction of the ions with water achieves equilibrium, influencing the pH of the solution.
For NaF, equilibrium is reached with the fluoride ions converting to HF and hydroxide ions: \( F鈦 + H_2O \rightleftharpoons HF + OH鈦 \). The extent of this reaction is described by the base ionization constant, \( K_b \).
Similarly, NaOCl establishes an equilibrium: \( OCl鈦 + H_2O \rightleftharpoons HOCl + OH鈦 \). Each salt has a specific \( K_b \) value indicative of its ability to produce hydroxide ions. Calculating these equilibria allows us to understand the pH of the resulting solution, as seen with the pH values around 8.08 and 9.12.
Solution Chemistry
Solution chemistry deals with the study of solutes dissolved in a solvent, often water, to form a solution. Understanding the composition and concentration of a solution is crucial in calculating properties like pH.
The exercise involves dissolving 0.050 mol of a salt in 0.500 L of water. This sets the stage for analyzing how much the dissolved ions will shift the chemical equilibrium and impact the solution's pH. The concentration of ions like OH鈦 at equilibrium is key to this analysis.
In the example, both NaF and NaOCl dissolve to generate OH鈦 ions, affecting the pH. Knowing the molar concentrations and using ionization constants, you can predict the pH by calculating the concentrations of ions in the solution: \( [OH鈦籡 = \frac{x}{0.5~L} \). This approach allows students to determine the salt behind a given pH.

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Most popular questions from this chapter

Caproic acid \(\left(\mathrm{C}_{5} \mathrm{H}_{11} \mathrm{COOH}\right)\) is found in small amounts in coconut and palm oils and is used in making artificial flavors. A saturated solution of the acid contains \(11 \mathrm{~g} / \mathrm{L}\) and has a \(\mathrm{pH}\) of 2.94. Calculate \(K_{a}\) for the acid.

(a) Which of the following is the stronger Bronsted-Lowry acid, HBrO or HBr? (b) Which is the stronger Bronsted-Lowry base, \(\mathrm{F}^{-}\) or \(\mathrm{Cl}^{-}\) ? Briefly explain your choices.

The active ingredient in aspirin is acetylsalicylic acid \(\left(\mathrm{HC}_{9} \mathrm{H}_{7} \mathrm{O}_{4}\right),\) a monoprotic acid with \(K_{a}=3.3 \times 10^{-4}\) at \(25^{\circ} \mathrm{C}\). What is the \(\mathrm{pH}\) of a solution obtained by dissolving two extra-strength aspirin tablets, containing \(500 \mathrm{mg}\) of acetylsalicylic acid each, in \(250 \mathrm{~mL}\) of water?

Hemoglobin plays a part in a series of equilibria involving protonation- deprotonation and oxygenation-deoxygenation. The overall reaction is approximately as follows: $$ \mathrm{HbH}^{+}(a q)+\mathrm{O}_{2}(a q) \rightleftharpoons \mathrm{HbO}_{2}(a q)+\mathrm{H}^{+}(a q) $$ where \(\mathrm{Hb}\) stands for hemoglobin and \(\mathrm{HbO}_{2}\) for oxyhemoglobin. (a) The concentration of \(\mathrm{O}_{2}\) is higher in the lungs and lower in the tissues. What effect does high \(\left[\mathrm{O}_{2}\right]\) have on the position of this equilibrium? (b) The normal \(\mathrm{pH}\) of blood is 7.4. Is the blood acidic, basic, or neutral? (c) If the blood \(\mathrm{pH}\) is lowered by the presence of large amounts of acidic metabolism products, a condition known as acidosis results. What effect does lowering blood \(\mathrm{pH}\) have on the ability of hemoglobin to transport \(\mathrm{O}_{2} ?\)

Write the chemical equation and the \(K_{a}\) expression for the ionization of each of the following acids in aqueous solution. First show the reaction with \(\mathrm{H}^{+}(a q)\) as a product and then with the hydronium ion: (a) \(\mathrm{HBrO}_{2}\), (b) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\).

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