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Chapter 16: Problem 62

Determine the \(\mathrm{pH}\) of each of the following solutions \(\left(K_{a}\right.\) and \(K_{b}\) values are given in Appendix D): (a) \(0.095 M\) hypochlorous acid, (b) \(0.0085 \mathrm{M}\) phenol, (c) \(0.095 \mathrm{M}\) hydroxylamine.

Short Answer

Expert verified
(a) Hypochlorous acid: Using the given \(K_{a}\) value \(3.5 \times 10^{-8}\), we find the [H鈧僌鈦篯 concentration is approximately \(1.69 \times 10^{-5} M\). Thus, the pH is around 4.77. (b) Phenol: Using the given \(K_{a}\) value \(1.3 \times 10^{-10}\), we find the [H鈧僌鈦篯 concentration is approximately \(3.32 \times 10^{-6} M\). Thus, the pH is around 5.48. (c) Hydroxylamine: Using the given \(K_{b}\) value \(1.1 \times 10^{-8}\), we find the [OH鈦籡 concentration is approximately \(3.03 \times 10^{-5} M\). The pOH is around 4.52, indicating a pH of approximately 9.48.

Step by step solution

01

(a) Hypochlorous Acid Solution

1. Write the ionization equilibrium equation for hypochlorous acid (HClO) in water: \[HClO + H_{2}O \leftrightharpoons H_{3}O^{+} + ClO^{-}\] 2. Write the equilibrium expression using the \(K_{a}\) value: \[K_{a}=\frac{[H_{3}O^{+}][ClO^{-}]}{[HClO]}\] 3. Set up an ICE (initial, change, equilibrium) table to find the equilibrium concentrations: \[ \begin{array}{c | c c c} & HClO & H_{3}O^{+} & ClO^{-} \\ \hline \text{Initial} & 0.095 & 0 & 0 \\ \text{Change} & -x & +x & +x \\ \text{Equilibrium} & 0.095-x & x & x \end{array}\] 4. Substitute equilibrium concentrations into the expression and solve for x: \[K_{a}=\frac{x^2}{0.095-x}\] 5. Use Appendix D to find the \(K_{a}\) value for hypochlorous acid and solve for x, the [H鈧僌鈦篯 concentration. 6. Calculate the pH: \[pH = -log_{10}[H_{3}O^{+}]\]
02

(b) Phenol Solution

1. Write the ionization equilibrium equation for phenol (C鈧咹鈧匫H) in water: \[ C_{6}H_{5}OH + H_{2}O \leftrightharpoons H_{3}O^{+} + C_{6}H_{5}O^{-}\] 2. Write the equilibrium expression using the \(K_{a}\) value: \[K_{a}=\frac{[H_{3}O^{+}][C_{6}H_{5}O^{-}]}{[C_{6}H_{5}OH]}\] 3. Set up an ICE table to find the equilibrium concentrations: \[ \begin{array}{c | c c c} & C_{6}H_{5}OH & H_{3}O^{+} & C_{6}H_{5}O^{-} \\ \hline \text{Initial} & 0.0085 & 0 & 0 \\ \text{Change} & -x & +x & +x \\ \text{Equilibrium} & 0.0085-x & x & x \end{array}\] 4. Substitute equilibrium concentrations into the expression and solve for x: \[K_{a}=\frac{x^2}{0.0085-x}\] 5. Use Appendix D to find the \(K_{a}\) value for phenol and solve for x, the [H鈧僌鈦篯 concentration. 6. Calculate the pH: \[pH = -log_{10}[H_{3}O^{+}]\]
03

(c) Hydroxylamine Solution

1. Write the ionization equilibrium equation for hydroxylamine (NH鈧侽H) in water: \[ NH_{2}OH + H_{2}O \leftrightharpoons NH_{3}OH^{+} + OH^{-}\] 2. Write the equilibrium expression using the \(K_{b}\) value: \[K_{b}=\frac{[NH_{3}OH^{+}][OH^{-}]}{[NH_{2}OH]}\] 3. Set up an ICE table to find the equilibrium concentrations: \[ \begin{array}{c | c c c} & NH_{2}OH & NH_{3}OH^{+} & OH^{-} \\ \hline \text{Initial} & 0.095 & 0 & 0 \\ \text{Change} & -x & +x & +x \\ \text{Equilibrium} & 0.095-x & x & x \end{array}\] 4. Substitute equilibrium concentrations into the expression and solve for x: \[K_{b}=\frac{x^2}{0.095-x}\] 5. Use Appendix D to find the \(K_{b}\) value for hydroxylamine and solve for x, the [OH鈦籡 concentration. 6. Calculate the pOH using the [OH鈦籡 concentration: \[pOH = -log_{10}[OH^{-}]\] 7. Calculate the pH using the relation between pH and pOH: \[pH = 14 - pOH\]

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Key Concepts

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

Acid-Base Equilibrium
Acid-base equilibrium revolves around the concept of acids and bases reacting with each other, and how these reactions establish a balance between reactants and products. In aqueous solutions, acids tend to donate protons ( H鈦� ) while bases tend to accept them. In our context, the equilibrium involves weak acids like hypochlorous acid and phenol, or weak bases like hydroxylamine dissociating partially in water. When these substances enter the water, they create a slight ionic environment by producing ions such as H鈧僌鈦� or OH鈦� .
  • Acids generate H鈧僌鈦� ions increasing the hydronium concentration, contributing to the overall acidity of the solution.
  • Bases produce OH鈦� ions, increasing the hydroxide concentration, which increases the basicity of the solution.
An equilibrium is reached when the forward reaction rate of dissociation equals the reverse reaction rate of recombination, meaning concentrations remain stable over time.
Ionization Constant
The ionization constant, represented as K_{a} for acids and K_{b} for bases, is a pivotal parameter in understanding the extent of ionization of an acid or base in solution. It reflects the strength of an acid or base:
  • High K_{a} or K_{b} values indicate stronger acids or bases that ionize more completely in water.
  • Low values mean weaker ionization.
For a weak acid like hypochlorous acid, its K_{a} is relatively low, showing that only a small portion of the acid ionizes in water. Comparatively, hydroxylamine's K_{b} provides insight into its ability to release OH鈦� ions. Knowing these constants from reference materials (like Appendix D in textbooks) allows us to calculate the equilibrium concentrations required for calculating pH.
ICE Table
An ICE table is a valuable tool used to visually organize and solve equilibrium problems by breaking them down into Initial, Change, and Equilibrium concentrations. This step-by-step approach helps in quantifying the dissociation of acids and bases in solutions by representing initial concentrations, amount of change, and resulting equilibrium concentrations.
  • "Initial" row displays the starting concentrations of reactants and products before any reaction has occurred.
  • "Change" row shows how concentrations change as the reaction moves toward equilibrium, often denoted by -x for consumption and +x for formation.
  • "Equilibrium" row represents the net concentrations after the reaction has reached equilibrium.
By substituting these equilibrium concentrations into the K_{a} or K_{b} expression, one can solve for x to find out the concentrations of H鈧僌鈦� or OH鈦� , which are essential for further pH calculations.
Acid Dissociation Constant
The acid dissociation constant, K_{a} , is a specific type of ionization constant relevant to acids. It measures how an acid dissociates into its constituent ions in an aqueous solution, indicating its strength. For instance, hypochlorous acid, with its given ionization constant, partially dissociates into H鈧僌鈦� and ClO鈦� ions. This limited dissociation classifies it as a weak acid.
  • Identifying K_{a} assists in predicting how the acid will behave in different solutions or concentrations.
  • It also allows us to determine the position of equilibrium between the reactants and products, offering deeper insights into the acidity of the solution.
Understanding K_{a} values not only helps in calculating pH values but also gives a broader picture of the chemical nature and stability of acid in solutions.

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Most popular questions from this chapter

Indicate whether each of the following statements is true or false. For each statement that is false, correct the statement to make it true. (a) In general, the acidity of binary acids increases from left to right in a given row of the periodic table. (b) In a series of acids that have the same central atom, acid strength increases with the number of hydrogen atoms bonded to the central atom. (c) Hydrotelluric acid \(\left(\mathrm{H}_{2} \mathrm{Te}\right)\) is a stronger acid than \(\mathrm{H}_{2} \mathrm{~S}\) because Te is more electronegative than \(\mathrm{S}\).

The odor of fish is due primarily to amines, especially methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right) .\) Fish is often served with a wedge of lemon, which contains citric acid. The amine and the acid react forming a product with no odor, thereby making the less-than-fresh fish more appetizing. Using data from Appendix \(D\), calculate the equilibrium constant for the reaction of citric acid with methylamine, if only the first proton of the citric acid \(\left(K_{a 1}\right)\) is important in the neutralization reaction.

Calculate the number of \(\mathrm{H}^{+}(a q)\) ions in \(1.0 \mathrm{~mL}\) of pure water at \(25^{\circ} \mathrm{C}\).

The volume of an adult's stomach ranges from about \(50 \mathrm{~mL}\) when empty to \(1 \mathrm{~L}\) when full. If the stomach volume is \(400 \mathrm{~mL}\) and its contents have a \(\mathrm{pH}\) of 2 , how many moles of \(\mathrm{H}^{+}\) does the stomach contain? Assuming that all the \(\mathrm{H}^{+}\) comes from \(\mathrm{HCl}\), how many grams of sodium hydrogen carbonate will totally neutralize the stomach acid?

How does the acid strength of an oxyacid depend on (a) the electronegativity of the central atom; (b) the number of nonprotonated oxygen atoms in the molecule?
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