Chapter 17: Problem 106
Cacodylic acid is \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{AsO}_{2} \mathrm{H} .\) Its ionization constant is \(6.4 \times 10^{-7}\). (a) Calculate the \(\mathrm{pH}\) of \(50.0 \mathrm{~mL}\) of a \(0.10-M\) solution of the acid. (b) Calculate the pH of 25.0 \(\mathrm{mL}\) of \(0.15 \mathrm{M}\left(\mathrm{CH}_{3}\right)_{2} \mathrm{AsO}_{2} \mathrm{Na}\). (c) Mix the solutions in parts (a) and (b). Calculate the pH of the resulting solution.
Short Answer
Step by step solution
Understand the Acid Dissociation in Part (a)
Set Up ICE Table for Cacodylic Acid
Calculate \([\mathrm{H}^{+}]\) Using Ionization Constant
Solve for \(x\) in Part (a)
Calculate the pH for Part (a)
Determine Concentration for Part (b)
Calculate pH for Part (b)
Mix Both Solutions for Part (c)
Calculate pH of Final Mixture
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Ionization Constant
In the exercise involving cacodylic acid ( \((\text{CH}_3)_2 \text{AsO}_2 \text{H}\)), the ionization constant is given as \(6.4 \times 10^{-7}\). This implies that it is a weak acid since the value is far less than 1. \(K_a\) is used in equilibrium calculations to determine \([\text{H}^+]\), essential for later \(\text{pH}\) calculations. By setting up an equilibrium concentration expression, this small \(K_a\) can be used to find the rate at which the acid dissociates into its ions. This is crucial for predicting and calculating solution behaviors like acidity.
Acid Dissociation
Every acid dissociation involves an equilibrium between the non-dissociated acid molecule and the ions produced. The initial concentration of the acid, changes due to dissociation, and equilibrium concentrations can be calculated using an ICE table (Initial, Change, Equilibrium).
- Initial: Start with the full concentration set as the acid form, for example, \([\text{HA}] = 0.10 \text{ M}\) and zero for products.
- Change: As dissociation occurs, the concentration of \([\text{HA}]\) decreases by \(x\), and \([\text{H}^+]\) and \([\text{A}^-]\) increase by \(x\).
- Equilibrium: Calculate new concentrations using these changes, which allows for solving \(x\), equating \([\text{H}^+]\) needed for \(\text{pH}\).
pH Calculation
For example, using \([\text{H}^+] = 8.0 \times 10^{-4}\), \(\text{pH} = -\log(8.0 \times 10^{-4}) = 3.10\). This value is typical for weak acids, indicating a slightly acidic solution.
In addition, for basic solutions such as in the presence of a salt of a weak acid, calculate the \([\text{OH}^-]\) instead, followed by using \(\text{pOH} = -\log[\text{OH}^-]\) and \(\text{pH} = 14 - \text{pOH}\). Such calculations are foundational for students to master the manipulation of logarithmic expressions essential in chemistry.
Henderson-Hasselbalch Equation
In the final exercise part where two solutions combine, creating a buffer, the Henderson-Hasselbalch equation becomes crucial. It bypasses more complex calculations to swiftly ascertain the final \(\text{pH}\) of a buffer solution. Here, knowing both initial concentrations and total solution volumes enables rapid \(\text{pH}\) calculation through this log-based equation.
- \(\text{pK}_a\) is determined from \(K_a\) as \(\text{pK}_a = -\log(K_a)\).
- Calculate the molar concentrations of \([\text{A}^-]\) and \([\text{HA}]\) in the new mixed solution volume.
- Insert these values into the equation to find the resulting \(\text{pH}\).