Problem 80 - Chemistry and Chemical Reactivity

Question

Place the following acids in order of (i) increasing strength and (ii) increasing \(\mathrm{pH}\). Assume you have a \(0.10 \mathrm{M}\) solution of each acid. (a) 4 -chlorobenzoic acid, \(\mathrm{ClC}_{6} \mathrm{H}_{4} \mathrm{CO}_{2} \mathrm{H}, K_{\mathrm{a}}=1.0 \times 10^{-4}\) (b) bromoacetic acid, \(\mathrm{BrCH}_{2} \mathrm{CO}_{2} \mathrm{H}, K_{\mathrm{a}}=1.3 \times 10^{-3}\) (c) trimethylammonium ion, \(\left(\mathrm{CH}_{3}\right)_{3} \mathrm{NH}^{+}, K_{\mathrm{a}}=1.6 \times 10^{-10}\)

Step-by-Step Solution

Answer

For strength: trimethylammonium ion < 4-chlorobenzoic acid < bromoacetic acid. For pH: bromoacetic acid < 4-chlorobenzoic acid < trimethylammonium ion.

Step 1: Understand Acid Strength

Acid strength is determined by the acid dissociation constant, denoted as \( K_a \). A larger \( K_a \) value indicates a stronger acid because it means the acid ionizes more completely in solution. Conversely, a smaller \( K_a \) indicates a weaker acid.

Step 2: Order Acid Strengths

Compare the \( K_a \) values for the acids: (a) \( K_a = 1.0 \times 10^{-4} \), (b) \( K_a = 1.3 \times 10^{-3} \), (c) \( K_a = 1.6 \times 10^{-10} \). From smallest to largest, the order of increasing strength is: trimethylammonium ion < 4-chlorobenzoic acid < bromoacetic acid.

Step 3: Understand Relationship with pH

pH is related to the concentration of hydrogen ions \( [H^+] \) in solution. A stronger acid will have a higher concentration of \( [H^+] \) in solution and thus a lower pH. Therefore, the acid with the smallest \( K_a \) will have the highest pH.

Step 4: Order Increasing pH

We now reverse the order of acid strength to determine pH. The order of increasing pH is: bromoacetic acid < 4-chlorobenzoic acid < trimethylammonium ion.

Key Concepts

Acid Dissociation Constant

The acid dissociation constant, represented as \( K_a \), plays a crucial role in understanding an acid's strength. It measures how well an acid can ionize, or release hydrogen ions \([H^+]\), into a solution. The ionization reaction can be represented as follows:\[HA \leftrightarrow H^+ + A^- \]where \( HA \) is the acid, and \( A^- \) is the conjugate base. The \( K_a \) value is calculated using the concentrations of these species at equilibrium:\[K_a = \frac{[H^+][A^-]}{[HA]} \]A high \( K_a \) means more ions are formed, indicating a stronger acid. In contrast, a low \( K_a \) reveals that the acid barely ionizes, pointing to a weaker acid. It is important to compare these constants when evaluating various acids.

pH

The concept of pH is central to understanding acidity and is directly tied to the concentration of hydrogen ions \([H^+]\) in a solution. The relationship between \([H^+]\) and pH is given by the formula:\[pH = -\log [H^+] \]This equation shows that as the concentration of hydrogen ions increases, the pH value decreases, indicating a stronger acid (or greater acidity). A pH of 7 is neutral—pure water. Values below 7 represent acidic solutions, with lower numbers corresponding to stronger acids. Conversely, values above 7 are alkaline (basic) solutions. In assessing the strength of an acid and its corresponding pH, remember that a smaller \( Ka \) results in a higher, less acidic pH.

Acid Ionization

Acid ionization is the process by which an acid dissolves in water and releases hydrogen ions \([H^+]\). The extent of ionization reflects the strength of the acid, with stronger acids ionizing more completely than weaker ones. For example, an acid that ionizes entirely in solution is considered strong because it releases a high concentration of \([H^+]\). For weaker acids, only a fraction of the acid molecules donate \([H^+]\) ions, resulting in a partial ionization. This characteristic can often be anticipated based on the \( K_a \) values, where large values usually correlate with stronger, more fully ionizing acids, and smaller \( K_a \) values indicate limited ionization. Understanding this principle helps in predicting the behavior of different acids in solution.

Solution Concentration

Solution concentration, often expressed in molarity (M), indicates how much solute (in this case, the acid) is dissolved in a specific volume of solution. It is fundamental when discussing acidity because it affects the ionization process. For example, a 0.10 M solution means there are 0.10 moles of acid per liter of solution. This concentration directly influences the extent of ionization and thus the pH. While a higher concentration could imply more available ions to dissociate, the intrinsic strength of the acid (indicated by \( K_a \)) remains a deciding factor in how much ionization occurs. When computing pH and analyzing acidity, it's crucial to consider both \( K_a \) and the concentration to gain an accurate understanding of the solution's behavior.