Problem 106 - Chemistry The Molecular Nature of Matter

Question

The conjugate acid of a molecular base has the general formula \(B \mathrm{H}^{+}\) and a \(\mathrm{p} K_{\mathrm{a}}\) of \(5.00 .\) A solution of a salt of this cation, \(B \mathrm{H} Y\), tests slightly basic. Will the conjugate acid of \(Y^{-}, \mathrm{H} Y\), have a \(\mathrm{p} K_{\mathrm{a}}\) greater than 5.00 or less than 5.00? Explain.

Step-by-Step Solution

Answer

The pKa of HY will be greater than 5.00 because its conjugate base Y^- is strong enough to make the salt solution slightly basic, indicating that HY is a weaker acid than BH^+.

Step 1: Understanding the Problem

Determine the nature of the solution formed by the salt of a cation, BH^+, which has a pKa of 5.00. If the solution is slightly basic, infer the pKa of the conjugate acid of the anion Y^-. Remember that the lower the pKa, the stronger the acid.

Step 2: Analyzing the Acid-Base Properties

In a salt formed by a weak acid and a weak base, the pH of the solution depends on the relative strengths of the acid and base in their conjugate forms. Since the solution of BHY is slightly basic, we know that the conjugate base (Y^-) of the acid HY must be strong enough to make the solution basic. A stronger conjugate base implies a weaker corresponding conjugate acid (HY).

Step 3: Determining the pKa of HY

The strength of an acid is inversely related to its pKa. Since the solution is slightly basic, HY must be a weaker acid than BH^+. Hence, the pKa of HY must be higher than the pKa of BH^+, which is 5.00.

Key Concepts

Understanding Conjugate Acids and Bases

In the world of chemistry, the terms 'conjugate acid' and 'conjugate base' play a crucial role in describing the participants in acid-base reactions. When a base gains a proton, it becomes a conjugate acid; conversely, when an acid loses a proton, it becomes a conjugate base. This transformation happens in a reversible reaction when an acid and a base interact.
For instance, if we start with a base, let's call it 'B', it can accept a hydrogen ion (H+) and transform into its conjugate acid, denoted as BH+. Similarly, an acid, say HY, can donate a proton to become its conjugate base Y-.

Importance of the Conjugate Pair in Solution

The behavior of conjugate pairs in a solution significantly determines the pH level. As we look at our example of the salt BHY, the slightly basic nature of the solution arises because the anion Y- is the conjugate base of a weak acid HY. By absorbing protons from the water, Y- causes an increase in the hydroxide ion concentration (OH-), making the solution basic.

The Meaning of pKa Value

The pKa value is a critical concept in acid-base chemistry. In simple terms, it's a measure of acid strength and is derived from the Ka value, which is the acid dissociation constant. The dissociation constant indicates how well an acid releases protons into a solution. The pKa is the negative logarithm of Ka, and this transformation into a logarithmic scale makes it easier to compare the strengths of different acids.
Smaller pKa values correspond to stronger acids because this means the acid dissociates more readily, releasing more protons into the solution. A high pKa value, on the other hand, signals a weaker acid. With our original exercise in mind, the pKa value helps us to understand the relative strength of the conjugate acids in the reaction. Since BH+ has a pKa of 5.00, and we know the solution is slightly basic, we infer that HY must have a higher pKa, making it a weaker acid compared to BH+.

Understanding pH of Solution

pH is a scale used to specify the acidity or basicity (alkalinity) of an aqueous solution. It's the negative logarithm of the concentration of hydrogen ions in moles per liter. The pH scale ranges from 0 to 14, with lower values representing acidic solutions, higher values signify basic solutions, and 7 being neutral -- like pure water.
In the context of our exercise, because the salt BHY dissolves to produce a basic solution, it means that the concentration of hydroxide ions (OH-) is higher than the concentration of hydrogen ions (H+). This is typically the case when the conjugate base of the dissolved salt (Y-) is relatively stronger than the conjugate acid (BH+), leading to a pH greater than 7. The stronger the conjugate base in the equilibrium, the higher the pH of the solution will be, further reinforcing our understanding that HY is a weaker acid than BH+, as reflected by its higher pKa value.