Given the pK_b, calculate the pK_a of the conjugate acid.
(b)

Verified step by step guidance

1. Understand the relationship between pKa and pKb. The pKa of a conjugate acid and the pKb of its conjugate base are related by the equation: $pKa+pKb=\; 14$ (at 25°C). This is derived from the ionization constant of water, Kw, where $Kw=\; 10-14$.
2. Rearrange the equation to solve for pKa: $pKa=\; 14\; -pKb$.
3. Substitute the given value of pKb into the equation. For example, if pKb = 4.75, substitute it into the equation: $pKa=\; 14\; -\; 4.75$.
4. Perform the subtraction to determine the pKa value. This step involves simple arithmetic, but ensure you understand the concept of how pKa and pKb are inversely related.
5. Interpret the result. A lower pKa value indicates a stronger conjugate acid, while a higher pKa value indicates a weaker conjugate acid. This relationship is important in understanding acid-base chemistry.

Key Concepts

pKb and pKa Definitions

pKb is the negative logarithm of the base dissociation constant (Kb) of a weak base, indicating its strength. Conversely, pKa is the negative logarithm of the acid dissociation constant (Ka) of a weak acid. The relationship between pKa and pKb is crucial for understanding acid-base equilibria, as they are related through the equation: pKa + pKb = 14 at 25°C.

Conjugate Acid-Base Pairs

In acid-base chemistry, a conjugate acid is formed when a base accepts a proton (H+). Each acid has a corresponding conjugate base, which is what remains after the acid donates a proton. Understanding these pairs is essential for calculating pKa from pKb, as it allows for the identification of the acid's strength based on its conjugate base's properties.

Calculating pKa from pKb

To calculate the pKa of a conjugate acid from its pKb, one can use the formula: pKa = 14 - pKb. This equation reflects the inverse relationship between the strength of a base and its conjugate acid. By knowing the pKb value, one can easily determine the pKa, which is vital for predicting the behavior of acids and bases in various chemical reactions.