Question

Calculate the \(\mathrm{pH}\) of a solution that is \(0.60 \mathrm{M} \mathrm{HF}\) and \(1.00 M \mathrm{KF}\).

Short answer

The pH of the solution that is 0.60 M HF and 1.00 M KF is approximately 3.40.

Step-by-step solution

Find the pKa value for HF

Use the formula: \( pKa = -\log{Ka} \) Using the given Ka value for HF: \( pKa = -\log{(6.6 × 10^{-4})} \) Calculating the pKa value: \( pKa \approx 3.18 \)

Apply the Henderson-Hasselbalch equation

Use the formula: \( pH = pKa + \log{\frac{[A^-]}{[HA]}} \) Substitute the values we found in step 1 and the given concentrations: \( pH = 3.18 + \log{\frac{1.00}{0.60}} \) Simplify and calculate the pH value: \( pH = 3.18 + \log{1.67} \) \( pH \approx 3.18 + 0.22 \) \( pH \approx 3.40 \) So, the pH of the solution that is 0.60 M HF and 1.00 M KF is approximately 3.40.

Key concepts

Acid-Base Chemistry

Acid-base chemistry is a fundamental area of chemistry that explores how acids and bases interact in a solution. ### Understanding Acids and Bases In simple terms, acids are substances that can donate a proton ( H^+ ) to another substance, while bases are substances that can accept a proton. This interaction is crucial for many chemical reactions. * **Acid Example**: Hydrofluoric acid (HF) is an example of a weak acid, meaning it does not completely dissociate in water. * **Base Example**: Potassium fluoride (KF), on the other hand, acts as a base when it dissociates to form fluoride ions (F^-) in solution. ### Importance of Acid and Base Strength The strength of an acid or base affects how it behaves in a reaction. In this case, HF is a weak acid, which means only a small fraction of HF molecules donate their protons. The numerical constant that helps to describe this tendency is the acid dissociation constant (Ka), and its negative logarithm, pKa, is crucial for calculating pH with the Henderson-Hasselbalch equation.

pH Calculation

Calculating the ph of a solution involves understanding the concentration of hydrogen ions (H^+) in a solution. * **Formula**: The most common formula used for pH calculation is \( pH = -\log{[H^+]} \).In the specific exercise provided, we use a different approach called the Henderson-Hasselbalch equation, which is especially useful for buffer solutions. ### Henderson-Hasselbalch EquationThe Henderson-Hasselbalch equation is \( pH = pKa + \log{\frac{[A^-]}{[HA]}} \).* **pKa**: This is the negative log of the acid dissociation constant. For HF, \( pKa \approx 3.18 \).* **[A^-] and [HA]**: These represent the concentrations of the conjugate base (F^-) and the acid (HF), respectively.Inserting these values helps you calculate the pH effectively, especially when dealing with a buffer solution containing both the acid and its conjugate base.

Buffer Solution

A buffer solution is a special type of solution that resists changes in ph when small amounts of acid or base are added. ### How Buffers Work Buffers typically contain a weak acid and its conjugate base, or vice versa. They maintain pH stability by neutralizing added acids or bases. ### Components of a Buffer System For the given problem, the buffer solution is made from: * **Weak Acid**: HF (Hydrofluoric Acid) serves as the weak acid. * **Conjugate Base**: KF, which provides the F^- ions as the conjugate base. ### Why Buffers are Important Buffers are crucial in many biological and chemical processes. They help maintain the pH level necessary for reactions, ensuring that processes like enzyme function and nutrient absorption can proceed efficiently. Using the Henderson-Hasselbalch equation, you get an understanding of how the concentration of acid and base in the buffer solution impacts the overall pH. This stability is vital in many practical applications, from biological systems to industrial processes.