Calculating PH Of NaF And HF Buffer Solution A Step-by-Step Guide

In this article, we will delve into the calculation of the pH of a buffer solution prepared by mixing sodium fluoride (NaF) and hydrofluoric acid (HF). This is a classic chemistry problem that involves understanding the principles of acid-base equilibria and buffer solutions. Buffers are essential in many chemical and biological systems as they resist changes in pH upon the addition of small amounts of acid or base. This property is crucial for maintaining the stability of chemical reactions and biological processes. To accurately calculate the pH of this buffer solution, we will use the Henderson-Hasselbalch equation, which is a cornerstone in buffer calculations. We will also address the role of the acid dissociation constant ($K_a$) and how it influences the buffer's pH. This exploration will not only provide a step-by-step solution to the given problem but also enhance your understanding of buffer chemistry.

To fully grasp the problem at hand, it's crucial to first understand what buffer solutions are and how they function. A buffer solution is essentially an aqueous solution that resists changes in pH when small amounts of an acid or a base are added to it. This resistance to pH change is what makes buffers vital in various chemical and biological processes. They are composed of a weak acid and its conjugate base, or a weak base and its conjugate acid. The weak acid and its conjugate base work in tandem to neutralize added bases and acids, respectively, thereby maintaining a relatively stable pH. This buffering action is essential in maintaining the equilibrium of many chemical reactions and the stability of biological systems, such as blood, which has a very narrow pH range for proper functioning.

In our specific scenario, we have a buffer solution composed of hydrofluoric acid (HF), which is a weak acid, and sodium fluoride (NaF), which is its conjugate base. When a strong acid is added to this buffer, the fluoride ions ($F^−$) from NaF react with the added acid, neutralizing it and preventing a significant drop in pH. Conversely, when a strong base is added, the HF molecules in the buffer donate protons to neutralize the base, preventing a significant increase in pH. This dynamic equilibrium between the acid and its conjugate base is what allows the buffer to maintain a stable pH. The efficacy of a buffer is typically greatest when the concentrations of the weak acid and its conjugate base are equal or close to each other. This is because the buffer can effectively neutralize both added acids and bases. Understanding these fundamental principles of buffer solutions is key to solving the problem of determining the pH of a NaF and HF mixture.

We are tasked with calculating the pH of a buffer solution that is prepared by mixing 40.0 g of sodium fluoride (NaF) and 40.0 g of hydrofluoric acid (HF) in a 900 mL solution. The acid dissociation constant ($K_a$) for HF is given as $7.2 imes 10^{-4}$. This problem requires a step-by-step approach that involves converting the masses of NaF and HF into moles, calculating their concentrations in the solution, and then applying the Henderson-Hasselbalch equation to find the pH. The Henderson-Hasselbalch equation is particularly useful for calculating the pH of buffer solutions because it relates the pH to the $pK_a$ of the acid and the ratio of the concentrations of the conjugate base and the acid. Before we dive into the calculations, it’s important to understand the significance of each component in the solution. NaF, being the salt of a weak acid, provides the conjugate base ($F^−$) in the buffer system. HF, the weak acid, donates protons to neutralize any added base. The $K_a$ value provides a measure of the strength of the acid; a smaller $K_a$ indicates a weaker acid. The volume of the solution is crucial for calculating the molar concentrations of the acid and the base, which are necessary inputs for the Henderson-Hasselbalch equation. This problem is a practical application of buffer chemistry principles and demonstrates how buffers maintain pH stability in solutions.

To determine the pH of the buffer solution, we will follow a detailed, step-by-step approach. This will ensure clarity and accuracy in our calculations. Here’s how we’ll proceed:

Step 1: Calculate the Moles of NaF and HF

First, we need to convert the given masses of NaF and HF into moles. To do this, we will use the molar masses of NaF and HF. The molar mass of NaF (sodium fluoride) is approximately 41.99 g/mol, and the molar mass of HF (hydrofluoric acid) is approximately 20.01 g/mol.

For NaF:

$$\text{Moles of NaF} = \frac{\text{Mass of NaF}}{\text{Molar mass of NaF}} = \frac{40.0 \text{ g}}{41.99 \text{ g/mol}} \approx 0.9526 \text{ mol}$$

For HF:

$$\text{Moles of HF} = \frac{\text{Mass of HF}}{\text{Molar mass of HF}} = \frac{40.0 \text{ g}}{20.01 \text{ g/mol}} \approx 1.999 \text{ mol}$$

Step 2: Calculate the Molar Concentrations of NaF and HF

Next, we will calculate the molar concentrations of NaF and HF in the 900 mL solution. Molarity (M) is defined as moles of solute per liter of solution. Since the volume is given in milliliters, we will first convert it to liters (1 L = 1000 mL). So, 900 mL is equal to 0.900 L.

For NaF:

$$\text{Concentration of NaF} = \frac{\text{Moles of NaF}}{\text{Volume of solution}} = \frac{0.9526 \text{ mol}}{0.900 \text{ L}} \approx 1.058 \text{ M}$$

For HF:

$$\text{Concentration of HF} = \frac{\text{Moles of HF}}{\text{Volume of solution}} = \frac{1.999 \text{ mol}}{0.900 \text{ L}} \approx 2.221 \text{ M}$$

Step 3: Apply the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is used to calculate the pH of a buffer solution. It is given by:

$$pH = pK_a + \log_{10} \frac{[A^-]}{[HA]}$$

where:

• $pH$ is the pH of the buffer solution.
• $pK_a$ is the negative logarithm of the acid dissociation constant ($K_a$).
• $[A^-]$ is the concentration of the conjugate base (in this case, $F^−$ from NaF).
• $[HA]$ is the concentration of the weak acid (in this case, HF).

First, we calculate the $pK_a$:

$$pK_a = -\log_{10}(K_a) = -\log_{10}(7.2 imes 10^{-4}) \approx 3.14$$

Now, we substitute the concentrations of NaF and HF and the $pK_a$ value into the Henderson-Hasselbalch equation:

$$pH = 3.14 + \log_{10} \frac{1.058 \text{ M}}{2.221 \text{ M}}$$

$$pH = 3.14 + \log_{10}(0.4764)$$

$$pH = 3.14 + (-0.3216)$$

$$pH \approx 2.82$$

Step 4: Final Answer

The pH of the buffer solution is approximately 2.82. Therefore, the closest answer from the given options is 2.8.

In summary, we have successfully calculated the pH of a buffer solution composed of 40.0 g of NaF and 40.0 g of HF in 900 mL of solution. The process involved several key steps, including converting the masses of the compounds into moles, determining their molar concentrations, and applying the Henderson-Hasselbalch equation. The final pH of the buffer solution was found to be approximately 2.8, demonstrating the acidic nature of the buffer due to the presence of hydrofluoric acid (HF). This problem underscores the practical application of buffer chemistry principles, which are crucial in maintaining pH stability in various chemical and biological systems. Understanding buffers and their behavior is essential for anyone studying chemistry, biochemistry, or related fields. The Henderson-Hasselbalch equation is a powerful tool for these calculations, and mastering its use is fundamental to understanding buffer systems. By following this detailed, step-by-step solution, you can apply these principles to similar problems and further enhance your understanding of acid-base chemistry and buffer solutions.

Buffer solution, pH calculation, Henderson-Hasselbalch equation, Sodium fluoride (NaF), Hydrofluoric acid (HF), Acid dissociation constant ($K_a$), Molar concentration, Acid-base equilibria, Buffer chemistry, Weak acid, Conjugate base.