Question

Calculate the \(\mathrm{pH}\) of a solution that is \(0.25 \mathrm{M}\) in \(\mathrm{HF}\) and \(0.10 \mathrm{M}\) in NaF.

Short answer

The pH of the solution is 2.77.

Step-by-step solution

Identify Components of the Solution

Firstly, recognize that HF is a weak acid and NaF is its salt. In this buffer solution, HF partially dissociates into \( ext{H}^+ \) and \( ext{F}^- \). NaF dissociates completely into \( ext{Na}^+ \) and \( ext{F}^- \), contributing to the \( ext{F}^- \) concentration in the solution.

Use the Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation for a buffer solution is \( \text{pH} = \text{p}K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \). Here, \( \text{A}^- \) is \( \text{F}^- \) and \( \text{HA} \) is HF. We know \( [\text{A}^-] = 0.10 \) M and \( [\text{HA}] = 0.25 \) M.

Find the Acid Dissociation Constant and pKa

The acid dissociation constant \( K_a \) of HF is approximately \( 6.8 \times 10^{-4} \). Calculate the \( \text{p}K_a \) using \( \text{p}K_a = -\log(K_a) \). Therefore, \( \text{p}K_a \approx \log(6.8 \times 10^{-4}) \approx 3.17 \).

Substitute Values into the Equation

Substitute \( \text{p}K_a = 3.17 \), \( [\text{A}^-] = 0.10 \) M, and \( [\text{HA}] = 0.25 \) M into the Henderson-Hasselbalch equation: \( \text{pH} = 3.17 + \log \left( \frac{0.10}{0.25} \right) \).

Calculate the Logarithmic Term

Calculate \( \log \left( \frac{0.10}{0.25} \right) = \log(0.4) \approx -0.40 \).

Final Calculation of pH

Combine the values to find the pH: \( \text{pH} = 3.17 - 0.40 = 2.77 \). This is the pH of the solution.

Key concepts

Henderson-Hasselbalch equation

When working with buffer solutions, the Henderson-Hasselbalch equation is a crucial tool. It provides a simple way to calculate the pH of a buffered solution utilizing the concentrations of an acid and its conjugate base. The formula is given by: \[ \text{pH} = \text{p}K_a + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \] Here, \([\text{A}^-]\) represents the concentration of the conjugate base, and \([\text{HA}]\) is the concentration of the undissociated weak acid. This equation is particularly useful because it turns complex ideas about acid-base chemistry into simple arithmetic, making pH calculations straightforward.

• Helps in assessing the pH by considering log ratios.
• Ideal for solutions containing a weak acid and its salt.

By knowing the pKa (which we will discuss further), and the concentrations of the acid and base, you can easily determine the pH of the solution. This formula assumes that the solutions are ideal and that the ion pairs' behavior aligns with theoretical limits.

acid dissociation constant

The acid dissociation constant, \( K_a \), is a measure of the strength of an acid in solution. It represents how completely the acid dissociates into ions. Higher values of \( K_a \) indicate a stronger acid that dissociates more completely. For our exercise, HF (hydrofluoric acid) is considered a weak acid, meaning it only partially dissociates in water.

1. HF \( \rightleftharpoons \text{H}^+ + \text{F}^- \)
2. The \( K_a \) value helps in understanding this balance.

The general expression for \( K_a \) is: \[ K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]} \] In simple terms, it compares the concentration of the ions produced to their original undissociated form. The lower the \( K_a \), the weaker the acid. As you calculate and interpret \( K_a \), remember that the value profoundly affects pH calculations and buffer performance.

weak acid dissociation

Weak acids dissociate only partly in water. This is a key characteristic that differentiates them from strong acids, which dissociate completely. In a solution of HF and NaF, HF acts as a weak acid. Here is what the dissociation looks like: \[ \text{HF} \rightleftharpoons \text{H}^+ + \text{F}^- \] The "double arrow" indicates that the dissociation is not complete and exists in equilibrium. This means that in the solution, there is a dynamic balance between the undissociated weak acid and the dissociated ions.

• Partial dissociation influences buffer capacity.
• Essential aspect for applying the Henderson-Hasselbalch equation.

Understanding this equilibrium is critical to explain why weak acid dissociation is integral to calculating pH and designing buffer systems. The extent of dissociation is governed by the acid dissociation constant \( K_a \), as discussed earlier.

pKa calculation

The \( \text{p}K_a \) value is another vital component in the world of chemistry, specifically in pH calculations. \( \text{p}K_a \) is simply the negative logarithm (\( \text{p}K_a = -\log K_a \)) of the acid dissociation constant, \( K_a \). It provides a more manageable number to convey the strength of an acid. Lower \( \text{p}K_a \) values indicate a stronger acid. For HF, the \( \text{p}K_a \) is approximately 3.17, as obtained by substituting its \( K_a \) value into the logarithmic equation.

• Simplifies comparison of acid strength.
• Essential in the Henderson-Hasselbalch equation.

Using \( \text{p}K_a \), chemists can easily assess how an acid will behave in solution, aiding in the determination of pH and stability of buffer solutions. It broadens one's understanding of acid-base chemistry by distilling complex concepts into more practical values for everyday calculations.