Question

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

Short answer

The pH of the solution containing 0.60 M HF and 1.00 M KF is approximately 3.39.

Step-by-step solution

Write the chemical equation for the acidic dissociation of HF

First, we need to write the chemical equation for the acidic dissociation of HF in aqueous solution: \[HF \rightleftharpoons H^+ + F^-\]

Find the \(K_a\) value for HF

Next, we need to find the acid dissociation constant (\(K_a\)) for HF. We can obtain it from a table of common \(K_a\) values in any chemistry textbook or online source. For HF, the \(K_a\) value is \(6.8\times10^{-4}\).

Use the Henderson-Hasselbalch equation

To find the \(\mathrm{pH}\) of the buffer solution, we will use the Henderson-Hasselbalch equation: \[\mathrm{pH} =\mathrm{p}K_a + \log \frac{[\mathrm{F^-}]}{[\mathrm{HF}]}\] where \([\mathrm{F^-}]\) and \([\mathrm{HF}]\) are the molar concentrations of F⁻ and HF, respectively.

Plug in the given values and solve for pH

Now plug in the given values of \([\mathrm{F^-}]\), \([\mathrm{HF}]\) and \(K_a\), and calculate the \(\mathrm{pH}\) of the buffer solution: \[ \mathrm{pH} = -\log (6.8\times10^{-4}) + \log \frac{1.0\,\mathrm{M}}{0.60\,\mathrm{M}}\] \[ \mathrm{pH} = 3.17 + \log 1.67\] \[ \mathrm{pH} \approx 3.17 + 0.22\] \[ \mathrm{pH} \approx 3.39 \] So, the \(\mathrm{pH}\) of the solution containing 0.60 M HF and 1.00 M KF is approximately 3.39.

Key concepts

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation is a simple and reliable tool for estimating the pH of buffer solutions. It is specifically useful when dealing with weak acids and their conjugate bases. This equation simplifies the process of finding the pH by relating it directly to the concentration of the acid and its conjugate base.

The Henderson-Hasselbalch equation is expressed as:
\[\mathrm{pH} = \mathrm{p}K_a + \log \frac{[\mathrm{A^-}]}{[\mathrm{HA}]}\]
In this equation:

• \(\mathrm{pH}\) represents the acidity or alkalinity of the solution.
• \(\mathrm{p}K_a\) is the negative logarithm of the acid dissociation constant \(K_a\).
• \([\mathrm{A^-}]\) is the concentration of the conjugate base.
• \([\mathrm{HA}]\) is the concentration of the weak acid.

The equation only requires basic algebra skills: you need to take the logarithm of the ratio of the base-to-acid concentrations and add it to the \(\mathrm{p}K_a\) of the acid. This formula comes in handy because it allows for quick calculations and adjustments of pH in buffer solutions.

acid dissociation constant

The acid dissociation constant, often denoted as \(K_a\), is a key value that indicates the strength of an acid in a solution. It provides insights into how completely an acid dissociates into its ions in water. Understanding \(K_a\) helps predict the behavior of acids and the pH of the solutions they form.

For a general acid dissociation reaction:
\[\mathrm{HA} \rightleftharpoons \mathrm{H^+} + \mathrm{A^-}\]
The corresponding expression for the acid dissociation constant, \(K_a\), is:
\[K_a = \frac{[\mathrm{H^+}][\mathrm{A^-}]}{[\mathrm{HA}]}\]
Where:

• \([\mathrm{H^+}]\) is the concentration of hydrogen ions.
• \([\mathrm{A^-}]\) is the concentration of the conjugate base ions.
• \([\mathrm{HA}]\) is the concentration of the undissociated acid.

The lower the \(K_a\) value, the weaker the acid and the less it dissociates in solution. Conversely, a higher \(K_a\) points to a stronger acid. For example, in our calculation, we used the \(K_a\) value for \(\mathrm{HF}\), which is \(6.8 \times 10^{-4}\). This indicates it is a weak acid.

pH calculation

pH calculation is a fundamental aspect of chemistry, especially when dealing with acids, bases, and buffer solutions. Understanding how to calculate pH is crucial, as it affects everything from chemical reactions to biological systems.

The pH scale ranges from 0 to 14, where:

• Values below 7 indicate acidic solutions.
• Values above 7 indicate basic (alkaline) solutions.
• A pH of 7 is neutral, such as pure water.

Calculating pH typically involves using the formula:
\[\mathrm{pH} = -\log[\mathrm{H^+}]\]
For buffer solutions, like in our initial example, the Henderson-Hasselbalch equation provides a more practical approach to finding the pH by incorporating the concentrations of both the weak acid and its conjugate base.

When given the concentrations and \(K_a\) for a weak acid, you can quickly calculate the pH. First, identify the \([\mathrm{A^-}]\) and \([\mathrm{HA}]\) values, compute the \(\log\) of their ratio, and add this to \(\mathrm{p}K_a\). This makes predicting the behavior of buffer solutions straightforward, aiding many practical chemical applications.