Question

Consider an aqueous solution of HF. The molar heat of formation for aqueous \(\mathrm{HF}\) is \(-320.1 \mathrm{~kJ} / \mathrm{mol}\). (a) What is the pH of a \(0.100 \mathrm{M}\) solution of \(\mathrm{HF}\) at \(100^{\circ} \mathrm{C} ?\) (b) Compare with the pH of a \(0.100 \mathrm{M}\) solution of HF at \(25^{\circ} \mathrm{C}\).

Short answer

Based on the provided information, we were able to calculate the pH of a 0.100 M HF solution at 25°C, which is approximately 2.09. Unfortunately, we cannot find the pH at 100°C due to the missing Ka value at that temperature. However, we can expect that the pH of the solution at 100°C would be lower than at 25°C, as the acidity of weak acids generally increases with temperature.

Step-by-step solution

Find the acid dissociation constant (Ka) of HF at the given temperatures

To find the pH, we need to have the Ka values of \(\mathrm{HF}\) at the given temperatures. Unfortunately, these values aren't provided in the exercise. We need to use the following information to find the Ka values: At \(25^\circ \mathrm{C}\), the Ka value of \(\mathrm{HF}\) is approximately \(6.8 \times 10^{-4}\). Please note that the given heat of formation is not needed for this problem since it is not related to the acidity of the solution.

Use the ICE table to find the concentration of H+ ions

To find the concentration of \(\mathrm{H^+}\) ions in the HF solution, we will use the ICE table. Here we represent HF as HX where H is for the proton (H+) and X is for the fluoride ion (F-). Initial (M): [H] = 0, [X] = 0, [HX] = 0.100 Change (M): [-x], [+x], [+x] Equilibrium (M): [H] = x, [X] = x, [HX] = 0.100 - x Ka = [H][X]/[HX] Since we're assuming x is very small compared to 0.100, the equilibrium expression becomes: Ka = x^2/(0.100) At 100°C:

Solve for x (concentration of H+ ions) at 100°C

Since we don't have the Ka value of \(\mathrm{HF}\) at 100°C, we cannot perform an exact calculation. If it were given, we would calculate x as follows: Ka = x^2/0.100 x = \(\sqrt{Ka \times 0.100}\) At 25°C:

Solve for x (concentration of H+ ions) at 25°C

Using the provided Ka value at 25°C, we can calculate x: Ka = \(6.8 \times 10^{-4}\) x = \(\sqrt{Ka \times 0.100}\) x = \(\sqrt{6.8 \times 10^{-4} \times 0.100}\) x ≈ 0.0082 M

Calculate the pH

To find the pH, we use the pH formula: pH = -log10[H] At 100°C: pH = can't be found as we don't have the Ka value at 100°C At 25°C: pH = -log10(0.0082) ≈ 2.09

Compare the pH values

Since we couldn't find the pH at 100°C due to missing Ka value, we only have the pH value for the 0.100 M \(\mathrm{HF}\) solution at 25°C, which is approximately 2.09. To compare the acidity of the solution at different temperatures, we would need the Ka value at 100°C. Generally, the acidity of a weak acid like HF tends to increase with temperature, so we can expect the pH at 100°C to be lower than the pH at 25°C.

Key concepts

Acid Dissociation Constant (Ka)

Understanding the acid dissociation constant (Ka) is crucial in chemistry, particularly in pH calculations. It's a quantitative measure of an acid's strength in water. The lower the Ka value, the weaker the acid. Ka is defined by the equilibrium equation:

Ka = [H+][A-]/[HA]

where [H+] is the concentration of hydrogen ions, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the undissociated acid. For the case of hydrofluoric acid (HF), the dissociation in water can be written as: HF ⇌ H+ + F-. To calculate the pH of a solution, we need to know the Ka value at the solution's temperature. The provided value at 25°C is useful, but a different temperature would affect the dissociation equilibrium, altering the Ka and consequently the pH.

ICE Table

The ICE table is a valuable tool used for visualizing the changes in concentration during chemical reactions, particularly in acid-base equilibria. ICE stands for Initial, Change, and Equilibrium concentrations. When hydrofluoric acid dissolves in water, we initially have a concentration of 0.100 M HF and virtually 0 M for H+ and F-. As the acid dissociates, we see an increase in H+ and F- and a decrease in HF concentration. The table helps by organizing these changes in a clear manner, making it easier to set up an equilibrium expression necessary to solve for x, representing the H+ concentration. This simplifies the process of finding the pH of the solution. The ICE table is especially powerful for educational purposes, as it provides a clear and methodical way to approach equilibrium problems.

Concentration of H+ Ions

The concentration of H+ ions is a direct indicator of a solution's acidity. The more H+ ions present, the more acidic the solution is. Through the ICE table, we estimated the concentration of H+ ions in HF to be 'x'. Using the acid dissociation constant, we derived a formula to calculate 'x'. In our case, 'x' is the square root of the product of Ka and the initial concentration of HF for a given temperature. This H+ ion concentration is then used to compute the pH, with the understanding that in dilute solutions, the concentration of H+ ions from water's autoionization is negligible compared to that from the acid.

Aqueous Solution Acidity

Aqueous solution acidity, measured on the pH scale, is a critical concept that has widespread implications across chemistry and biology. The pH scale is logarithmic, meaning each whole pH value below 7 (which is neutral like pure water) is ten times more acidic than the next higher value. In our example with HF, the pH determines how acidic the solution is, with lower pH values indicating higher acidity. Temperature also plays a significant role; as a general rule, the dissociation of weak acids like HF increases with temperature, which would result in more H+ ions and a lower pH at 100°C compared to 25°C, assuming the acid dissociates more at the higher temperature and Ka increases correspondingly.