Question

Determine the \(\mathrm{pH}\) of each solution. a. \(0.048 \mathrm{M} \mathrm{HI}\) b. \(0.0895 \mathrm{M} \mathrm{HClO}_{4}\) c. a solution that is \(0.045 \mathrm{M}\) in \(\mathrm{HClO}_{4}\) and \(0.048 \mathrm{M}\) in \(\mathrm{HCl}\) d. a solution that is \(1.09 \%\) HCl by mass (assume a density of \(1.01 \mathrm{~g} / \mathrm{mL}\) for the solution \()\)

Short answer

The pH values of the solutions are: a) 1.32, b) 1.05, c) 1.03, and d) approximately 1.08.

Step-by-step solution

Calculate the pH of 0.048 M HI solution

Hydroiodic acid (HI) is a strong acid, so it dissociates completely in water. Therefore, the concentration of hydronium ions, \( \mathrm{[H_3O^+]} \), is equal to the concentration of HI. To calculate the pH, use the equation \( pH = -\log([H_3O^+]) \). Using the given concentration, \( pH = -\log(0.048) \).

Calculate the pH of 0.0895 M HClO4 solution

Perchloric acid (HClO4) is also a strong acid and thus dissociates completely in water. As with HI, the concentration of \( \mathrm{[H_3O^+]} \) is the same as the concentration of HClO4. To find the pH, \( pH = -\log(0.0895) \).

Determine the pH of a mixed solution of 0.045 M HClO4 and 0.048 M HCl

Both HClO4 and HCl are strong acids. Their effects are additive, so the total concentration of \( \mathrm{[H_3O^+]} \) is the sum of the individual concentrations of the acids. Thus: \( \mathrm{[H_3O^+]} = 0.045 + 0.048 = 0.093 \). The pH is then \( pH = -\log(0.093) \).

Calculate the pH of a 1.09% HCl solution by mass

First, find the concentration (molarity) of HCl. A 1.09% solution by mass means 1.09 g of HCl per 100 g of solution. Assume 100 mL of solution due to the density given, so the mass of the solution is 101 g (since the density is 1.01 g/mL). The number of moles of HCl is \( \frac{1.09 \mathrm{g}}{36.46 \mathrm{g/mol}} \) (since the molar mass of HCl is approximately 36.46 g/mol). Calculate the volume in liters \( \frac{100 \mathrm{mL}}{1000 \mathrm{mL/L}} = 0.1 \mathrm{L} \). The molarity of HCl is then \( \frac{\text{moles of HCl}}{volume in liters} \), and finally, the pH is \( pH = -\log([HCl]) \) with the calculated molarity.

Key concepts

Strong Acids

Understanding strong acids is critical for pH calculation exercises. Strong acids are chemicals that completely dissociate into their ions in water. This means that they release all of their hydrogen ions, contributing to the acidity of the solution. Examples of strong acids include hydroiodic acid (HI) and perchloric acid (HClO₄), both mentioned in the exercise.

Due to their complete dissociation, the concentration of hydrogen ions (or hydronium ions, H₃O⁺) released by a strong acid is equal to the molarity of the acid itself. Therefore, for strong acids, calculating the pH comes down to simply finding the negative logarithm of the molarity of the acid in question.

It's important to remember that the strong acids' behavior allows for straightforward pH calculations, a characteristic not shared with weak acids, which only partially dissociate in water.

pH Calculation

The pH scale is a measure of how acidic or basic a solution is. It ranges from 0 to 14, with 7 being neutral. The calculation of pH is based on the concentration of hydronium ions in a solution and is expressed by the formula: pH = -log([H₃O⁺]).

To calculate the pH from a given molarity of a strong acid, we use their equivalence to [H₃O⁺], as mentioned earlier. For example, if a solution has a molarity of 0.048 M HI, then the pH equals -log(0.048). pH calculation is essential in many chemistry applications, from industrial processes to biological systems.

Hydronium Ion Concentration

Hydronium ion concentration, denoted as [H₃O⁺], indicates the amount of hydronium ions in a solution. It's a key component in the pH calculation of solutions. For strong acids, the initial molarity of the acid equals the concentration of hydronium ions because they completely dissociate in water.

For instance, if you have a 0.0895 M HClO₄ solution, the concentration of hydronium ions is also 0.0895 M. This directly corresponds to the pH value, which is determined by using the pH formula. In cases where multiple strong acids are present, such as a mixed solution of HClO₄ and HCl, you simply add their hydronium ion contributions together before calculating the pH.

Molarity

Molarity is a measure of the concentration of a solute in a solution and is expressed in moles per liter (M). Specifically, it's the number of moles of solute divided by the volume of solution in liters. This concept is indispensable for understanding the relationship between the amount of acid present in a solution and its corresponding pH level.

When dealing with solutions like a 1.09% HCl by mass, molarity can be determined by converting the mass of HCl to moles (using the molar mass of HCl), and then dividing by the volume of the solution (taking into account the density if needed). The molarity can then be used to determine the [H₃O⁺] and thus calculate the pH. Accurately determining molarity is fundamental for precise pH calculations in chemistry.