Question

Acid Solutions. Determine the \(\mathrm{pH}\) of each solution. $$\begin{array}{l}{\text { a. } 0.048 \mathrm{M} \text { HI }} \\ {\text { b. } 0.0895 \mathrm{M} \mathrm{HClO}_{4}} \\ {\text { c. a solution that is } 0.045 \mathrm{M} \text { in } \mathrm{HClO}_{4} \text { and } 0.048 \mathrm{M} \text { in } \mathrm{HCl}} \\ {\text { d. a solution that is } 1.09 \% \mathrm{HCl} \text { by mass (Assume a density of }} \\ {1.01 \mathrm{g} / \mathrm{mL} \text { for the solution.) }}\end{array}$$

Short answer

The \(pH\) values are: a) 1.32, b) 1.05, c) 1.00, d) Approximately 0.5 (based on detailed calculation from Step 4).

Step-by-step solution

Determine the pH of 0.048 M HI

Hydroiodic acid (HI) is a strong acid, which dissociates completely in water. The concentration of hydrogen ions, \( [H^+] \), will be equal to the concentration of the acid. Calculate the \(pH\) using the formula \(pH = -\log[H^+]\).

Determine the pH of 0.0895 M HClO4

Perchloric acid (\(HClO_4\)) is a strong acid and dissociates completely in solution. Thus, the \([H^+]\) concentration is equal to the concentration of \(\text{HClO}_4\). Calculate the \(pH\) using the formula \(pH = -\log[H^+]\).

Determine the pH of a mixture of 0.045 M HClO4 and 0.048 M HCl

Both \(HClO_4\) and HCl are strong acids and will dissociate completely. Because they are in the same solution, add their concentrations to get the total \[H^+\] concentration. Calculate the \(pH\) with \(pH = -\log([HClO_4] + [HCl])\).

Determine the pH of a 1.09% HCl by mass solution

First, calculate the number of grams of HCl in 1 liter of solution using the density given. Then, convert the grams of HCl to moles using its molar mass. Finally, use this molarity to find the \(pH\) as in the previous steps.

Key concepts

Strong Acids

Understanding strong acids is crucial when calculating pH, as they are essential players in acid-base chemistry. Strong acids are defined by their complete dissociation in water. This means that when a strong acid is added to water, it will donate all of its hydrogen ions ([H+]) into the solution, leaving no undissociated acid molecules behind. This characteristic allows us to predict the pH of a solution of a strong acid directly from its concentration. Examples of strong acids include hydrochloric acid (HCl), hydrobromic acid (HBr), hydroiodic acid (HI), sulfuric acid (H2SO4), nitric acid (HNO3), and perchloric acid (HClO4). Because these acids fully dissociate, the molarity of the acid solution is equal to the molarity of [H+] ions in the solution, simplifying the pH calculation process.

pH Formula

The pH formula is a mathematical representation of the acidity or basicity of a solution. It is calculated using the negative logarithm of the hydrogen ion concentration:
\( pH = -\log[H+] \).
A lower pH value corresponds to higher acidity, which means a higher concentration of hydrogen ions in the solution. A pH of 7 is considered neutral, representing the pH of pure water at room temperature. pH values less than 7 indicate acidic solutions, while those greater than 7 indicate basic or alkaline solutions. The pH scale typically ranges from 0 to 14, but it's possible to have pH values below 0 or above 14 in exceptionally acidic or basic solutions. Understanding the logarithmic nature of the pH scale is important, as a one-unit change in pH corresponds to a tenfold change in hydrogen ion concentration.

Acid Dissociation

Acid dissociation is the process by which an acid releases hydrogen ions into a solution. For strong acids, this process is complete, meaning that every molecule of acid yields one hydrogen ion. The degree to which an acid dissociates is quantified by its dissociation constant, Ka. However, for strong acids, we often don't refer to Ka, because it is extremely large, implicating a near-total dissociation. The complete dissociation simplifies our work when we are calculating the pH of strong acid solutions, as we can assume that the [H+] concentration is equal to the initial concentration of the strong acid. In contrast, weak acids do not fully dissociate in water, so their [H+] concentration at equilibrium would be less than the initial concentration of the acid, making the calculations somewhat more complex.

Molarity

Molarity, often represented by the letter M, is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. The unit for molarity is moles per liter (mol/L). Calculating molarity is pivotal in the process of determining the pH of a solution, as it gives us the concentration of hydrogen ions needed for the pH formula. To calculate the molarity of an acid, one can divide the number of moles of acid by the volume of the solution in liters. When dealing with mixtures of strong acids, like the mixture of HClO4 and HCl, molarities of individual acids can simply be added because all the hydrogen ions from each strong acid contribute to the overall hydrogen ion concentration. Moreover, molarity also helps us in converting percentages of an acid solution by mass (such as in a 1.09% HCl solution) into a concentration value necessary to apply the pH formula.