Question

What is the \(\mathrm{pH}\) of these aqueous solutions? (a) \(1.0 \mathrm{M} \mathrm{HCl}\), (b) \(0.1 \mathrm{M} \mathrm{HCl}\), (c) \(0.001 \mathrm{M} \mathrm{HCl}\), (d) \(1.0 \times 10^{-5} \mathrm{M} \mathrm{HCl}\), (e) \(1.10 \times 10^{-7} \mathrm{M} \mathrm{HCl}\)

Short answer

The pH values of the given aqueous solutions are: (a) pH = 0 (b) pH = 1 (c) pH = 3 (d) pH = 5 (e) pH = 6.96 (approx.)

Step-by-step solution

Determine the hydrogen ion concentration [H+]

HCl is a strong acid, which means it ionizes completely in water, so its concentration equal to the hydrogen ion concentration i.e., [H+] = [HCl] (a) [H+] = 1.0 M (b) [H+] = 0.1 M (c) [H+] = 0.001 M (d) [H+] = 1.0 × 10⁻⁵ M (e) [H+] = 1.10 × 10⁻⁷ M

Calculate the pH of each solution

Now, we will apply the pH formula: pH = - log([H+]) for each solution. (a) pH = - log(1.0) = 0 (b) pH = - log(0.1) = 1 (c) pH = - log(0.001) = 3 (d) pH = - log(1.0 × 10⁻⁵) = 5 (e) pH = - log(1.10 × 10⁻⁷) = 6.96 (approx.) The pH values of the given aqueous solutions are: (a) pH = 0 (b) pH = 1 (c) pH = 3 (d) pH = 5 (e) pH = 6.96 (approx.)

Key concepts

Strong Acid Ionization

Understanding the concept of strong acid ionization is crucial when discussing pH calculation. A strong acid is characterized by its ability to completely dissociate in water. This means that every molecule of a strong acid, such as hydrochloric acid (HCl), will separate into its constituent ions, namely hydrogen ions (H+) and the corresponding anion (in this case, Cl-), once dissolved.

When a strong acid ionizes, the concentration of hydrogen ions in the solution becomes equal to the initial concentration of the strong acid. For instance, if you have a 1.0 M solution of HCl, the concentration of hydrogen ions will also be 1.0 M. This is a critical step in pH calculation as it directly correlates to the acidity of the solution. Let's remember this point—it simplifies the process by allowing us to directly use the given acid concentration for subsequent pH calculations.

Hydrogen Ion Concentration

Moving on to the concept of hydrogen ion concentration, it refers to the number of moles of hydrogen ions per liter of solution. In the context of acid solutions, this is a measure of the acid's strength. Higher concentrations of hydrogen ions indicate a more acidic (and therefore lower pH) solution, while lower concentrations indicate a less acidic (higher pH) solution.

As seen from the strong acid ionization, the hydrogen ion concentration equates to the molarity of the strong acid for strong acids like HCl. This concentration is the basis for pH calculation and will influence the final result heavily. It determines where on the pH scale a solution will fall, a scale that ranges from 0 to 14, where lower values are more acidic, and higher values are more basic or alkaline.

pH Scale

The pH scale is a dimensionless unit that describes the acidity or basicity of an aqueous solution. The scale typically ranges from 0 to 14, with 7 being neutral (pure water). pH values lower than 7 represent acidic solutions, while values higher than 7 are basic or alkaline.

The pH scale is logarithmic, which implies that each whole number on the pH scale represents a tenfold change in hydrogen ion concentration. This means a solution with a pH of 4 has ten times more hydrogen ions than a solution with a pH of 5. Understanding this scale is essential for interpreting pH values. For example, in our original exercise, a pH value of 0 for a 1.0 M HCl solution indicates a very high concentration of hydrogen ions and a very acidic solution.

Logarithmic Calculations

Finally, the concept of logarithmic calculations is fundamental in determining pH. The pH of a solution is calculated by taking the negative logarithm (to base 10) of the hydrogen ion concentration. The formula used is: \[\text{pH} = -\log([H^+])\].

The logarithmic nature of the pH scale means that a one-unit change in pH corresponds to a tenfold change in the concentration of hydrogen ions. For our exercise examples, an HCl solution with a concentration of 0.001 M has a pH of 3. This is a reflection of logarithmic calculation, which turns multiplicative relationships into additive ones, allowing for a more straightforward way to express a wide range of hydrogen ion concentrations. It's important to feel comfortable with using a calculator or tools to compute logarithms when solving pH problems, as precise pH values often require such calculations.