Question

Calculate the hydrogen ion concentration and the \(\mathrm{pH}\) of each of the following solutions of strong acids. a. \(1.04 \times 10^{-4} M \mathrm{HCl}\) b. \(0.00301 M \mathrm{HNO}_{3}\) c. \(5.41 \times 10^{-4} M \mathrm{HClO}_{4}\) d. \(6.42 \times 10^{-2} M \mathrm{HNO}_{3}\)

Short answer

a. \([\mathrm{H}^{+}] = 1.04 \times 10^{-4} M\), pH ≈ 3.98 b. \([\mathrm{H}^{+}] = 0.00301 M\), pH ≈ 2.52 c. \([\mathrm{H}^{+}] = 5.41 \times 10^{-4} M\), pH ≈ 3.27 d. \([\mathrm{H}^{+}] = 6.42 \times 10^{-2} M\), pH ≈ 1.19

Step-by-step solution

Calculate the hydrogen ion concentration

Since HCl is a strong acid and dissociates completely in water, the concentration of hydrogen ions [H+] will be equal to the concentration of HCl: \([\mathrm{H}^{+}] = 1.04 \times 10^{-4} M\)

Calculate the pH of the solution

Now we will use the pH formula to find the value of pH: \[\mathrm{pH} = -\log_{10} [\mathrm{H}^{+}]\] \[\mathrm{pH} = -\log_{10} (1.04 \times 10^{-4})\] The pH of the solution is approximately 3.98. b. \(0.00301 M \mathrm{HNO}_{3}\)

Calculate the hydrogen ion concentration

HNO3 is a strong acid that dissociates completely, so the concentration of hydrogen ions [H+] will equal the concentration of HNO3. \([\mathrm{H}^{+}] = 0.00301 M\)

Calculate the pH of the solution

Now we will apply the pH formula to find the value of pH: \[\mathrm{pH} = -\log_{10} (0.00301)\] The pH of the solution is approximately 2.52. c. \(5.41 \times 10^{-4} M \mathrm{HClO}_{4}\)

Calculate the hydrogen ion concentration

HClO4 is a strong acid and dissociates completely in water. The concentration of hydrogen ions [H+] will equal the concentration of HClO4: \([\mathrm{H}^{+}] = 5.41 \times 10^{-4} M\)

Calculate the pH of the solution

Now we will use the pH formula to determine the pH: \[\mathrm{pH} = -\log_{10} (5.41 \times 10^{-4})\] The pH of the solution is approximately 3.27. d. \(6.42 \times 10^{-2} M \mathrm{HNO}_{3}\)

Calculate the hydrogen ion concentration

HNO3 is a strong acid that dissociates completely in water. The concentration of hydrogen ions [H+] will equal the concentration of HNO3: \([\mathrm{H}^{+}] = 6.42 \times 10^{-2} M\)

Calculate the pH of the solution

Now we will apply the pH formula to find the value of pH: \[\mathrm{pH} = -\log_{10} (6.42 \times 10^{-2})\] The pH of the solution is approximately 1.19.

Key concepts

Hydrogen Ion Concentration

Understanding the hydrogen ion concentrationis crucial when studying acidity and basicity in chemistry. The hydrogen ion concentration in a solution, often indicated as \( [H^+] \), is a measure of the number of hydrogen ions present per unit volume. In the context of strong acids, like HCl or \( HNO_3 \) as shown in the examples, these acids disassociate completely in water. This means every molecule of the acid breaks apart to release a hydrogen ion into the solution.

The concentration of these ions directly affects the solution's pH level – a measure of how acidic or basic the solution is. For example, if we have a 1.04 x 10^-4 M solution of HCl, it means there are 1.04 x 10^-4 moles of hydrogen ions in every liter of solution. Consequently, the hydrogen ion concentration for strong acids is equal to the molarity of the acid solution because it assumes that 100% of the acid disassociates to release that many moles of hydrogen ions into the solution.

Strong Acids

When dealing with strong acids, it is fundamental to comprehend that they are characterized by their ability to dissociate completely in aqueous solutions. This total dissociation into hydrogen ions \( (H^+) \) and their corresponding anions is what makes them 'strong'.

The commonly known strong acids include hydrochloric acid (HCl), nitric acid (\( HNO_3 \)), and perchloric acid (\( HClO_4 \)), among others. The significance of recognizing an acid as strong comes into play when carrying out pH calculations – knowing that the molarity of the strong acid directly translates into the molarity of the hydrogen ion concentration simplifies the process considerably and avoids additional steps that might be necessary for weak acids, which only partially dissociate.

pH Formula

The pH of a solution is a numerical representation of its acidity or basicity on a logarithmic scale. The formula to calculate pH is:\[\mathrm{pH} = -\log_{10} [\mathrm{H}^{+}]\]Using this equation, we can find the pH by taking the negative logarithm (base 10) of the hydrogen ion concentration. If you're given the molarity of a strong acid in a solution, such as 0.00301 M of \( HNO_3 \), you can directly take this value as the concentration of hydrogen ions. Then, you apply the pH formula to find that the pH is approximately 2.52, as seen in one of the previous examples.

It's important for students to feel comfortable using logarithms when dealing with pH calculations. Remember, a lower pH value indicates a more acidic solution, and by knowing how to convert hydrogen ion concentrations to pH values, you can assess the acidity of different solutions quickly and effectively.