Question

Calculate the \(\mathrm{pH}\) of each of the following solutions of strong acids. a. \(1.21 \times 10^{-3} M \mathrm{HNO}_{3}\) b. \(0.000199 \mathrm{M} \mathrm{HClO}_{4}\) c. \(5.01 \times 10^{-5} M \mathrm{HCl}\) d. \(0.00104 M \mathrm{HBr}\)

Short answer

The approximate pH values for each of the given strong acid solutions are: a. pH = 2.92 b. pH = 3.70 c. pH = 4.30 d. pH = 2.98

Step-by-step solution

Calculate the concentration of hydrogen ions using the strong acid concentration

Since strong acids fully dissociate in water, the concentration of hydrogen ions produced is the same as the concentration of the strong acid. Therefore, the given concentration of each acid is equal to the concentration of hydrogen ions.

Calculate the pH for each solution_a

For solution a with \(1.21 \times 10^{-3} M \mathrm{HNO}_{3}\), the concentration of hydrogen ions is \(1.21 \times 10^{-3} M\). The formula for pH is: \(pH = -\log_{10} [H^{+}]\) For solution a, we have: \(pH = -\log_{10} (1.21 \times 10^{-3})\)

Calculate the pH for solution b

For solution b with \(0.000199 \mathrm{M} \mathrm{HClO}_{4}\), the concentration of hydrogen ions is \(0.000199 M\). We calculate the pH as follows: \(pH = -\log_{10} (0.000199)\)

Calculate the pH for solution c

For solution c with \(5.01 \times 10^{-5} M \mathrm{HCl}\), the concentration of hydrogen ions is \(5.01 \times 10^{-5} M\). We calculate the pH as follows: \(pH = -\log_{10} (5.01 \times 10^{-5})\)

Calculate the pH for solution d

For solution d with \(0.00104 M \mathrm{HBr}\), the concentration of hydrogen ions is \(0.00104 M\). We calculate the pH as follows: \(pH = -\log_{10} (0.00104)\)

Find the pH values

Now find the pH values for each solution: a. \(pH = -\log_{10} (1.21 \times 10^{-3}) \approx 2.92\) b. \(pH = -\log_{10} (0.000199) \approx 3.70\) c. \(pH = -\log_{10} (5.01 \times 10^{-5}) \approx 4.30\) d. \(pH = -\log_{10} (0.00104) \approx 2.98\) The approximate pH values for each of the given solutions are as follows: a. pH = 2.92 b. pH = 3.70 c. pH = 4.30 d. pH = 2.98

Key concepts

Strong Acids

Strong acids are fascinating due to their complete dissociation in water. When a strong acid, such as hydrochloric acid \(\mathrm{HCl}\) or sulfuric acid \(\mathrm{H}_{2}\mathrm{SO}_{4}\), is dissolved in water, it separates entirely into ions.
This means every molecule of the acid turns into a hydrogen ion \(\mathrm{H}^{+}\) and its respective anion. This full dissociation is what characterizes strong acids and distinguishes them from weak acids.
Weak acids do not completely dissociate, which is a key difference in how to calculate their pH. For strong acids, we simplify the pH calculation since the concentration of \(\mathrm{H}^{+}\) ions is the same as the initial concentration of the acid.

• Examples of strong acids: \(\mathrm{HCl}\), \(\mathrm{HNO}_{3}\), \(\mathrm{HBr}\), and \(\mathrm{HClO}_{4}\).
• Completely dissociate in water into \(\mathrm{H}^{+}\) and the acidic anion.
• This characteristic allows straightforward pH calculations.

Understanding the behavior of strong acids is crucial in chemistry, especially when learning about acidity and pH levels.

Hydrogen Ion Concentration

The hydrogen ion concentration, typically noted as \([\mathrm{H}^{+}]\), is an essential concept when calculating pH. In any solution, a higher concentration of \(\mathrm{H}^{+}\) ions leads to a lower pH, indicating more acidity.
For solutions of strong acids, we calculate the hydrogen ion concentration by taking the initial concentration of the acid. This is because strong acids completely dissociate, releasing an equal amount of \(\mathrm{H}^{+}\) ions into the solution.

• The concentration \([\mathrm{H}^{+}]\) directly impacts the pH calculation, with higher concentrations creating a more acidic solution.
• Calculating \([\mathrm{H}^{+}]\) is simplified with strong acids, as it is equivalent to the concentration of the acid itself.
• For example, if the acid concentration is \(1.21 \times 10^{-3}\ M\), then \([\mathrm{H}^{+}] = 1.21 \times 10^{-3}\ M\).

Remember, this convenient method only applies to strong acids due to their full dissociation, making pH calculations more straightforward.

Logarithms

Logarithms are a critical mathematical concept used when calculating pH, which is the measure of hydrogen ion activity in a solution.
The pH is defined by the formula \(\mathrm{pH} = -\log_{10} [\mathrm{H}^{+}]\), meaning it is the negative base 10 logarithm of the hydrogen ion concentration.
This implies that for every tenfold change in \([\mathrm{H}^{+}]\), a change in 1 pH unit occurs.

• A higher \([\mathrm{H}^{+}]\) will result in a lower pH, showing a more acidic solution.
• The pH scale typically ranges from 0 to 14. Values below 7 indicate acidic solutions, while those above 7 indicate basic solutions.
• The logarithmic scale helps manage the wide range of hydrogen ion concentrations found in different solutions, ensuring easier representation and interpretation.

Mastering logarithms for pH calculation is indispensable for understanding the nuances of acidity and alkalinity, essential components of chemistry.