Question

What is the hydronium ion concentration of a \(1.2 \times 10^{-4} \mathrm{M}\) solution of \(\mathrm{HClO}_{4} ?\) What is its \(\mathrm{pH}\) ?

Short answer

The hydronium ion concentration is \\(1.2 \times 10^{-4} \, \mathrm{M}\\) and the \\(\mathrm{pH}\\) is approximately 3.92.

Step-by-step solution

Understand the acid's dissociation

Perchloric acid \(\mathrm{HClO}_4\) is a strong acid. This means it completely dissociates in water. The equation for its dissociation is: \[\mathrm{HClO}_{4(aq)} \rightarrow \mathrm{H}^{+}_{(aq)} + \mathrm{ClO}_{4}^{-}_{(aq)}\] Since it dissociates completely, the concentration of hydronium ions \(\mathrm{H}^{+}\) will be equal to the initial concentration of the acid.

Calculate the hydronium ion concentration

The concentration of hydronium ions \(\left[\mathrm{H}^{+}\right]\) is equal to the concentration of the \(\mathrm{HClO}_4\) solution since it dissociates completely. Thus, \[\left[\mathrm{H}^{+}\right] = 1.2 \times 10^{-4} \, \mathrm{M}\]

Use the hydronium concentration to find the pH

The \(\mathrm{pH}\) of a solution is calculated using the negative logarithm (base 10) of the hydronium ion concentration: \[\mathrm{pH} = -\log\left([\mathrm{H}^{+}]\right)\] Substituting in the given value: \[\mathrm{pH} = -\log\left(1.2 \times 10^{-4}\right)\] Using a calculator, this gives a \(\mathrm{pH}\) of approximately 3.92.

Key concepts

Perchloric Acid

Perchloric acid, commonly represented by the formula \(\mathrm{HClO}_4\), is known for being a strong acid. This means that when it is added to water, it dissociates completely into its constituent ions.
This dissociation can be expressed with the chemical equation:

• \(\mathrm{HClO}_{4(aq)} \rightarrow \mathrm{H}^{+}_{(aq)} + \mathrm{ClO}_{4}^{-}_{(aq)}\)

Complete dissociation implies that nearly all the \(\mathrm{HClO}_4\) molecules split apart to form hydronium ions and perchlorate ions.
Because of this characteristic, we can easily determine the concentration of hydronium ions in a solution if we know the initial concentration of the acid.

Acid Dissociation

Acid dissociation refers to the process where an acid breaks down in water to form its constituent ions. In strong acids like perchloric acid, this process is complete.
For weak acids, this is not the case, as they only partially dissociate, leading to an equilibrium between the un-dissociated molecules and the ions.
With strong acids, since dissociation is complete, the concentration of hydrogen ions \([\mathrm{H}^+]\) in the solution is equal to the initial concentration of the acid introduced.

• For example, if you started with a \( 1.2 \times 10^{-4} \mathrm{M} \) solution of \( \mathrm{HClO}_4\), the \([\mathrm{H}^+]\) after dissociation is also \( 1.2 \times 10^{-4} \mathrm{M} \).

This straightforward ratio is a defining feature of strong acids, facilitating easy calculations for chemistry students.

pH Calculation

The pH of a solution is a measure of its acidity or alkalinity. To find the pH of a solution, you use the formula:

• \(\mathrm{pH} = -\log([\mathrm{H}^+])\)

This formula indicates that pH is the negative logarithm (base 10) of the hydronium ion concentration.
Hence, a lower pH value signifies a higher concentration of \([\mathrm{H}^+]\) ions, which means greater acidity. For example, with a \( 1.2 \times 10^{-4} \mathrm{M} \) \( \mathrm{HClO}_4\) solution, the pH is calculated using the given concentration:

• \(\mathrm{pH} = -\log(1.2 \times 10^{-4})\)

Using a calculator, this results in a pH of approximately 3.92.
This demonstrates that the solution is acidic, as expected from a strong acid. Understanding this calculation is crucial for students as pH is a fundamental concept in chemistry.