Question

For each strong acid solution, determine \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right],\left[\mathrm{OH}^{-}\right]\), and \(\mathrm{pH}\). (a) \(0.0088 \mathrm{M} \mathrm{HClO}_{4}\) (b) \(1.5 \times 10^{-3} \mathrm{M} \mathrm{HBr}\) (c) \(9.77 \times 10^{-4} \mathrm{MHI}\) (d) \(0.0878 \mathrm{M} \mathrm{HNO}_{3}\)

Short answer

\(\left[\mathrm{H}_3\mathrm{O}^{+}\right] = \) given molarity of acid; \(\left[\mathrm{OH}^{-}\right] = \frac{1 \times 10^{-14}}{\left[\mathrm{H}_3\mathrm{O}^{+}\right]}\); \(\mathrm{pH} = -\log(\left[\mathrm{H}_3\mathrm{O}^{+}\right])\). Results vary for each acid.

Step-by-step solution

Calculate the concentration of Hydronium ions \(\left[\mathrm{H}_3\mathrm{O}^{+}\right]\)

For strong acids like \(\mathrm{HClO}_4\), \(\mathrm{HBr}\), \(\mathrm{HI}\), and \(\mathrm{HNO}_3\), the concentration of hydronium ions is equal to the concentration of the acid because they completely dissociate in water. Therefore, \(\left[\mathrm{H}_3\mathrm{O}^{+}\right] = \) the molarity of the acid.

Calculate the concentration of Hydroxide ions \(\left[\mathrm{OH}^{-}\right]\)

Use the formula \(\left[\mathrm{OH}^{-}\right] = \frac{1 \times 10^{-14}}{\left[\mathrm{H}_3\mathrm{O}^{+}\right]}\) to find the concentration of hydroxide ions, as the product of \(\left[\mathrm{H}_3\mathrm{O}^{+}\right]\) and \(\left[\mathrm{OH}^{-}\right]\) is always \(1 \times 10^{-14} \(\text{M}^2\)\) in pure water at 25°C.

Calculate the pH

The pH is calculated using the formula \(\mathrm{pH} = -\log(\left[\mathrm{H}_3\mathrm{O}^{+}\right])\). Take the negative logarithm of the hydronium ion concentration to determine the pH of the solution.

Apply calculations for each solution

Repeat Steps 1, 2, and 3 for each given concentration of the acid. Since each acid is a strong acid, \(\left[\mathrm{H}_3\mathrm{O}^{+}\right]\) is equal to the original molarity of the acid, and the pH and \(\left[\mathrm{OH}^{-}\right]\) can be calculated directly from there.

Key concepts

Strong Acid Properties

Strong acids are substances that exhibit certain distinctive characteristics when in aqueous solutions. A key property of strong acids is that they completely dissociate into their constituent ions. This means that when a strong acid is dissolved in water, it releases all its hydrogen ions, resulting in a high concentration of hydronium ions \(\left[\mathrm{H}_3\mathrm{O}^{+}\right]\).

Examples of strong acids include hydrochloric acid (HCl), hydrobromic acid (HBr), and nitric acid (HNO3). Because they dissociate completely, the original concentration of the strong acid is directly equal to the concentration of hydronium ions produced in the solution. This complete dissociation is pivotal for understanding how to calculate the pH of a solution and is particularly important in titrations and other chemical processes where the precise concentration of ions must be known.

Hydronium Ion Concentration

The concentration of hydronium ions \(\left[\mathrm{H}_3\mathrm{O}^{+}\right]\) in a solution is central to many aspects of acid-base chemistry. For strong acids, determining the concentration of hydronium ions is straightforward because it is equal to the acid's molarity. This is due to their complete dissociation in water.

The hydronium ion is responsible for the acidic properties of a solution. When discussing acid strength and pH levels, the focus is on the amount of these ions present. Higher concentrations of hydronium ions result in a more acidic solution and therefore a lower pH value.

Hydroxide Ion Concentration

The concentration of hydroxide ions \(\left[\mathrm{OH}^{-}\right]\) is another vital component of acid-based reactions. It has an inverse relationship with the concentration of hydronium ions in a solution, as described by the water dissociation constant \(K_w = 1 \times 10^{-14} \text{M}^2\) at 25°C. The hydroxide ion concentration can be calculated using the formula \(\left[\mathrm{OH}^{-}\right] = \frac{1 \times 10^{-14}}{\left[\mathrm{H}_3\mathrm{O}^{+}\right]}\).

This relationship means that in a solution with high hydronium ion concentration, the hydroxide ion concentration will be low, and vice versa. Such balance is crucial for maintaining the pH levels of various environments, from biological systems to industrial processes.

pH Level Determination

Determining the pH level of a solution is a fundamental practice in chemistry, with pH being a measure of acidity or basicity. The pH scale typically ranges from 0 to 14, with lower values being more acidic and higher values being more alkaline or basic. To calculate the pH, we use the formula \(\mathrm{pH} = -\log(\left[\mathrm{H}_3\mathrm{O}^{+}\right])\). This equation provides the direct relationship between the concentration of hydronium ions and the pH level of the solution.

For strong acids, once we have determined the hydronium ion concentration, we can calculate the pH by taking the negative logarithm of that concentration. This is a logarithmic scale, meaning that each whole number change in pH represents a tenfold change in \(\left[\mathrm{H}_3\mathrm{O}^{+}\right]\), which provides a more manageable way to express the wide range of hydronium ion concentrations that one might encounter in various solutions.