Problem 156 - Introductory Chemistry Atoms First

Question

The pH of a solution is \(-1\). What are the \(\mathrm{H}_{3} \mathrm{O}^{+}\) and OH concentrations? Is the solution acidic or basic?

Step-by-Step Solution

Answer

Given the pH of -1, the concentration of H₃O⁺ ions can be calculated as \( [H_{3}O^+] = 10^{-(-1)} = 10 \) moles/L. Using the ion product of water, the concentration of OH⁻ ions is found to be \( [OH^-] = \frac{1 \times 10^{-14}}{10} = 1 \times 10^{-15} \) moles/L. Since the H₃O⁺ concentration is greater than the OH⁻ concentration, the solution is acidic.

Step 1: Recall the definition of pH

The pH of a solution is defined as the negative logarithm of the H₃O⁺ concentration: \( pH = -\log{[H_{3}O^+]} \) where [H₃O⁺] represents the concentration of hydronium ions in the solution,

Step 2: Calculate the H₃O⁺ concentration

Given the pH value of -1, we can rearrange the formula to find the H₃O⁺ concentration: \[ [H_{3}O^+] = 10^{-pH} \] Substitute pH value and compute the concentration: \[ [H_{3}O^+] = 10^{-(-1)} = 10 \] So, the concentration of H₃O⁺ in the solution is 10 moles/L.

Step 3: Recall the relationship between H₃O⁺ and OH⁻ concentrations

The relationship between H₃O⁺ and OH⁻ concentrations can be described using the ion product of water (Kw): \[ K_w = [H_{3}O^+][OH^-] \] For pure water at 25°C, Kw value is 1 x 10⁻¹⁴.

Step 4: Calculate the OH⁻ concentration

Using the Kw value and the calculated H₃O⁺ concentration, find the concentration of OH⁻ ions: \[ [OH^-] = \frac{K_w}{[H_{3}O^+]} \] Substitute the values and compute the concentration: \[ [OH^-] = \frac{1 \times 10^{-14}}{10} = 1 \times 10^{-15} \] So, the concentration of OH⁻ ions in the solution is 1 x 10⁻¹⁵ moles/L.

Step 5: Determine if the solution is acidic or basic

A solution is considered acidic if the H₃O⁺ concentration is greater than the OH⁻ concentration, and it's considered basic if the OH⁻ concentration is greater than the H₃O⁺ concentration. Since the H₃O⁺ concentration (10 moles/L) is greater than the OH⁻ concentration (1 x 10⁻¹⁵ moles/L), the solution is acidic.

Key Concepts

Hydronium Ion Concentration

The hydronium ion concentration, often represented as \[H_{3}O^+\], is a key factor in determining the acidity of a solution. It reflects the amount of hydronium ions present, which are formed when water molecules gain a hydrogen ion \((H^+)\). \[H_{3}O^+\] is connected to the pH scale, which measures how acidic or basic a solution is.

The pH is calculated using the formula:

\( pH = -\log{[H_{3}O^+]} \)

When you have a pH value, you can easily determine the \[H_{3}O^+\] concentration by rearranging the equation:

\[ [H_{3}O^+] = 10^{-pH} \]

• If a solution has a high \[H_{3}O^+\] concentration, it means the solution is more acidic.
• Given a pH of -1, the \[H_{3}O^+\] concentration in our example turns out to be 10 moles/L, reflecting very high acidity.

OH Minus Concentration

The concentration of hydroxide ions in a solution is denoted as \[OH^-\]. This component is crucial in determining the basicity of the solution. Hydroxide ions are essentially part of the balance between acids and bases in water.

To find the \[OH^-\] concentration, we use the relationship between \[H_{3}O^+\] and \[OH^-\] concentrations which is governed by the ion product of water (\(K_w\)):

\[ K_w = [H_{3}O^+][OH^-] \]

For pure water at 25°C, \(K_w\) is constant, equal to \(1 \times 10^{-14}\). This means we can explore how acid and base concentrations are inversely related:

\[ [OH^-] = \frac{K_w}{[H_{3}O^+]} \]

• Substituting values allows calculation: \([OH^-] = \frac{1 \times 10^{-14}}{10}\), resulting in \([OH^-] = 1 \times 10^{-15} \) moles/L.
• A low \[OH^-\] concentration alongside a high \[H_{3}O^+\] concentration reinforces the acidity of the solution.

Acidic or Basic Solution

To determine whether a solution is acidic or basic, compare the concentrations of hydronium ions (\(H_{3}O^+\)) and hydroxide ions (\(OH^-\)). The nature of the solution is judged by this comparison:

• If \[H_{3}O^+\] concentration is greater than \[OH^-\], the solution is acidic.
• If \[OH^-\] concentration exceeds \[H_{3}O^+\], the solution is basic.

From the provided example, where \[H_{3}O^+\] concentration is 10 moles/L and \[OH^-\] concentration is \(1 \times 10^{-15}\) moles/L, it's evident that:

• The solution has significantly more hydronium ions than hydroxide ions.
• This results in an acidic solution, confirming the direct impact of these ion concentrations on the nature of the solution.

Thus, understanding these ion concentrations helps classify a solution and predict its behavior in chemical reactions.