Question

Which of the following conditions indicate an acidic solution at \(25^{\circ} \mathrm{C} ?\) a. \(\mathrm{pH}=3.04\) b. \(\left[\mathrm{H}^{+}\right]>1.0 \times 10^{-7} \mathrm{M}\) c. \(\mathrm{pOH}=4.51\) d. \(\left[\mathrm{OH}^{-}\right]=3.21 \times 10^{-12} \mathrm{M}\)

Short answer

Conditions (a), (b), and (d) indicate an acidic solution at \(25^{\circ} \mathrm{C}\). Condition (a) has pH = 3.04 which is less than 7. Condition (b) has [\(\mathrm{H}^{+}\)] > \(1.0 \times 10^{-7} \mathrm{M}\), higher than pure water. Condition (d) has [\(\mathrm{OH}^{-}\)] = \(3.21 \times 10^{-12} \mathrm{M}\), lesser than the concentration in pure water, indicating a higher concentration of \(\mathrm{H}^{+}\) ions.

Step-by-step solution

Analyzing the first condition (pH = 3.04)

As an acidic solution has a pH less than 7, we can see that the given pH = 3.04 is lesser than 7, which indicates an acidic solution. So, condition (a) is true.

Analyzing the second condition ([\(\mathrm{H}^{+}\)] > \(1.0 \times 10^{-7} \mathrm{M}\))

In pure water at \(25^{\circ}\mathrm{C}\), the concentration of \(\mathrm{H}^{+}\) ions is \(1.0 \times 10^{-7} \mathrm{M}\). Since an acidic solution has a higher concentration of \(\mathrm{H}^{+}\) ions than pure water, this condition indicates an acidic solution. So, condition (b) is true.

Analyzing the third condition (pOH = 4.51)

An acidic solution is characterized by a pOH greater than 7. The given pOH = 4.51, which is less than 7. This condition does not indicate an acidic solution. So, condition (c) is false.

Analyzing the fourth condition ([\(\mathrm{OH}^{-}\)] = \(3.21 \times 10^{-12} \mathrm{M}\))

An acidic solution is characterized by a higher concentration of \(\mathrm{H}^{+}\) ions than \(\mathrm{OH}^{-}\) ions. In pure water at \(25^{\circ}\mathrm{C}\), the concentration of \(\mathrm{OH}^{-}\) ions is also \(1.0 \times 10^{-7} \mathrm{M}\). Since the given \(\mathrm{OH}^{-}\) concentration is \(3.21 \times 10^{-12} \mathrm{M}\) which is lesser than the concentration in pure water, this condition indicates an acidic solution as the concentration of \(\mathrm{H}^{+}\) ions must be higher. So, condition (d) is true. Answer: Conditions (a), (b), and (d) indicate an acidic solution at \(25^{\circ}\mathrm{C}.\)

Key concepts

pH level

The pH scale measures how acidic or basic a solution is. It ranges from 0 to 14, where 7 is neutral, below 7 is acidic, and above 7 is basic. The pH value is calculated using the formula: \[ \text{pH} = -\log [\text{H}^+] \] This equation shows that pH is inversely related to the concentration of hydrogen ions. When the concentration of hydrogen ions increases, the pH level decreases, indicating an acidic solution.

• A pH less than 7 means the solution is acidic.
• A pH of 7 is neutral, like pure water.
• A pH greater than 7 denotes a basic (alkaline) solution.

In the exercise, a pH of 3.04 is clearly less than 7, confirming that the solution is acidic.

hydrogen ion concentration

Hydrogen ion concentration refers to the amount of \(\text{H}^{+}\) ions present in a solution. It's a crucial determinant of a solution's acidity. Pure water at 25°C has a \(\text{H}^{+}\) concentration of \(1.0 \times 10^{-7} \text{M}\).

• If the \(\text{H}^{+}\) concentration is greater than \(1.0 \times 10^{-7} \text{M}\), the solution is acidic.
• If it equals \(1.0 \times 10^{-7} \text{M}\), the solution is neutral.
• Less than \(1.0 \times 10^{-7} \text{M}\) indicates a basic solution.

In our exercise, the condition \([\text{H}^{+}] > 1.0 \times 10^{-7} \text{M}\) confirms that the solution is acidic, as it has more hydrogen ions compared to neutral water.

pOH value

The pOH value is similar to the pH but it indicates the alkalinity of a solution. It is calculated using the concentration of hydroxide ions, \([\text{OH}^-]\): \[ \text{pOH} = -\log [\text{OH}^-] \] The pH and pOH are related by the equation: \[ \text{pH} + \text{pOH} = 14 \] When dealing with acidic solutions, it’s important to remember:

• Acidic solutions typically have a pOH value greater than 7.
• The provided condition \(\text{pOH} = 4.51\) does not suggest acidity because it is less than 7.

hydroxide ion concentration

Hydroxide ion concentration \([\text{OH}^-]\) refers to the amount of hydroxide ions present in a solution. It is an indicator of basicity, as higher \([\text{OH}^-]\) ions would usually mean a more basic solution. In pure water at 25°C, \([\text{OH}^-]\) is \(1.0 \times 10^{-7} \text{M}\).

• If \([\text{OH}^-]\) is less than \(1.0 \times 10^{-7} \text{M}\), the solution is likely acidic.
• If \([\text{OH}^-]\) equals \(1.0 \times 10^{-7} \text{M}\), the solution is neutral.
• Greater than \(1.0 \times 10^{-7} \text{M}\) implies a basic solution.

The exercise showed \([\text{OH}^-] = 3.21 \times 10^{-12} \text{M}\), which is substantially less than neutral water, thus confirming the solution’s acidic nature.