Question

Make the following conversions. In each case, tell whether the solution is acidic or basic. \(\mathbf{p} \mathbf{H}$$\quad$$\left[\mathbf{H}_{3} \mathbf{O}^{*}\right]\) (a) \(\quad\)______\(\quad 6.7 \times 10^{-10} \mathrm{M}\) (b) \(\quad\)______\(\quad2.2 \times 10^{-6} \mathrm{M}\) (c) 5.25\(\quad\)_____ (d) ______\(\quad2.5 \times 10^{-2} \mathrm{M}\)

Short answer

(a) pH 9.17, basic; (b) pH 5.66, acidic; (c) [H3O+] = 5.62 × 10^-6 M, acidic; (d) pH 1.60, acidic.

Step-by-step solution

Understanding pH and Hydronium Ion Concentration

In chemistry, pH is a measure of the acidity or basicity of an aqueous solution. It is calculated using the formula: \[ \text{pH} = -\log[\text{H}_3\text{O}^+] \]where \([\text{H}_3\text{O}^+]\) is the hydronium ion concentration. A pH less than 7 is acidic, while a pH greater than 7 is basic.

Calculate pH for (a)

For (a), given the hydronium ion concentration \([\text{H}_3\text{O}^+] = 6.7 \times 10^{-10} \text{M}\), calculate the pH:\[\text{pH} = -\log(6.7 \times 10^{-10}) = 9.17\]Since the pH is greater than 7, the solution is basic.

Calculate pH for (b)

For (b), given the hydronium ion concentration \([\text{H}_3\text{O}^+] = 2.2 \times 10^{-6} \text{M}\), calculate the pH:\[\text{pH} = -\log(2.2 \times 10^{-6}) = 5.66\]Since the pH is less than 7, the solution is acidic.

Calculate Hydronium Ion Concentration for (c)

For (c), given \(\text{pH} = 5.25\), calculate \([\text{H}_3\text{O}^+]\):\[[\text{H}_3\text{O}^+] = 10^{-5.25} = 5.62 \times 10^{-6} \text{M}\]Since the pH is less than 7, the solution is acidic.

Calculate pH for (d)

For (d), given the hydronium ion concentration \([\text{H}_3\text{O}^+] = 2.5 \times 10^{-2} \text{M}\), calculate the pH:\[\text{pH} = -\log(2.5 \times 10^{-2}) = 1.60\]Since the pH is less than 7, the solution is acidic.

Key concepts

Acid-Base Chemistry

Understanding whether a solution is acidic or basic is central to acid-base chemistry. At the heart of this concept is the pH scale, which is a numeric scale used to specify the acidity or basicity of an aqueous solution.
A pH value is a simple way to measure the activity of hydrogen ions in a solution. If a solution has a pH less than 7, it is acidic, meaning it has more hydrogen ions ( [H^+ ]) than hydroxide ions ( [OH^- ]). Conversely, a pH greater than 7 indicates a basic solution, where hydroxide ions outnumber hydrogen ions.

• An acidic solution has a higher concentration of hydronium ions (H₃O⁺).
• A basic solution has a lower concentration of hydronium ions compared to pure water.
• Neutral solutions, like pure water, have a pH of 7.

This concept is fundamental in chemical reactions, biological systems, and industrial processes, as it influences how substances interact and behave.

Hydronium Ion Concentration

The concentration of hydronium ions ([H_3O^+]) in a solution directly influences its acidity or basicity. The hydronium ion is a water molecule with an extra hydrogen ion, commonly formed when an acid is dissolved in water.
Hydronium ion concentration can be derived from or used to calculate pH values, establishing a clear relationship between them. For example, using the formula:\[ [\text{H}_3\text{O}^+] = 10^{-\text{pH}} \]
This formula shows how to reverse the pH calculation to find [H_3O^+] from a known pH value.

• Higher concentrations of hydronium ions result in a lower pH, meaning the solution is more acidic.
• Lower hydronium ion concentrations increase the pH, indicating a more basic solution.
• This concentration is crucial in explaining why different solutions have different pH values.

Understanding hydronium ion concentration helps students link the molecular world to observable properties, like acidity.

Logarithmic Function in Chemistry

In chemistry, the logarithmic function plays a crucial role in simplifying calculations related to acidity and basicity. The pH scale is logarithmic, meaning each whole number change in pH represents a tenfold change in hydronium ion concentration.
This can be expressed mathematically as:\[ \text{pH} = -\log[\text{H}_3\text{O}^+] \]
This formula shows that when the hydronium concentration changes by a factor of ten, the pH changes by 1. The negative sign in the function is essential because it converts smaller, more positive concentrations into larger, manageable pH numbers.

• This property makes the logarithmic function valuable as it compresses a vast range of hydrogen ion activities into a convenient scale.
• This function aids in understanding non-linear relationships in chemistry.
• The use of a base-10 logarithm is practical for simplifying the multiplicative relationship between ion concentrations and their observed pH values.

Grasping the use of logarithms helps students better understand how dramatically small changes in ion concentration can affect pH and consequently the behavior of the solution.