Problem 36 - Chemistry: An Atoms-Focused Approach

Question

Calculate the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of the solutions with the following hydronium ion or hydroxide ion concentrations. Indicate which solutions are acidic, basic, or neutral. a. \(\left[\mathrm{OH}^{-}\right]=8.2 \times 10^{-11} \mathrm{M}\) b. \(\left[\mathrm{OH}^{-}\right]=7.7 \times 10^{-6} \mathrm{M}\) c. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.2 \times 10^{-4} \mathrm{M}\) d. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}\)

Step-by-Step Solution

Answer

Question: Classify each solution as acidic, basic, or neutral based on the given ion concentrations. a. \(\left[\mathrm{OH}^{-}\right]=8.2 \times 10^{-11} \mathrm{M}\) b. \(\left[\mathrm{OH}^{-}\right]=7.7 \times 10^{-6} \mathrm{M}\) c. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.2 \times 10^{-4} \mathrm{M}\) d. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}\) Answer: a. \(\mathrm{pH} = 10.09\) - The solution is basic. b. \(\mathrm{pH} = 5.11\) - The solution is acidic. c. \(\mathrm{pH} = 3.49\) - The solution is acidic. d. \(\mathrm{pH} = 7.00\) - The solution is neutral.

Step 1: Find pOH

Find the \(\mathrm{pOH}\) of the solution using the formula \(\mathrm{pOH} = -\log_{10}[\mathrm{OH}^-]\):$$\mathrm{pOH} = -\log_{10}(8.2 \times 10^{-11})$$

Step 2: Find pH

Find the \(\mathrm{pH}\) of the solution using the formula \(\mathrm{pH} + \mathrm{pOH} = 14\):$$\mathrm{pH} = 14 - \mathrm{pOH}$$

Step 3: Classify the solution

Based on the \(\mathrm{pH}\) value, classify the solution as acidic, basic, or neutral. b. \(\left[\mathrm{OH}^{-}\right]=7.7 \times 10^{-6} \mathrm{M}\)

Step 1: Find pOH

Find the \(\mathrm{pOH}\) of the solution using the formula \(\mathrm{pOH} = -\log_{10}[\mathrm{OH}^-]\):$$\mathrm{pOH} = -\log_{10}(7.7 \times 10^{-6})$$

Step 2: Find pH

Find the \(\mathrm{pH}\) of the solution using the formula \(\mathrm{pH} + \mathrm{pOH} = 14\):$$\mathrm{pH} = 14 - \mathrm{pOH}$$

Step 3: Classify the solution

Based on the \(\mathrm{pH}\) value, classify the solution as acidic, basic, or neutral. c. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.2 \times 10^{-4} \mathrm{M}\)

Step 1: Find pH

Find the \(\mathrm{pH}\) of the solution using the formula \(\mathrm{pH} = -\log_{10}[\mathrm{H}_3\mathrm{O}^+]\):$$\mathrm{pH} = -\log_{10}(3.2 \times 10^{-4})$$

Step 2: Find pOH

Find the \(\mathrm{pOH}\) of the solution using the formula \(\mathrm{pH} + \mathrm{pOH} = 14\):$$\mathrm{pOH} = 14 - \mathrm{pH}$$

Step 3: Classify the solution

Based on the \(\mathrm{pH}\) value, classify the solution as acidic, basic, or neutral. d. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}\)

Step 1: Find pH

Find the \(\mathrm{pH}\) of the solution using the formula \(\mathrm{pH} = -\log_{10}[\mathrm{H}_3\mathrm{O}^+]\):$$\mathrm{pH} = -\log_{10}(1.0 \times 10^{-7})$$

Step 2: Find pOH

Find the \(\mathrm{pOH}\) of the solution using the formula \(\mathrm{pH} + \mathrm{pOH} = 14\):$$\mathrm{pOH} = 14 - \mathrm{pH}$$

Step 3: Classify the solution

Based on the \(\mathrm{pH}\) value, classify the solution as acidic, basic, or neutral.

Key Concepts

Acidic solutions

Acidic solutions are characterized by having a higher concentration of hydronium ions (\([H_3O^+]\))in comparison to hydroxide ions (\([OH^-]\)).The pH scale, which ranges from 0 to 14, helps us determine the acidity of a solution.Solutions with a pH less than 7 are considered acidic.To determine the pH of an acidic solution, you use the formula:

• \(\mathrm{pH} = -\log_{10}[H_3O^+]\)

The lower the pH value, the more acidic the solution.For instance, a solution with \([H_3O^+]\) of \( 3.2 \times 10^{-4} \mathrm{M} \) would have a pH of approximately 3.5.This indicates a strong acidic nature since the pH is significantly below 7.In acidic solutions, knowing the pH is crucial, as it affects the overall chemical reactivity and solubility of other substances present in the solution.These solutions often have a sharp, sour taste and are corrosive to metals and skin.It’s vital to handle them with care and proper safety precautions.

Basic solutions

Basic solutions, also known as alkaline solutions, are those in which the concentration of hydroxide ions (\([OH^-]\))is greater than that of hydronium ions (\([H_3O^+]\)).In the pH scale, solutions with a pH greater than 7 are deemed basic.These solutions can be analyzed by calculating the pOH, given by:

• \(\mathrm{pOH} = -\log_{10}[OH^-]\)

Then, find the pH using the relation \(\mathrm{pH} = 14 - \mathrm{pOH}\).For example, a solution with \([OH^-]\) of \( 7.7 \times 10^{-6} \mathrm{M} \) would have a pOH of approximately 5.1, resulting in a pH of 8.9.Basic solutions can feel slippery to touch and are often characterized by a bitter taste.They play significant roles in various industries, from cleaning products to chemical manufacturing.Moreover, they are integral to many biological systems, where maintaining the right pH balance is crucial for life.

Neutral solutions

Neutral solutions have a unique quality where the concentrations of hydronium ions (\([H_3O^+]\))and hydroxide ions (\([OH^-]\))are equal.This equal balance results in a pH of exactly 7, positioning neutral solutions at the midpoint of the pH scale.One classic example is pure water, which at 25°C, maintains both \([H_3O^+]\)and \([OH^-]\) at \( 1.0 \times 10^{-7} \mathrm{M} \).The calculation for such solutions doesn't involve intricate numerics, but understanding this balance is critical.It's the basis for comparing other solutions' acidity or basicity.Neutral solutions are neither acidic nor basic.They don't exhibit the corrosive characteristics typical of acidic solutions, nor the slippery feel of basic solutions.This neutrality makes them ideal as a reference point in scientific research and various industrial applications.They are pivotal in maintaining life, as bodily fluids typically hover near neutral pH to support physiological processes.