Question

Indicate whether each of the following is acidic, basic, or neutral: a. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=2.0 \times 10^{-5} \mathrm{M}\) b. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.4 \times 10^{-9} \mathrm{M}\) c. \(\left[\mathrm{OH}^{-}\right]=8.0 \times 10^{-3} \mathrm{M}\) d. \(\left[\mathrm{OH}^{-}\right]=3.5 \times 10^{-10} \mathrm{M}\)

Short answer

a) Acidic b) Basic c) Basic d) Acidic

Step-by-step solution

Determine pH from \(\text{[H}_3\text{O}^+]\) for part a

Use the formula \(\text{pH} = -\text{log}[\text{H}_3\text{O}^+]\) to find the pH. For \(\text{[H}_3\text{O}^+] = 2.0 \times 10^{-5} \text{M}\), \(\text{pH} = -\text{log}(2.0 \times 10^{-5}) \approx 4.7\). Since pH < 7, the solution is acidic.

Determine pH from \(\text{[H}_3\text{O}^+]\) for part b

Again, use the formula \(\text{pH} = -\text{log}[\text{H}_3\text{O}^+]\). For \(\text{[H}_3\text{O}^+] = 1.4 \times 10^{-9} \text{M}\), \(\text{pH} = -\text{log}(1.4 \times 10^{-9}) \approx 8.85\). Since pH > 7, the solution is basic.

Determine pOH from \(\text{[OH}^-]\) for part c

Use the formula \(\text{pOH} = -\text{log}[\text{OH}^-]\). For \(\text{[OH}^-] = 8.0 \times 10^{-3} \text{M}\), \(\text{pOH} = -\text{log}(8.0 \times 10^{-3}) \approx 2.1\). Since \(\text{pOH} < 7\), the solution is basic.

Determine pOH from \(\text{[OH}^-]\) for part d

Use the formula \(\text{pOH} = -\text{log}[\text{OH}^-]\). For \(\text{[OH}^-] = 3.5 \times 10^{-10} \text{M}\), \(\text{pOH} = -\text{log}(3.5 \times 10^{-10}) \approx 9.46\). Since \(\text{pOH} > 7\), the solution is acidic.

Key concepts

acidic and basic solutions

To determine if a solution is acidic or basic, you need to understand the pH scale. The pH scale ranges from 0 to 14 and indicates how acidic or basic a solution is. A pH value:

• Below 7 means the solution is acidic.
• Above 7 means the solution is basic.
• Exact 7 means the solution is neutral.

Acidity comes from the presence of hydronium ions (H₃O⁺), while basicity comes from the presence of hydroxide ions (OH^-). By calculating pH or pOH, you can determine a solution's acidity or basicity.

pH formula

The pH formula is central to understanding a solution's acidity. To calculate pH, use the formula: \( \text{pH} = -\log[\text{H}_3\text{O}^+] \)This formula tells you that pH is the negative logarithm of the hydronium ion concentration, [H₃O⁺]. For example:

• If [H₃O⁺] = 2.0 × 10^-5 M, then \( \text{pH} = -\log(2.0 \times 10^{-5}) \approx 4.7 \), indicating an acidic solution.
• If [H₃O⁺] = 1.4 × 10^-9 M, then \( \text{pH} = -\log(1.4 \times 10^{-9}) \approx 8.85 \), indicating a basic solution.

The value you get from this formula helps you quickly determine if the solution is acidic or basic.

pOH formula

The pOH formula allows you to understand the basicity of a solution. To find pOH, use the formula: \( \text{pOH} = -\log[\text{OH}^-] \)Just like with pH, pOH is the negative logarithm of the hydroxide ion concentration, [OH^-]. For example:

• If [OH^-] = 8.0 × 10^-3 M, then \( \text{pOH} = -\log(8.0 \times 10^{-3}) \approx 2.1 \), showing the solution is basic.
• If [OH^-] = 3.5 × 10^-10 M, then \( \text{pOH} = -\log(3.5 \times 10^{-10}) \approx 9.46 \), indicating an acidic solution due to pOH being greater than 7.

Remember, the pH and pOH together always sum to 14 in pure water.

hydronium ion concentration

Hydronium ion concentration, written as [H₃O⁺], measures the amount of hydronium ions present in a solution. This concentration directly affects the pH of the solution. The more hydronium ions, the lower the pH:

• High [H₃O⁺] = low pH (acidic solution)
• Low [H₃O⁺] = high pH (basic solution)

Use \( [\text{H}_3\text{O}^+] \) in the pH formula to find pH values and determine the acidity of the solution. For instance, solving for [H₃O⁺]:
[list value] = 2.0 × 10^-5 M gives pH 4.7, meaning the solution is acidic.

hydroxide ion concentration

Hydroxide ion concentration, written as [OH^-], measures the amount of hydroxide ions in a solution. This directly influences the pOH of the solution. More hydroxide ions result in lower pOH values:

• High [OH^-] = low pOH (basic solution)
• Low [OH^-] = high pOH (acidic solution)

To convert between pH and pOH, remember that their sum is always 14 in pure water. For example, solving for [OH^-]:
[list value] = 8.0 × 10^-3 M, results in pOH 2.1, indicating that the solution is basic.