Problem 35 - Chemistry: An Atoms-Focused Approach

Question

Calculate the \(\mathrm{pH}\) and \(\mathrm{pOH}\) of solutions with the following \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) or \(\left[\mathrm{OH}^{-}\right]\) values. Indicate which solutions are acidic, basic, or neutral. a. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=5.3 \times 10^{-3} \mathrm{M}\) b. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=3.8 \times 10^{-9} \mathrm{M}\) c. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=7.2 \times 10^{-6} \mathrm{M}\) d. \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-14} \mathrm{M}\)

Step-by-Step Solution

Answer

Question: Determine the nature (acidic, basic, or neutral) of the following solutions and calculate their pH and pOH values: a. A solution with a concentration of H₃O⁺ ions of 5.3 x 10⁻³ M. b. A solution with a concentration of H₃O⁺ ions of 3.8 x 10⁻⁹ M. c. A solution with a concentration of H₃O⁺ ions of 7.2 x 10⁻⁶ M. d. A solution with a concentration of OH⁻ ions of 1.0 x 10⁻¹⁴ M.

Step 1: Calculate the pH

We first need to calculate the pH using the formula: pH = -log\(_{10}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\). pH = -log\(_{10}(5.3 \times 10^{-3}) = 2.28\)

Step 2: Calculate the pOH

Now, we can calculate the pOH using the formula: pOH = 14 - pH. pOH = 14 - 2.28 = 11.72

Step 3: Determine the nature of the solution

The solution is acidic, as its pH is less than 7. b.

Step 4: Calculate the pH

Calculate the pH using the formula: pH = -log\(_{10}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\). pH = -log\(_{10}(3.8 \times 10^{-9}) = 8.42\)

Step 5: Calculate the pOH

Calculate the pOH using the formula: pOH = 14 - pH. pOH = 14 - 8.42 = 5.58

Step 6: Determine the nature of the solution

The solution is basic, as its pH is greater than 7. c.

Step 7: Calculate the pH

Calculate the pH using the formula: pH = -log\(_{10}\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\). pH = -log\(_{10}(7.2 \times 10^{-6}) = 5.14\)

Step 8: Calculate the pOH

Calculate the pOH using the formula: pOH = 14 - pH. pOH = 14 - 5.14 = 8.86

Step 9: Determine the nature of the solution

The solution is acidic, as its pH is less than 7. d.

Step 10: Calculate the pOH

Calculate the pOH using the formula: pOH = -log\(_{10}\left[\mathrm{OH}^{-}\right]\). pOH = -log\(_{10}(1.0 \times 10^{-14}) = 14\)

Step 11: Calculate the pH

Calculate the pH using the formula: pH = 14 - pOH. pH = 14 - 14 = 0

Step 12: Determine the nature of the solution

The solution is acidic, as its pH is less than 7.