Problem 21 - Chemistry

Question

Which of the following conditions indicate a basic solution at \(25^{\circ} \mathrm{C} ?\) a. \(\mathrm{pOH}=11.21\) b. \(\mathrm{pH}=9.42\) c. \(\left[\mathrm{OH}^{-}\right]>\left[\mathrm{H}^{+}\right]\) d. \(\left[\mathrm{OH}^{-}\right]>1.0 \times 10^{-7} M\)

Step-by-Step Solution

Answer

The conditions that indicate a basic solution at 25°C are: b. \(\mathrm{pH}=9.42\), c. \(\left[\mathrm{OH}^{-}\right]>\left[\mathrm{H}^{+}\right]\), and d. \(\left[\mathrm{OH}^{-}\right]>1.0 \times 10^{-7} M\).

Step 1: pH and pOH relationship

At 25°C, the relationship between the pH and pOH of a solution is given by the following equation: \[pH + pOH = 14\]

Step 2: Analyzing option a

The pOH value given in this option is 11.21. We can use the pH and pOH relationship to find its corresponding pH value: \[pH = 14 - 11.21 = 2.79\] Since pH < 7, option a indicates an acidic solution, not a basic one.

Step 3: Analyzing option b

The pH value given in this option is 9.42. Since pH > 7, option b indicates a basic solution.

Step 4: Analyzing option c

This option states that the concentration of hydroxide ions (OH-) is greater than the concentration of hydrogen ions (H+). As mentioned in the analysis, a solution is considered basic when the concentration of its OH- ions is higher than its H+ ions. Therefore, option c indicates a basic solution.

Step 5: Analyzing option d

This option states that the concentration of OH- ions is greater than 1.0 x 10^(-7) M. The ion product constant of water (Kw) at 25°C is given by: \[K_w = [H^+][OH^-] = 1.0 \times 10^{-14}\] Since the concentration of OH- ions is given to be greater than 1.0 x 10^(-7) M, the concentration of H+ ions will be smaller: \[[H^+] < 1.0 \times 10^{-7} M\] As the concentration of OH- ions is higher than the concentration of H+ ions, option d also indicates a basic solution.

Step 6: Conclusion

Out of the given conditions, options b, c, and d indicate a basic solution at 25°C.