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. \(\left[\mathrm{OH}^{-}\right]>1.0 \times 10^{-7} M\)

Short Answer

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

Step by step solution

01

Recall the pH scale

The pH scale ranges from 0 to 14, where 7 is considered neutral. Values below 7 indicate an acidic solution, while values above 7 indicate a basic (alkaline) solution.
02

Relationship between pH and pOH

At 25°C, we know that: $$ pH + pOH = 14 $$
03

Evaluate Option a

Given pOH = 11.21, we can infer the pH using the relationship: $$ pH= 14 - pOH $$ $$ pH = 14 - 11.21 = 2.79 $$ Since the pH is less than 7, it represents an acidic solution. Therefore, option a is incorrect.
04

Evaluate Option b

Given pH = 9.42, it is clear that the solution is basic as the pH value is greater than 7. Therefore, option b indicates a basic solution.
05

Evaluate Option c

The presence of a higher concentration of hydroxide ions \([\mathrm{OH}^{-}]\) compared to hydrogen ions \([\mathrm{H}^{+}]\) indicates a basic solution. Therefore, option c indicates a basic solution.
06

Evaluate Option d

At 25°C, the neutral concentration of hydroxide ions \([\mathrm{OH}^{-}]\) and hydrogen ions \([\mathrm{H}^{+}]\) is given by: $$[\mathrm{OH}^{-}]=[\mathrm{H}^{+}]=1.0 \times 10^{-7} M$$ If \([\mathrm{OH}^{-}]>1.0 \times 10^{-7} M\), it indicates a basic solution. Therefore, option d also indicates a basic solution.
07

Conclusion

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

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