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How is K_w defined, and what is its numerical value at 25 °C?
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14. Acids and Bases
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Chemistry student prepared an aqueous solution at 30ºC. If the solutions contains 7.42 × 10−9 M of hydroxide ions, calculate the pH.
A
5.703
B
8.130
C
8.300
D
5.980
검증된 단계별 안내1
Identify the given information: the concentration of hydroxide ions, \([\mathrm{OH}^-] = 7.42 \times 10^{-9} \; M\), and the temperature, which is 30ºC.
Recall the relationship between the ion product of water (\(K_w\)), hydroxide ion concentration, and hydrogen ion concentration: \(K_w = [\mathrm{H}^+][\mathrm{OH}^-]\). At 30ºC, find the value of \(K_w\) (note that \(K_w\) changes with temperature and is not \(1.0 \times 10^{-14}\) at 30ºC).
Calculate the hydrogen ion concentration \([\mathrm{H}^+]\) using the formula: \([\mathrm{H}^+] = \frac{K_w}{[\mathrm{OH}^-]}\).
Use the definition of pH to find the pH value: \(\mathrm{pH} = -\log [\mathrm{H}^+]\).
Perform the logarithmic calculation to determine the pH, which will give you the final answer.
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