Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![### Calculating Hydroxide Ion Concentration from Hydrogen Ion Concentration
To find the hydroxide ion concentration \([OH^-]\) when given the hydrogen ion concentration \([H^+]\), we use the relationship defined by the ion-product constant for water (\(K_w\)). The expression is:
\[ K_w = [H^+][OH^-] \]
At 25°C (298 K), the value of \(K_w\) is \(1.0 \times 10^{-14}\).
Given:
\[ [H^+] = 2.5 \times 10^{-6} \]
We need to find \([OH^-]\). Rearrange the formula to solve for \([OH^-]\):
\[ [OH^-] = \frac{K_w}{[H^+]} \]
Substituting the values:
\[ [OH^-] = \frac{1.0 \times 10^{-14}}{2.5 \times 10^{-6}} \]
To perform the division:
\[ [OH^-] = 4.0 \times 10^{-9} \]
So, the hydroxide ion concentration \([OH^-]\) is:
\[ [OH^-] = 4.0 \times 10^{-9} \]
This means that for a hydrogen ion concentration of \(2.5 \times 10^{-6}\), the corresponding hydroxide ion concentration is \(4.0 \times 10^{-9}\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F11cb493f-74d8-445b-bfd0-ead085c73a2d%2Fdf3ffc83-3147-473c-b30f-0b8f91f703ef%2Flu6jbz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating Hydroxide Ion Concentration from Hydrogen Ion Concentration
To find the hydroxide ion concentration \([OH^-]\) when given the hydrogen ion concentration \([H^+]\), we use the relationship defined by the ion-product constant for water (\(K_w\)). The expression is:
\[ K_w = [H^+][OH^-] \]
At 25°C (298 K), the value of \(K_w\) is \(1.0 \times 10^{-14}\).
Given:
\[ [H^+] = 2.5 \times 10^{-6} \]
We need to find \([OH^-]\). Rearrange the formula to solve for \([OH^-]\):
\[ [OH^-] = \frac{K_w}{[H^+]} \]
Substituting the values:
\[ [OH^-] = \frac{1.0 \times 10^{-14}}{2.5 \times 10^{-6}} \]
To perform the division:
\[ [OH^-] = 4.0 \times 10^{-9} \]
So, the hydroxide ion concentration \([OH^-]\) is:
\[ [OH^-] = 4.0 \times 10^{-9} \]
This means that for a hydrogen ion concentration of \(2.5 \times 10^{-6}\), the corresponding hydroxide ion concentration is \(4.0 \times 10^{-9}\).
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