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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![**Determining the Concentration of \[H_3O^+\] in Water at 40°C**
The ion product constant for water \(K_w\) at 40°C is given by:
\[ K_w = 2.92 \times 10^{-14} \, \text{at} \, 40^\circ \text{C} \]
Given this information, you are asked to find the concentration of hydronium ions ( \[H_3O^+\] ) in water under these conditions.
**Question:**
What is the concentration of \[H_3O^+\] in water at 40°C?
\[ H_3O^+ = [?] \times 10^{[?]} \, \text{M} \]
**Solution:**
To solve this problem, you must understand that \(K_w\) at a given temperature is the product of the concentrations of hydronium ions (\[H_3O^+\]) and hydroxide ions (\[OH^-\]) in pure water. Therefore:
\[ K_w = [H_3O^+][OH^-] \]
For pure water at 40°C:
\[ [H_3O^+] = [OH^-] \]
Since both the hydronium ion and hydroxide ion concentrations are equal, you can express this as:
\[ [H_3O^+]^2 = K_w \]
To find \[H_3O^+\], take the square root of \(K_w\):
\[ [H_3O^+] = \sqrt{K_w} \]
\[ [H_3O^+] = \sqrt{2.92 \times 10^{-14}} \]
Calculate the value to find the concentration of \[H_3O^+\].
**Interactive Input:**
Please enter your answers below,
Coefficient (green): ____
Exponent (yellow): ____
Once you have calculated the correct values, press the "Enter" button. This will help you validate your solution and ensure you understand how to determine the concentration of hydronium ions in water at any given temperature.
Remember, understanding these calculations is crucial for mastering acid-base chemistry and environmental science principles!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44b0d593-f487-4f0d-923f-5b6d8a9e98f3%2F540ad75b-d163-4ce6-b5ea-3e1694e7f99d%2Fuqo4qs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Determining the Concentration of \[H_3O^+\] in Water at 40°C**
The ion product constant for water \(K_w\) at 40°C is given by:
\[ K_w = 2.92 \times 10^{-14} \, \text{at} \, 40^\circ \text{C} \]
Given this information, you are asked to find the concentration of hydronium ions ( \[H_3O^+\] ) in water under these conditions.
**Question:**
What is the concentration of \[H_3O^+\] in water at 40°C?
\[ H_3O^+ = [?] \times 10^{[?]} \, \text{M} \]
**Solution:**
To solve this problem, you must understand that \(K_w\) at a given temperature is the product of the concentrations of hydronium ions (\[H_3O^+\]) and hydroxide ions (\[OH^-\]) in pure water. Therefore:
\[ K_w = [H_3O^+][OH^-] \]
For pure water at 40°C:
\[ [H_3O^+] = [OH^-] \]
Since both the hydronium ion and hydroxide ion concentrations are equal, you can express this as:
\[ [H_3O^+]^2 = K_w \]
To find \[H_3O^+\], take the square root of \(K_w\):
\[ [H_3O^+] = \sqrt{K_w} \]
\[ [H_3O^+] = \sqrt{2.92 \times 10^{-14}} \]
Calculate the value to find the concentration of \[H_3O^+\].
**Interactive Input:**
Please enter your answers below,
Coefficient (green): ____
Exponent (yellow): ____
Once you have calculated the correct values, press the "Enter" button. This will help you validate your solution and ensure you understand how to determine the concentration of hydronium ions in water at any given temperature.
Remember, understanding these calculations is crucial for mastering acid-base chemistry and environmental science principles!
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