### Problem StatementDr. Dahm has a 0.4 M solution of nitrous acid. If he takes 3 mL of this solution and dilutes it to 100 mL, calculate the pH of the new solution. Assume that no dissociation takes place until the new solution is made. The dissociation constant, $ K_a $, for nitrous acid is $ 4.6 \times 10^{-4} $.### Chemical Reaction\[ \text{HNO}_2(aq) + \text{H}_2\text{O}(l) \rightarrow \text{H}_3\text{O}^+(aq) + \text{NO}_2^-(aq) \]### Explanation1. **Dilution Calculation:** - Initial concentration ($ C_i $) = 0.4 M - Initial volume ($ V_i $) = 3 mL - Final volume ($ V_f $) = 100 mL Use the dilution formula: \[ C_f = \frac{C_i \times V_i}{V_f} \] Calculate the new concentration ($ C_f $) after dilution.2. **pH Calculation:** - Use the dissociation constant ($ K_a $) to find the concentration of $ \text{H}_3\text{O}^+ $. - Calculate the pH using: \[ \text{pH} = -\log [\text{H}_3\text{O}^+] \]The task involves using chemical equilibrium concepts to find the pH of the solution after dilution.

we have to calculate the pH of solution

2. Dr. Dahm has a 0.4 M solution of nitrous acid. If he takes 3 mL of this solution and dilutes it to 100 mL calculate the pH of the new solution. (assume that no dissociation takes place until the new solution is made.) Ka = 4.6´ 10-4 HNO₂(aq) + H₂O(1) NO₂ (aq) H,O*(aq) +

2. Dr. Dahm has a 0.4 M solution of nitrous acid. If he takes 3 mL of this solution and dilutes it to 100 mL calculate the pH of the new solution. (assume that no dissociation takes place until the new solution is made.) Ka = 4.6´ 10-4 HNO₂(aq) + H₂O(1) NO₂ (aq) H,O*(aq) +

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

Chapter17: Spontaneity, Entropy, And Free Energy

Section: Chapter Questions

Problem 110CWP

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Concept explainers

Acid Base Titration

An acid-base titration is the method of quantitative analysis for determining the concentration of an acid and base by exactly neutralizing it with a standard solution of base or acid having known concentration.

Question

### Problem Statement

Dr. Dahm has a 0.4 M solution of nitrous acid. If he takes 3 mL of this solution and dilutes it to 100 mL, calculate the pH of the new solution. Assume that no dissociation takes place until the new solution is made. The dissociation constant, $ K_a $, for nitrous acid is $ 4.6 \times 10^{-4} $.

### Chemical Reaction

\[ \text{HNO}_2(aq) + \text{H}_2\text{O}(l) \rightarrow \text{H}_3\text{O}^+(aq) + \text{NO}_2^-(aq) \]

### Explanation

1. **Dilution Calculation:**
- Initial concentration ($ C_i $) = 0.4 M
- Initial volume ($ V_i $) = 3 mL
- Final volume ($ V_f $) = 100 mL

Use the dilution formula:

\[
C_f = \frac{C_i \times V_i}{V_f}
\]

Calculate the new concentration ($ C_f $) after dilution.

2. **pH Calculation:**
- Use the dissociation constant ($ K_a $) to find the concentration of $ \text{H}_3\text{O}^+ $.
- Calculate the pH using:

\[
\text{pH} = -\log [\text{H}_3\text{O}^+]
\]

The task involves using chemical equilibrium concepts to find the pH of the solution after dilution.

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