A student combined 37.2 mL of 1.69 M KMnO4 solution with 15.50 mL of a 0.891 M KMnO solution. Calculate the concentration of the final solution.
A student combined 37.2 mL of 1.69 M KMnO4 solution with 15.50 mL of a 0.891 M KMnO solution. Calculate the concentration of the final solution.
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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![**Title: Calculation of Final Solution Concentration**
**Problem Statement:**
A student combined 37.2 mL of 1.69 M KMnO₄ solution with 15.50 mL of a 0.891 M KMnO₄ solution. Calculate the concentration of the final solution.
**Solution:**
To solve this problem, we utilize the formula for the dilution and mixing of solutions:
\[ C_{1}V_{1} + C_{2}V_{2} = C_f (V_{1} + V_{2}) \]
Where:
- \( C_{1} \) and \( C_{2} \) are the concentrations of the initial solutions.
- \( V_{1} \) and \( V_{2} \) are the volumes of the initial solutions.
- \( C_f \) is the concentration of the final solution.
- \( V_f \) is the total volume of the final solution, i.e., \( V_{1} + V_{2} \).
Let's input the known values:
- \( C_{1} = 1.69 \) M
- \( V_{1} = 37.2 \) mL
- \( C_{2} = 0.891 \) M
- \( V_{2} = 15.50 \) mL
First, calculate the total volume \( V_f \):
\[ V_f = V_{1} + V_{2} = 37.2 \, \text{mL} + 15.50 \, \text{mL} = 52.7 \, \text{mL} \]
Next, calculate the total moles of KMnO₄:
\[ \text{Total moles} = (C_{1} \times V_{1}) + (C_{2} \times V_{2}) \]
\[ \text{Total moles} = (1.69 \, \text{M} \times 37.2 \, \text{mL}) + (0.891 \, \text{M} \times 15.50 \, \text{mL}) \]
\[ \text{Total moles} = 62.868 \, \text{mmol} + 13.8105 \, \text{mmol} = 76.6785 \, \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc3b72c7-eb99-406f-83fe-82fc41b2a8b5%2F17930649-859c-4062-956e-05b59e214867%2Fb5dmqrz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Calculation of Final Solution Concentration**
**Problem Statement:**
A student combined 37.2 mL of 1.69 M KMnO₄ solution with 15.50 mL of a 0.891 M KMnO₄ solution. Calculate the concentration of the final solution.
**Solution:**
To solve this problem, we utilize the formula for the dilution and mixing of solutions:
\[ C_{1}V_{1} + C_{2}V_{2} = C_f (V_{1} + V_{2}) \]
Where:
- \( C_{1} \) and \( C_{2} \) are the concentrations of the initial solutions.
- \( V_{1} \) and \( V_{2} \) are the volumes of the initial solutions.
- \( C_f \) is the concentration of the final solution.
- \( V_f \) is the total volume of the final solution, i.e., \( V_{1} + V_{2} \).
Let's input the known values:
- \( C_{1} = 1.69 \) M
- \( V_{1} = 37.2 \) mL
- \( C_{2} = 0.891 \) M
- \( V_{2} = 15.50 \) mL
First, calculate the total volume \( V_f \):
\[ V_f = V_{1} + V_{2} = 37.2 \, \text{mL} + 15.50 \, \text{mL} = 52.7 \, \text{mL} \]
Next, calculate the total moles of KMnO₄:
\[ \text{Total moles} = (C_{1} \times V_{1}) + (C_{2} \times V_{2}) \]
\[ \text{Total moles} = (1.69 \, \text{M} \times 37.2 \, \text{mL}) + (0.891 \, \text{M} \times 15.50 \, \text{mL}) \]
\[ \text{Total moles} = 62.868 \, \text{mmol} + 13.8105 \, \text{mmol} = 76.6785 \, \
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