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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![**Osmotic Pressure Calculation**
*Problem Statement:*
What will be the osmotic pressure exerted by an aqueous solution of 500 mL volume at 25°C if it contains 12.54 g of dissolved magnesium chloride?
*Explanation:*
To solve this problem, we'll need to use the formula for osmotic pressure:
\[ \pi = iMRT \]
where:
- \( \pi \) is the osmotic pressure,
- \( i \) is the van’t Hoff factor,
- \( M \) is the molarity of the solution,
- \( R \) is the ideal gas constant (0.0821 L·atm/mol·K),
- \( T \) is the temperature in Kelvin.
**Steps to solve:**
1. **Determine the molarity (\( M \)) of the solution:**
- Calculate the moles of magnesium chloride (MgCl\(_2\)). The molar mass of MgCl\(_2\) is approximately 95.21 g/mol.
- Convert the mass of MgCl\(_2\) to moles:
\[ \text{moles of MgCl}_2 = \frac{12.54 \, \text{g}}{95.21 \, \text{g/mol}} \]
- Convert the volume from mL to L:
\[ 500 \, \text{mL} = 0.500 \, \text{L} \]
- Molarity \( M \) = \(\frac{\text{moles of solute}}{\text{volume of solution in L}}\).
2. **Identify the van't Hoff factor (\( i \)) for MgCl\(_2\):**
- MgCl\(_2\) dissociates into three ions: \( \text{Mg}^{2+} \) and \( 2 \, \text{Cl}^- \), so \( i = 3 \).
3. **Calculate the osmotic pressure using the formula:**
- Convert the temperature to Kelvin: \( T = 25°C + 273.15 \).
- Substitute the values into the osmotic pressure formula to find \( \pi \).
Use this framework to perform the calculations and arrive at the final osmotic pressure.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d2b8eef-4fbe-4a55-b286-a596fe8c553e%2Fef692a4a-fdf0-4bc6-ba1a-825d257232a6%2F0pids7_processed.png&w=3840&q=75)
Transcribed Image Text:**Osmotic Pressure Calculation**
*Problem Statement:*
What will be the osmotic pressure exerted by an aqueous solution of 500 mL volume at 25°C if it contains 12.54 g of dissolved magnesium chloride?
*Explanation:*
To solve this problem, we'll need to use the formula for osmotic pressure:
\[ \pi = iMRT \]
where:
- \( \pi \) is the osmotic pressure,
- \( i \) is the van’t Hoff factor,
- \( M \) is the molarity of the solution,
- \( R \) is the ideal gas constant (0.0821 L·atm/mol·K),
- \( T \) is the temperature in Kelvin.
**Steps to solve:**
1. **Determine the molarity (\( M \)) of the solution:**
- Calculate the moles of magnesium chloride (MgCl\(_2\)). The molar mass of MgCl\(_2\) is approximately 95.21 g/mol.
- Convert the mass of MgCl\(_2\) to moles:
\[ \text{moles of MgCl}_2 = \frac{12.54 \, \text{g}}{95.21 \, \text{g/mol}} \]
- Convert the volume from mL to L:
\[ 500 \, \text{mL} = 0.500 \, \text{L} \]
- Molarity \( M \) = \(\frac{\text{moles of solute}}{\text{volume of solution in L}}\).
2. **Identify the van't Hoff factor (\( i \)) for MgCl\(_2\):**
- MgCl\(_2\) dissociates into three ions: \( \text{Mg}^{2+} \) and \( 2 \, \text{Cl}^- \), so \( i = 3 \).
3. **Calculate the osmotic pressure using the formula:**
- Convert the temperature to Kelvin: \( T = 25°C + 273.15 \).
- Substitute the values into the osmotic pressure formula to find \( \pi \).
Use this framework to perform the calculations and arrive at the final osmotic pressure.
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