A sucrose (non-electrolyte) solution has an osmotic pressure of 1.55 atm at 32°C. If the total volume of the solution is 2.55 Liters, how many moles of sucrose are present?
A sucrose (non-electrolyte) solution has an osmotic pressure of 1.55 atm at 32°C. If the total volume of the solution is 2.55 Liters, how many moles of sucrose are present?
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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![**Problem:**
A sucrose (non-electrolyte) solution has an osmotic pressure of 1.55 atm at 32°C. If the total volume of the solution is 2.55 liters, how many moles of sucrose are present?
**Explanation:**
In this problem, we are given the osmotic pressure, temperature, and volume of a sucrose solution. Our goal is to calculate the number of moles of sucrose present in the solution.
The osmotic pressure (π) can be calculated using the formula:
\[ \pi = iMRT \]
Where:
- \( \pi \) is the osmotic pressure,
- \( i \) is the van 't Hoff factor (for sucrose, a non-electrolyte, \( i = 1 \)),
- \( M \) is the molarity (moles of solute per liter of solution),
- \( R \) is the ideal gas constant (0.0821 L·atm·K⁻¹·mol⁻¹),
- \( T \) is the temperature in Kelvin.
To find the number of moles of sucrose (\( n \)), we'll first need to determine the molarity (\( M \)) of the solution and then use the volume to find \( n \).
1. **Convert Temperature to Kelvin:**
\[ T(K) = T(°C) + 273.15 = 32 + 273.15 = 305.15 K \]
2. **Calculate Molarity (M):**
\[ 1.55 \, \text{atm} = (1) (M) (0.0821 \, \text{L·atm·K⁻¹·mol⁻¹}) (305.15 \, \text{K}) \]
\[ M = \frac{1.55}{0.0821 \times 305.15} \]
\[ M = 0.0618 \, \text{M} \]
3. **Calculate the Number of Moles (n):**
Since molarity \( M \) is moles per liter,
\[ M = \frac{n}{V} \]
\[ n = M \times V \]
\[ n = 0.0618 \, \text{M} \times 2.55 \, \text{L} \]
\[ n = 0.157](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff2609b9a-bccc-4ea0-ab3c-7cfd8cf7907c%2F18812124-d77e-4068-82d0-573884675102%2Fca4ar7f_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:**
A sucrose (non-electrolyte) solution has an osmotic pressure of 1.55 atm at 32°C. If the total volume of the solution is 2.55 liters, how many moles of sucrose are present?
**Explanation:**
In this problem, we are given the osmotic pressure, temperature, and volume of a sucrose solution. Our goal is to calculate the number of moles of sucrose present in the solution.
The osmotic pressure (π) can be calculated using the formula:
\[ \pi = iMRT \]
Where:
- \( \pi \) is the osmotic pressure,
- \( i \) is the van 't Hoff factor (for sucrose, a non-electrolyte, \( i = 1 \)),
- \( M \) is the molarity (moles of solute per liter of solution),
- \( R \) is the ideal gas constant (0.0821 L·atm·K⁻¹·mol⁻¹),
- \( T \) is the temperature in Kelvin.
To find the number of moles of sucrose (\( n \)), we'll first need to determine the molarity (\( M \)) of the solution and then use the volume to find \( n \).
1. **Convert Temperature to Kelvin:**
\[ T(K) = T(°C) + 273.15 = 32 + 273.15 = 305.15 K \]
2. **Calculate Molarity (M):**
\[ 1.55 \, \text{atm} = (1) (M) (0.0821 \, \text{L·atm·K⁻¹·mol⁻¹}) (305.15 \, \text{K}) \]
\[ M = \frac{1.55}{0.0821 \times 305.15} \]
\[ M = 0.0618 \, \text{M} \]
3. **Calculate the Number of Moles (n):**
Since molarity \( M \) is moles per liter,
\[ M = \frac{n}{V} \]
\[ n = M \times V \]
\[ n = 0.0618 \, \text{M} \times 2.55 \, \text{L} \]
\[ n = 0.157
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