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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![### Calculating Osmotic Pressure of a Solution
#### Question 8 of 8:
**Question:**
What is the osmotic pressure, in atm, of a 0.285 M solution of MgCl₂ at 37.0 °C in atm? (Assume complete dissociation).
**Solution:**
To calculate the osmotic pressure (π), we use the formula:
\[
\pi = iMRT
\]
where:
- \( i \) is the van 't Hoff factor,
- \( M \) is the molarity of the solution,
- \( R \) is the ideal gas constant (\(0.0821 \, \text{L·atm·mol}^{-1}\text{K}^{-1}\)),
- \( T \) is the temperature in Kelvin.
Given data:
- Molarity (M): \( 0.285 \, \text{M} \)
- Temperature (T): \( 37.0 \, \text{°C} \)
First, convert the temperature to Kelvin:
\[
T = 37.0 + 273.15 = 310.15 \, \text{K}
\]
Magnesium chloride (MgCl₂) dissociates completely into one Mg²⁺ ion and two Cl⁻ ions. Thus, \( i \) = 3.
Plugging in the values:
\[
\pi = 3 \times 0.285 \, \text{M} \times 0.0821 \, \text{L·atm·mol}^{-1}\text{K}^{-1} \times 310.15 \, \text{K}
\]
Perform the multiplication:
\[
\pi = 3 \times 0.285 \times 0.0821 \times 310.15
\]
\[
\pi ≈ 21.7261 \, \text{atm}
\]
So, the osmotic pressure of the 0.285 M MgCl₂ solution at 37.0 °C is approximately 21.73 atm.
**Graph/Diagram Explanation:**
The image does not contain any graphs or diagrams. It depicts a numerical keypad allowing input of the answer in atmospheric pressure (atm). The interface suggests a user interaction with a field labeled "atm," likely to input the solution to the problem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d924445-39e4-4bb2-9286-0ab6470dbf21%2F6939ca25-a726-4a72-9ac8-ad1927f63821%2Fqo0rysl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating Osmotic Pressure of a Solution
#### Question 8 of 8:
**Question:**
What is the osmotic pressure, in atm, of a 0.285 M solution of MgCl₂ at 37.0 °C in atm? (Assume complete dissociation).
**Solution:**
To calculate the osmotic pressure (π), we use the formula:
\[
\pi = iMRT
\]
where:
- \( i \) is the van 't Hoff factor,
- \( M \) is the molarity of the solution,
- \( R \) is the ideal gas constant (\(0.0821 \, \text{L·atm·mol}^{-1}\text{K}^{-1}\)),
- \( T \) is the temperature in Kelvin.
Given data:
- Molarity (M): \( 0.285 \, \text{M} \)
- Temperature (T): \( 37.0 \, \text{°C} \)
First, convert the temperature to Kelvin:
\[
T = 37.0 + 273.15 = 310.15 \, \text{K}
\]
Magnesium chloride (MgCl₂) dissociates completely into one Mg²⁺ ion and two Cl⁻ ions. Thus, \( i \) = 3.
Plugging in the values:
\[
\pi = 3 \times 0.285 \, \text{M} \times 0.0821 \, \text{L·atm·mol}^{-1}\text{K}^{-1} \times 310.15 \, \text{K}
\]
Perform the multiplication:
\[
\pi = 3 \times 0.285 \times 0.0821 \times 310.15
\]
\[
\pi ≈ 21.7261 \, \text{atm}
\]
So, the osmotic pressure of the 0.285 M MgCl₂ solution at 37.0 °C is approximately 21.73 atm.
**Graph/Diagram Explanation:**
The image does not contain any graphs or diagrams. It depicts a numerical keypad allowing input of the answer in atmospheric pressure (atm). The interface suggests a user interaction with a field labeled "atm," likely to input the solution to the problem.
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