Nitrox is a gas mixture containing additional oxygen, often used in scuba diving. A particular nitrox mixture of O2 and N2 contains 32.2% oxygen by mass. What is the partial pressure of N2 in the mixture, if the total pressure is 1520 mm Hg? PN₂ = [?] atm Pressure N, (mm Hg) Enter
Nitrox is a gas mixture containing additional oxygen, often used in scuba diving. A particular nitrox mixture of O2 and N2 contains 32.2% oxygen by mass. What is the partial pressure of N2 in the mixture, if the total pressure is 1520 mm Hg? PN₂ = [?] atm Pressure N, (mm Hg) Enter
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
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![### Understanding Partial Pressure in Gas Mixtures
**Question:**
Nitrox is a gas mixture containing additional oxygen, often used in scuba diving. A particular nitrox mixture of O₂ and N₂ contains 32.2% oxygen by mass.
**Problem Statement:**
What is the partial pressure of N₂ in the mixture, if the total pressure is 1520 mm Hg?
\[ P_{\text{N}_2} = [?] \text{ atm} \]
**Input Field:**
- **Label:** Pressure N₂ (mm Hg)
- **Input Box**
- **Submit Button:** Enter
**Explanation:**
To find the partial pressure of N₂, we can use Dalton's Law of Partial Pressures which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture. The partial pressure of each gas can be found using its mole fraction in the mixture.
Given:
- The total pressure (P_total) = 1520 mm Hg
- The percentage of O₂ by mass = 32.2%
Steps to solve:
1. Convert the percentage of oxygen to a fraction:
\[ \text{Fraction of O}_2 = \frac{32.2}{100} = 0.322 \]
2. Calculate the partial pressure of O₂ using the fraction:
\[ P_{\text{O}_2} = \text{Fraction of O}_2 \times P_{\text{total}} \]
\[ P_{\text{O}_2} = 0.322 \times 1520 \, \text{mm Hg} \]
\[ P_{\text{O}_2} = 489.44 \, \text{mm Hg} \]
3. Calculate the partial pressure of N₂ (P_N₂) by subtracting the partial pressure of O₂ from the total pressure:
\[ P_{\text{N}_2} = P_{\text{total}} - P_{\text{O}_2} \]
\[ P_{\text{N}_2} = 1520 \, \text{mm Hg} - 489.44 \, \text{mm Hg} \]
\[ P_{\text{N}_2} \approx 1030.56 \, \text{mm Hg} \]
4. Convert the partial pressure of N₂ to atm (1 atm = 760 mm Hg):
\[ P_{\text{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3a6c8a3a-a03f-49e8-8199-eeea6dc66d27%2F2851ec65-03f9-4ef6-8f8b-3f83030fb60f%2Fnrvygde_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Partial Pressure in Gas Mixtures
**Question:**
Nitrox is a gas mixture containing additional oxygen, often used in scuba diving. A particular nitrox mixture of O₂ and N₂ contains 32.2% oxygen by mass.
**Problem Statement:**
What is the partial pressure of N₂ in the mixture, if the total pressure is 1520 mm Hg?
\[ P_{\text{N}_2} = [?] \text{ atm} \]
**Input Field:**
- **Label:** Pressure N₂ (mm Hg)
- **Input Box**
- **Submit Button:** Enter
**Explanation:**
To find the partial pressure of N₂, we can use Dalton's Law of Partial Pressures which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture. The partial pressure of each gas can be found using its mole fraction in the mixture.
Given:
- The total pressure (P_total) = 1520 mm Hg
- The percentage of O₂ by mass = 32.2%
Steps to solve:
1. Convert the percentage of oxygen to a fraction:
\[ \text{Fraction of O}_2 = \frac{32.2}{100} = 0.322 \]
2. Calculate the partial pressure of O₂ using the fraction:
\[ P_{\text{O}_2} = \text{Fraction of O}_2 \times P_{\text{total}} \]
\[ P_{\text{O}_2} = 0.322 \times 1520 \, \text{mm Hg} \]
\[ P_{\text{O}_2} = 489.44 \, \text{mm Hg} \]
3. Calculate the partial pressure of N₂ (P_N₂) by subtracting the partial pressure of O₂ from the total pressure:
\[ P_{\text{N}_2} = P_{\text{total}} - P_{\text{O}_2} \]
\[ P_{\text{N}_2} = 1520 \, \text{mm Hg} - 489.44 \, \text{mm Hg} \]
\[ P_{\text{N}_2} \approx 1030.56 \, \text{mm Hg} \]
4. Convert the partial pressure of N₂ to atm (1 atm = 760 mm Hg):
\[ P_{\text{
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