13) Your lungs hold 4.2 L of air at a temperature of 27°C and a pressure of 101.3 kPa. How many moles of air do your lungs hold? (R = 8.31 J/mol. K) A) 0.19 moles B) 0.15 moles C) 0.23 moles D) 0.17 moles E) 0.21 moles
13) Your lungs hold 4.2 L of air at a temperature of 27°C and a pressure of 101.3 kPa. How many moles of air do your lungs hold? (R = 8.31 J/mol. K) A) 0.19 moles B) 0.15 moles C) 0.23 moles D) 0.17 moles E) 0.21 moles
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Chapter1: Units, Trigonometry. And Vectors
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![**Question 13: Calculating Moles of Air in the Lungs**
**Problem Statement:**
Your lungs hold 4.2 L of air at a temperature of 27°C and a pressure of 101.3 kPa. How many moles of air do your lungs hold? (R = 8.31 J/mol·K)
**Options:**
A) 0.19 moles
B) 0.15 moles
C) 0.23 moles
D) 0.17 moles
E) 0.21 moles
### Explanation:
To solve this problem, we use the Ideal Gas Law equation:
\[ PV = nRT \]
where:
- \( P \) = pressure (in kPa)
- \( V \) = volume (in liters)
- \( n \) = number of moles (what we need to find)
- \( R \) = ideal gas constant (8.31 J/mol·K)
- \( T \) = temperature (in Kelvin, K)
**Step-by-Step Solution:**
1. **Convert Temperature to Kelvin:**
\[ T(K) = 27°C + 273 = 300K \]
2. **Rearrange the Ideal Gas Law Equation to Solve for \( n \):**
\[ n = \frac{PV}{RT} \]
3. **Plug the Given Values into the Equation:**
\[ P = 101.3 kPa \]
\[ V = 4.2 L \]
\[ T = 300 K \]
\[ R = 8.31 J/mol·K \]
4. **Calculate using the Ideal Gas Law:**
\[
n = \frac{(101.3 \, \text{kPa}) (4.2 \, \text{L})}{(8.31 \, \frac{J}{\text{mol} \cdot K})(300 \, \text{K})}
\]
To ensure the units are consistent for R, we may need to convert kPa to Pa (1 kPa = 1000 Pa):
\[
n = \frac{(101300 \, \text{Pa}) (4.2 \, \text{L})}{(8.31 \, \frac{J}{\text{mol}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3997526e-7cda-40d8-9b92-5ffe558ca7d8%2F2da29593-d625-43dc-a74a-8b56d88cd102%2Fe9ui76n_processed.png&w=3840&q=75)
Transcribed Image Text:**Question 13: Calculating Moles of Air in the Lungs**
**Problem Statement:**
Your lungs hold 4.2 L of air at a temperature of 27°C and a pressure of 101.3 kPa. How many moles of air do your lungs hold? (R = 8.31 J/mol·K)
**Options:**
A) 0.19 moles
B) 0.15 moles
C) 0.23 moles
D) 0.17 moles
E) 0.21 moles
### Explanation:
To solve this problem, we use the Ideal Gas Law equation:
\[ PV = nRT \]
where:
- \( P \) = pressure (in kPa)
- \( V \) = volume (in liters)
- \( n \) = number of moles (what we need to find)
- \( R \) = ideal gas constant (8.31 J/mol·K)
- \( T \) = temperature (in Kelvin, K)
**Step-by-Step Solution:**
1. **Convert Temperature to Kelvin:**
\[ T(K) = 27°C + 273 = 300K \]
2. **Rearrange the Ideal Gas Law Equation to Solve for \( n \):**
\[ n = \frac{PV}{RT} \]
3. **Plug the Given Values into the Equation:**
\[ P = 101.3 kPa \]
\[ V = 4.2 L \]
\[ T = 300 K \]
\[ R = 8.31 J/mol·K \]
4. **Calculate using the Ideal Gas Law:**
\[
n = \frac{(101.3 \, \text{kPa}) (4.2 \, \text{L})}{(8.31 \, \frac{J}{\text{mol} \cdot K})(300 \, \text{K})}
\]
To ensure the units are consistent for R, we may need to convert kPa to Pa (1 kPa = 1000 Pa):
\[
n = \frac{(101300 \, \text{Pa}) (4.2 \, \text{L})}{(8.31 \, \frac{J}{\text{mol}
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