To determine the number of moles of oxygen in the lung at maximum capacity, we can use the Ideal Gas Law equation:
[tex]\[ PV = nRT \][/tex]
where:
- [tex]\( P \)[/tex] is the pressure,
- [tex]\( V \)[/tex] is the volume,
- [tex]\( n \)[/tex] is the number of moles,
- [tex]\( R \)[/tex] is the ideal gas constant,
- [tex]\( T \)[/tex] is the temperature in Kelvin.
Here's how we can find the number of moles step-by-step:
1. Identify the given values:
- Volume ([tex]\( V \)[/tex]) = 3.0 liters
- Pressure ([tex]\( P \)[/tex]) = 21.1 kilopascals
- Temperature ([tex]\( T \)[/tex]) = 295 Kelvin
- Ideal gas constant ([tex]\( R \)[/tex]) = 8.314 L·kPa/(mol·K)
2. Rearrange the Ideal Gas Law to solve for [tex]\( n \)[/tex] (the number of moles):
[tex]\[ n = \frac{PV}{RT} \][/tex]
3. Substitute the given values into the equation:
[tex]\[ n = \frac{(21.1 \text{ kPa}) \times (3.0 \text{ L})}{(8.314 \text{ L·kPa/(mol·K)}) \times (295 \text{ K})} \][/tex]
4. Perform the calculation:
[tex]\[ n = \frac{63.3 \text{ kPa·L}}{2459.13 \text{ L·kPa/(mol·K)}} \][/tex]
5. Simplify the fraction to find the number of moles [tex]\( n \)[/tex]:
[tex]\[ n = 0.02580902949079152 \text{ mol} \][/tex]
6. Rounding the answer to an appropriate number of significant figures:
Given that the initial values (3.0, 21.1, and 295) have three significant figures, the result should be rounded to three significant figures as well:
[tex]\[ n \approx 0.026 \text{ mol} \][/tex]
So, the number of moles of oxygen in the lung at maximum capacity is closest to option A.
Final Answer:
A. [tex]\(\quad 0.026 \text{ mol} \)[/tex]
