To solve this problem, we will use the Ideal Gas Law, which is stated as:
[tex]\[ PV = nRT \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure of the gas,
- [tex]\( V \)[/tex] is the volume of the gas,
- [tex]\( n \)[/tex] is the number of moles of the gas,
- [tex]\( R \)[/tex] is the ideal gas constant,
- [tex]\( T \)[/tex] is the temperature of the gas in Kelvin.
We are given the following data:
- Volume of the lung, [tex]\( V = 3.0 \)[/tex] liters
- Partial pressure of oxygen, [tex]\( P = 21.1 \)[/tex] kilopascals
- Temperature, [tex]\( T = 295 \)[/tex] Kelvin
- Ideal gas constant, [tex]\( R = 8.314 \frac{L \cdot kPa}{mol \cdot K} \)[/tex]
We need to find the number of moles of oxygen, [tex]\( n \)[/tex]. We can rearrange the Ideal Gas Law to solve for [tex]\( n \)[/tex]:
[tex]\[ n = \frac{PV}{RT} \][/tex]
Substitute the provided values into the equation:
[tex]\[ n = \frac{(21.1 \, kPa) \cdot (3.0 \, L)}{(8.314 \, \frac{L \cdot kPa}{mol \cdot K}) \cdot (295 \, K)} \][/tex]
Now, calculate the number of moles:
[tex]\[ n \approx 0.0258 \][/tex]
Therefore, the number of moles of oxygen in the lung is approximately [tex]\( 0.0258 \)[/tex] moles. Given the options, the closest value to our calculated result is:
A. [tex]\( 0.026 \)[/tex] moles
So, the correct answer is:
[tex]\[ \boxed{0.026 \, mol} \][/tex]
