Sure! Let's solve the problem step-by-step.
To determine the moles of air contained in a 165-liter cylinder at a pressure of 1.48 atm and a temperature of 339 K, we can use the Ideal Gas Law, which is formulated as:
[tex]\[ \text{PV = nRT} \][/tex]
Where:
- [tex]\( P \)[/tex] is the pressure of the gas in atmospheres (atm),
- [tex]\( V \)[/tex] is the volume of the gas in liters (L),
- [tex]\( n \)[/tex] is the number of moles of the gas,
- [tex]\( R \)[/tex] is the ideal gas constant ([tex]\( R = 0.0821 \ \text{L·atm/(mol·K)} \)[/tex]),
- [tex]\( T \)[/tex] is the temperature of the gas in Kelvin (K).
To find the number of moles ([tex]\( n \)[/tex]), we can rearrange the equation to:
[tex]\[ n = \frac{PV}{RT} \][/tex]
Now, let's plug in the given values:
- [tex]\( P = 1.48 \ \text{atm} \)[/tex]
- [tex]\( V = 165 \ \text{L} \)[/tex]
- [tex]\( T = 339 \ \text{K} \)[/tex]
Substitute these values into the equation:
[tex]\[
n = \frac{(1.48 \ \text{atm}) \times (165 \ \text{L})}{(0.0821 \ \text{L·atm/(mol·K)}) \times (339 \ \text{K})}
\][/tex]
When you compute this, you will get:
[tex]\[
n \approx 8.774104534724541
\][/tex]
Therefore, the moles of air contained in the cylinder are approximately:
[tex]\[ 8.77 \ \text{moles} \][/tex]
Thus, we have determined that the cylinder contains about 8.77 moles of air.
