Answer: The mass of air is 0.00260 lbs.
Explanation:
To calculate the number of moles, we use the equation given by ideal gas equation:
PV = nRT
Or,
[tex]PV=\frac{m}{M}RT[/tex]
where,
P = pressure of the gas = 150 psia = 10.2 atm (Conversion factor: 1 psia = 0.068 atm)
V = Volume of gas = [tex]10in^3=0.164L[/tex] (Conversion factor: [tex]1in^3=0.0164L[/tex] )
m = mass of air = ?
M = Average molar mass of air = 28.97 g/mol
R = Gas constant = [tex]0.0820\text{ L atm }mol^{-1}K^{-1}[/tex]
T = temperature of the gas = [tex]440^oF=499.817K[/tex] (Conversion factor: [tex](T(K)-273.15)=(T(^oF)-32)\times \frac{5}{9}[/tex] )
Putting values in above equation, we get:
[tex]10.2atm\times 0.164L=\frac{m}{28.97g/mol}\times 0.0820\text{ L atm }mol^{-1}K^{-1}\times 499.817K\\\\m=1.18g[/tex]
Converting this mass into lbs, we use the conversion factor:
1 lbs = 454 g
So, [tex]1.18g\times \frac{1lbs}{454g}=0.00260lbs[/tex]
Hence, the mass of air is 0.00260 lbs.
