Answer: The temperature of the system is 273 K
Explanation:
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Given mass of carbon dioxide = 1 lb = 453.6 g (Conversion factor: 1 lb = 453.6 g)
Molar mass of carbon dioxide = 44 g/mol
Putting values in above equation, we get:
[tex]\text{Moles of carbon dioxide}=\frac{453.6g}{44g/mol}=10.31mol[/tex]
To calculate the temperature of gas, we use the equation given by ideal gas equation:
PV = nRT
where,
P = Pressure of carbon dioxide = 200 psia = 13.6 atm (Conversion factor: 1 psia = 0.068 atm)
V = Volume of carbon dioxide = [tex]0.6ft^3=16.992L[/tex] (Conversion factor: [tex]1ft^3=28.32L[/tex] )
n = number of moles of carbon dioxide = 10.31 mol
R = Gas constant = [tex]0.0821\text{ L atm }mol^{-1}K^{-1}[/tex]
T = temperature of the system = ?
Putting values in above equation, we get:
[tex]13.6atm\times 16.992L=10.31mol\times 0.0821\text{ L atm }mol^{-1}K^{-1}\times T\\\\T=273K[/tex]
Hence, the temperature of the system is 273 K
