Question

1 lb of CO2 occupies 0.6 ft^3 at a pressure of 200 psi. Determine the temperature of the system.

Answer 1

Answer: The temperature of the system is 273 K

Explanation:

To calculate the number of moles, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$  

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:

$\text{Moles of carbon dioxide}=\frac{453.6g}{44g/mol}=10.31mol$

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 = $0.6ft^3=16.992L$    (Conversion factor:  $1ft^3=28.32L$ )

n = number of moles of carbon dioxide = 10.31 mol

R = Gas constant = $0.0821\text{ L atm }mol^{-1}K^{-1}$

T = temperature of the system = ?

Putting values in above equation, we get:

$13.6atm\times 16.992L=10.31mol\times 0.0821\text{ L atm }mol^{-1}K^{-1}\times T\\\\T=273K$

Hence, the temperature of the system is 273 K