Question

Assuming that carbon dioxide obeys ideal gas law, the density of carbon dioxide \((\text{Kg/m}^3)\) at \(263^\circ C\) and \(2\) atm is

• A. \(1\)
• B. \(2\)
• C. \(3\)
• D. \(4\)

Hint:

For gas density, use \(\rho=\frac{PM}{RT}\). Always convert temperature into Kelvin.

Answer 1

The Correct Option is B

For an ideal gas: \[ PV=nRT. \] Density form of ideal gas equation is: \[ \rho=\frac{PM}{RT}. \] For carbon dioxide: \[ M=44\text{ kg/kmol}. \] Temperature: \[ T=263^\circ C=263+273=536\text{ K}. \] Pressure: \[ P=2\text{ atm}. \] Using: \[ 1\text{ atm}=101.325\text{ kPa}, \] we get: \[ P=202.65\text{ kPa}. \] Use: \[ R=8.314\ \text{kPa}\cdot\text{m}^3/(\text{kmol}\cdot\text{K}). \] Now: \[ \rho=\frac{202.65\times44}{8.314\times536}. \] Calculate numerator: \[ 202.65\times44=8916.6. \] Calculate denominator: \[ 8.314\times536=4456.3. \] Therefore: \[ \rho=\frac{8916.6}{4456.3}. \] \[ \rho\approx2\text{ kg/m}^3. \] Hence, the density of carbon dioxide is: \[ 2\text{ kg/m}^3. \]