Answer to Question #251427 in Molecular Physics | Thermodynamics for Bebe

Question

. A one cubic meter tank contains a mixture of 2.5 kg of nitrogen and 4.5 kg of the unknown gas. The mixture pressure and temperature are 350 kPa and 80°c respectively. The gas constant for nitrogen is 0.2968 kJ*/kg- °K. Determine the gas constant of the unknown gas in kJ/kg-°K.   

Answer 1

We have to use the ideal gas law, but this equation has to be modified to include both R constants for each of the substances with mass m₁ and m₂:

$PV=nRT=(m_1R_1+m_2R_2)T \\ \implies R_2=\cfrac{\frac{PV}{T}-m_1R_1}{m_2}$

We proceed to substitute and find R₂:

$R_2=\cfrac{\cfrac{(350\,kPa)(1\,m^3)\times\frac{1\,kJ}{1\,kPa\cdot m^3}}{353.15\,K}-(2.5\,kg)(0.2968\frac{kJ}{kg\cdot K})}{4.5\,kg} \\ \text{ } \\ \therefore R_2=\frac{0.249080277}{4.5} \frac{kJ}{kg\cdot K}=0.0554 \frac{kJ}{kg\cdot K}$

In conclusion, the gas constant of the unknown gas is 0.0554 kJ/kg-°K.

Reference

• Chang, R., & Goldsby, K. A. (2010). Chemistry. Chemistry, 10th ed.; McGraw-Hill Education: New York, NY, USA.