Answer to Question #213406 in Molecular Physics | Thermodynamics for Yomna

Question

The pressure and temperature of mixture of 4 kg of O2 and 6 kg of N2 are 4 bar 

and 27°C respectively. For the mixture determine the following ) :i) The mole 

fraction of each component ; (ii) The average molecular weight; (iii) The specific 

gas constant ; (iv) The volume and density ;(v) The partial pressures and partial 

volumes

Answer 1

Mole fraction of oxygen

$n_{o_2}=\frac{gm weight}{moleculer weight}=\frac{4}{32}=0.125$

$n_{N_2}=\frac{gm weight}{moleculer weight}=\frac{6}{28}=0.214$

Molecular weight

Molecular weight for

oxygen =2$\times$ atomic weights

$(W_m)_{o_2}=2\times16=32$

Nitrogen molecular weight

=$2\times$ atomic weights

$(W_m)_{N_2}=2\times14=28$

Specific gas constan

$R_s=\frac{R}{M{_o}_{2}}=\frac{8.31}{32}=0.2596$

$R_s=\frac{R}{M{_N}_{2}}=\frac{8.31}{28}=0.296$

Volume and density

$V=\frac{nRT}{P}$

$V_o=\frac{0.125\times8.314\times300}{4}=77.94m^3$

$V_N=\frac{0.214\times8.314\times300}{4}=133.43m^3$

$d_o=\frac{M}{V}=\frac{32}{77.94}=0.4105kg/m^3$

$d_o=\frac{M}{V}=\frac{28}{133.43}=0.2098kg/m^3$

Partial pressure

$P_o=n\times$ pressure

$P_o=0.125\times4=0.5 bar$

$P_N=n\times$ pressure

$P_N=$ $0.214\times4=0.856$ bar

Partial volume

$V_o=n\times$ volume

$V_o=0.125\times77.94=9.74kg$

$V_N=n\times$ volume

$V_N=0.214\times133.43=28.55kg$