Calculation of Equilibrium Constant (Kp)
- The dissociation reaction of N2O4 can be written as: N2O4(g) ⇌ 2NO2(g)
- At 27 ' C and 1 atm pressure, the equilibrium constant (Kp) can be calculated using the expression: Kp = (PNO2)2 / PN2O4
- Since N2O4 is 20% dissociated, the partial pressure of NO2 is 0.2 atm (20% of 1 atm) and the partial pressure of N2O4 is 0.8 atm (80% of 1 atm)
- Substituting these values into the expression for Kp gives: Kp = (0.2)2 / 0.8 = 0.05 atm

Calculation of Molar Concentration of N2O4 and NO2
- The ideal gas law can be used to calculate the molar concentration of N2O4 and NO2 in the equilibrium mixture
- The ideal gas law equation is: PV = nRT, where P is pressure, V is volume, n is number of moles, R is the gas constant, and T is temperature
- Rearranging the equation gives: n = PV / RT
- Since the pressure and temperature are given, we need to calculate the volume of the equilibrium mixture
- The volume of the mixture can be calculated using the partial pressures of N2O4 and NO2 and the total pressure of 1 atm: V = (0.8 + 0.2) / (1 * 0.0821 * 300) = 0.0347 m3/mol
- Substituting these values into the equation for n gives: n(N2O4) = (0.8 * 1) / (0.0821 * 300) = 0.0324 mol and n(NO2) = (0.2 * 1) / (0.0821 * 300) = 0.0081 mol

Calculation of Density of Equilibrium Mixture
- The density of the equilibrium mixture can be calculated using the equation: d = m/V, where d is density, m is mass, and V is volume
- The total mass of the equilibrium mixture can be calculated by adding the masses of N2O4 and NO2
- The molar mass of N2O4 is 92 g/mol and the molar mass of NO2 is 46 g/mol
- The mass of N2O4 in the equilibrium mixture is: m(N2O4) = n(N2O4) * M(N2O4) = 0.0324 * 92 = 2.98 g
- The mass of NO2 in the equilibrium mixture is: m(NO2) = n(NO2) * M(NO2) = 0.0081 * 46 = 0.373 g
- The total mass of the equilibrium mixture is: m(total) = m(N2O4) + m(NO2) = 2.98 + 0.373 = 3.35 g
- Substituting these values into the equation for density gives: d = m/V = 3.35 / 0.0347 = 96.5 g/m3 or 3.