Draw and label the given streams and derive expressions for the indicated quantities in terms of labeled variables. The solution of Part (a) is given as an illustration. 

(a) A continuous stream contains 40.0 mole% benzene and the balance toluene. Write expressions for the molar and mass flow rates of benzene, ṅ_B(mol C₆H₆/s) and ṁ_B(kg C₆H₆/s), in terms of the total molar flow rate of the stream, ṅ(mol/s).

(b) The feed to a batch process contains equimolar quantities of nitrogen and methane. Write an expression for the kilograms of nitrogen in terms of the total moles n(mol) of this mixture. 

(c) A stream containing ethane, propane, and butane has a mass flow rate of 100.0 g/s. Write an expression for the molar flow rate of ethane, ṅ_E(lb-mole C₂H₆/h), in terms of the mass fraction of this species, x_E. 

(d) A continuous stream of humid air contains water vapor and dry air, the latter containing approximately 21 mole% O₂ and 79% N₂. Write expressions for the molar flow rate of O₂ and for the mole fractions of H₂O and O₂ in the gas in terms of ṅ₁(lb-mole H₂O/s) and ṅ₂(lb-mole dry air/s). 

(e) The product from a batch reactor contains NO, NO₂, and N₂O₄. The mole fraction of NO is 0.400. Write an expression for the gram-moles of N₂O₄ in terms of n(mol mixture) and y_NO2 (mol NO₂/mol).

n(mol/s) 0.400 mol C,H6/mol 0.600 mol C,Hg/mol ng = 0.400h (mol C,H6/s) 0.400h (mol C6H6) 78.1 g C6H6 mB = 31.2h(g C6H6/s) mol