HW 4 solution

# HW 4 solution - PGE 312 Physical and Chemical Behavior of...

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Unformatted text preview: PGE 312 Physical and Chemical Behavior of Fluids Home Work 4 – Solutions Problem 12-1 The Raoult’s equation is given by Σ P j = Σ x j P vj = P --- (1) Rewriting equation (1) for the two component system we have x A P vA + x B P vB = P --- (2) We know that the sum of the liquid mole fractions should equal 1.0 x A + x B = 1.0 --- (3) Multiplying equation (3) by p vA and subtracting from (2) we solve for x B as x B = gGg ¡¢ g ¡£ Gg ¡¢ Similarly solving for x A , we get x A = gGg ¡£ g ¡¢ Gg ¡£ The composition of the gas phase can be calculated from equation 12-2 as ¤ ¥ = ¦ ¥ g ¡¢ g , ¤ § = ¦ § g ¡£ g Problem 12-6 Pressure = 5 psia Temperature = 100°F Subscripts: A = 2,2-dimethylbutane, B = 2,2,4-trimethylpentane 3 A m = lb mass 2 B m = lb mass 3 2 5 A B m m m = + = + = lb mass of mixture The molecular weights are given in Appendix A as 86.177 A M = lb mass/lb mole 114.231 B M = lb mass/lb mole The overall composition of the mixture is calculated as follows: 3 0.0348 86.177 A A A m n M = = = lb mole 2 0.0175 114.231 B B B m n M = = = lb mole 0.0348 0.0175 0.0523 A B n n n = + = + = lb mole of mixture 0.0348 0.6654 0.0523 A A n z n = = = 0.0175 0.3346 0.0523 B B n z n = = = For an ideal solution, 9.2 1.84 5 vA A P k P = = = 1.65 0.33 5 vB B P k P = = = ( )( ) ( )( ) 0.6654 1.84 0.3346 0.33 1.2243 0.1104 1.3348 1.0 i i z k = + = + = > ∑ 0.6654 0.3346 1.84 0.33 0.3616 1.0139 1.3756 1.0 i i z k = + = + = > ∑ Since 1 i i z k > ∑ and 1 i i z k > ∑ , we have a 2-phase system. We can proceed with the flash calculation. For a binary system, the flash calculation can be performed directly, without trial and error. Will a trial and error approach work? Yes, but it is less accurate and takes longer to accomplish. Solving the flash problem directly gives 1 1 0.33 0.4437 1.84 0.33 B A A B k x k k-- = = =-- 1 1 0.4437 0.5563 B A x x = - = - = ( ) ( ) 1 1.84 1 0.33 0.8164 1.84 0.33 A B A A B k k y k k-- = = =-- 1 1 0.8164 0.1836 B A y y = - = - = 0.6654 0.8164 g A A g A A n z x n n y x-- = = =-- 1 1 0.5948 L L g n n n n = = - = - = The apparent molecular w ( )( 0.4437 86 38.2367 63 101.7834 lb L i i M x M = = = + = ∑ ( )( 0.8164 86 70.3549 20 91.3277 lb m g i i M y M = = = + = ∑ The moles of gas and liqui ( )( * 0.5948 0.052 g g n n n = = ( )( * 0.4052 0.0523 L L n n n = = As a check, the moles of g lb mole of mixture. 0.0311 0.0212 g L n n + = + = The masses of gas and liq ( )( * 0.0311 91....
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HW 4 solution - PGE 312 Physical and Chemical Behavior of...

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