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Chem 300 - Ch 24/#1 Today’s To Do List

Chem 300 - Ch 24/#1 Today’s To Do List. Henry’s Law A Molecular Interpretation Gibbs-Duhem Equation Applications of G-D Eq. Critical behavior in L-L solutions. Henry’s Law: P j = k j X j Limiting value as X j  0. Gibbs-Duhem Equation. G total = n 1 m 1 + n 2 m 2

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Chem 300 - Ch 24/#1 Today’s To Do List

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  1. Chem 300 - Ch 24/#1 Today’s To Do List • Henry’s Law • A Molecular Interpretation • Gibbs-Duhem Equation • Applications of G-D Eq. • Critical behavior in L-L solutions

  2. Henry’s Law: Pj = kjXjLimiting value as Xj 0

  3. Gibbs-Duhem Equation • Gtotal = n1m1 + n2 m2 • mj = (G/ nj)P,T,n’ • dG = m1 dn1 + n1 dm1 + m2 dn2 + n2 dm2 • dG = -SdT + VdP + m1 dn1 + m2 dn2 • At const T, P  dG = m1 dn1 + m2 dn2 • n1 dm1 + n2 dm2 = 0Gibbs-Duhem Eq.

  4. So… • n1 dm1 + n2 dm2 = 0Gibbs-Duhem Eq. • Ties together the behavior of the components in a Solution. • Divide by dX1 and rearrange: • dm1/dX1 = - (n2/n1)(dm2/dX1) • Multiply RHS by ntot/ntot • dm1/dX1 = - (X2/X1)(dm2/dX1)

  5. PMV of H2O & Ethanol @ 25 ºC

  6. P-X & P-Y Diagrams • From Raoult: • Ptotal = P1 + P2 = x1P*1 + x2P*2 = (1 – x2)P*1 + x2P*2 = P*1 + x2(P*2 –P*1) • Thus Ptotal vs x2 is a straight line. • As a function of vap phase comp (y): • Dalton: P1 = y1Ptot y1 = P1/Ptot = x1P*1/Ptot y1 =x1P*1 / [P*1 + x2(P*2 –P*1)]

  7. Example 24-3 etc. • 1- & 2-propanol @ 298 K • P*1 = 20.9 torr P*2 = 45.2 torr • Calc. Ptot & y2 at x2 = 0.75 • Ptot = x1P*1 + x2P*2 = (0.25)(20.9) + (0.75)(45.2) = 39.1 torr • y2 = P2/Ptot = x2P*2/Ptot = (0.75)(45.2)/(39.1) = 0.87

  8. P-x/y Plot for 1-/2-propanol

  9. T-x Diagram • Consider Ptot = 760 torr • 760 = P*1 + x2(P*2 –P*1) Rearrange: • x2 = (P*1 – 760) / (P*1 – P*2) • y2 = (x2P*2 ) / 760 • Recall C-C eq.  ln P* = A – B/T • Substitute P*(T) = eA-B/T • x2 = (eA(1)-B(1)/T– 760) / (eA(1)-B(1)/T–eA(2)-B(2)/T) • y2 = (x2eA(2)-B(2)/T) / 760 • Thus T-x and T-y plots both nonlinear.

  10. T-x/y Plot

  11. NonIdeal SolnsAzeotropes

  12. Extremes in Positive Deviations from RL: 2 Liquid Phases

  13. Next Time Activity Excess Thermo Functions

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