6. The vapor pressure of pure, solid pyrene at 25 ° C is given by the variable P
ID: 892684 • Letter: 6
Question
6. The vapor pressure of pure, solid pyrene at 25 °C is given by the variable P1 atm. The solubility of pyrene in H2O at 25 °C is 1.0 x 10-4 M, whereas the solubility in ethanol at 25 °C is greater than 1 x 10-4 M.
(a) Derive an expression for the vapor pressure of pyrene above a saturated solution in water at 25 °C
(b) If ethanol is added to the saturated aqueous soln, more pyrene dissolves. When equilibrium is reached again, will the vapor pressure of the pyrene above the new solution be greater than, less than, or equal to that in part (a)?
Explanation / Answer
From Clausius Clapeyron relationship:
Ln(P0s)=Ln(P0l)-DHf/R*(1/T-1/Tm)
P0s = vapor pressure of pure solid pyrene = P1
P0l = vapor pressure of pure liquid pyrene
DHf = Enthalpy of fusion of pyrene
R = Gas constant
Tm = melting point of pyrene = 156 C = 156+273=429 K
T = temperature = 25C = 25+273 = 298K
(a)
Vapor pressure of saturated solution of pyrene
solubility, S = 1E-4 M
For 1 liter solution, moles of pyrene, np = 1E-4
Molar mass of pyrene(C16H10), MWp = 202.3 gm/mol
If the density of solution = 1 gm/ml
Mass of 1L solution, W = 1000 gm
Mass of solute, pyrene Wp = np*MWp = 202.3*1E-4 = 0.02023 gm
Mass of water, Ww = 1000 - 0.02 = 999.98gm
Moles of water, nw = Ww/18=55.55
mole fraction of pyrene, xpw = np/(np+nw)=1E-4/(1E-4+55.55)= 1.8E-6
vapor pressure of pyrene, Ppw = P0l*xpw
(b)
If ethanol is added to the saturated aqueous soln, more pyrene dissolves.
When equilibrium is reached again, will the vapor pressure of the pyrene above the new solution be greater than, less than, or equal to that in part (a)?
Let the mole fraction of pyrene in ethanol is xpe
The new pyrene vapor pressure, Ppnew = Ppw + Ppethanol = P0l*xpw+P0l*xpe
The new vapor pressure is greater than in part(a).
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