Explanation:
Psol = Pmeth * Xmeth + Pprop * Xprop
Where,
Psol = vapor pressure of the solution
Pmeth = vapor pressure of methanol
Pprop = vapor pressure of propanol
Xmeth = mole fraction methanol
Xprop = mole fraction propanol
Therefore,
174 = 303 Xmeth + 44.6 Xprop
Xmeth + Xprop = 1
Xmeth = 1 - Xprop
174 = 303 ( 1 - Xprop ) + 44.6 Xprop
174 = 303 - 303 Xprop + 44.6 Xprop
129 = 258.4 * Xprop
Xprop = 0.499
Xmeth = 1 - 0.499
= 0.501
Since Xprop = 0.499,
But Xprop = moles propanol / (moles propanol + moles methanol)
Since, moles propanol + moles methanol = 1,
moles of propanol, mprop = 0.499
moles methanol, mmeth = 0.501
Molar mass of propanol = (12*3) + (1*8) + 16
= 60 g/mol.
mass of propanol, Mprop = 0.499 x 60 g/mol
= 3.00 g
Molar mass of methanol = (12*1) + (1*4) + 16
= 32 g/mol.
mass of methanol, Mmeth = 0.501 x 32
= 16.1 g.
Following are the calculation to the Mole fraction:
Given:
[tex]P = 135\ torr \\\\P_1 = 303\ torr \\\\P_2 = 44.6\ torr[/tex]
To find:
Mole fraction=?
Solution:
Therefore,
[tex]\to x_1 + x_2 = 1\\\\\to x_2 = 1-x_1\\\\[/tex]
[tex]\to P = x_1P_1+x_2P_2\\\\\to 135 = x_1(303)+ x_2(44.6)\\\\\to 135 = x_1(303)+ (1-x_1)(44.6)\\\\\to 135 = 303x_1 + 44.6 -44.6 x_1\\\\\to 135-44.6 = (303-44.6)x_1\\\\\to 90.4 = 258.4 x_1\\\\\to x_1 = 0.35\\\\\to x_2 = 1-x_1 = 1-0.35 = 0.65[/tex]
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