Respuesta :
Answer:
The vapor pressure of the solution is 284.29 mmHg
Explanation:
From Raoult's law
Vapor pressure of solution = mole fraction of solvent × vapor pressure of solvent
Mass of solute (acetone) = 30.5 g
MW of acetone (CH3COCH3) = 58 g/mol
Number of moles of solute = mass/MW = 30.5/58 = 0.526 mol
Mass of solvent (ethyl acetate) = 23.5g
MW of ethyl acetate (CH3COOC2H5) = 88 g/mol
Number of moles of solvent = mass/MW = 23.5/88 = 0.267 mol
Volume of solvent = 0.267×22.4×1000 = 5980.8 cm^3
Vapor pressure of solvent (P) = nRT/V
n is number of moles of solvent = 0.267 mol
R is gas constant = 82.057 cm^3.atm/mol.K
T is temperature of solution = 30°C = 30+273 = 303 K
V is volume of the solvent = 5980.8 cm^3
P = 0.267×82.057×303/5980.8 = 1.11 atm = 1.11×760 = 843.6 mmHg
Total moles of solution = moles of solute + moles of solvent = 0.526 + 0.267 = 0.793 mol
Mole fraction of solvent = moles of solvent/moles of solution = 0.267/0.793 = 0.337
Vapor pressure of solution = 0.337 × 843.6 mmHg = 284.29 mmHg
The vapor pressure is the pressure exerted by the molecules in the gaseous phase. The vapor pressure of the given solution is 284.29 mm Hg.
What are the moles of solute and solvent?
The acetone is a solute having mass of 30.5 grams.
The mole of solute are:
[tex]\rm Moles\;solute=\dfrac{30.50\;g}{58\;g/mol}\\Moles\;solute=0.526\;mol[/tex]
The ethyl acetate is the solvent having a mass 23.5 g.
The moles of solvent are;
[tex]\rm Moles\;solvent=\dfrac{23.5\;g}{88g/mol}\\Moles\;solvent=0.267\;mol[/tex]
The total moles of the solution are:
[tex]\rm Total\;moles=solute\;+\;solvent\\Total\;moles=0.526+0.267\;mol\\Total\;moles=0.793\;mol[/tex]
The ethylacetate is assumed as ideal. The volume of a mole of gas is 22.4 L. The volume of 0.267 mol ethyl acetate is:
[tex]\rm 0.267\;mol\;ethyl\;acetate=0.267\;\times\;22.4\;\times\;1000\;cm^3\\ 0.267\;mol\;ethyl\;acetate=5980.8\;cm^3[/tex]
The pressure of ethyl acetate in the solution is:
[tex]\rm PV=nRT[/tex]
Substituting the values of gas constant (R), moles (n), volume (V), and temperature (T), pressure (P) can be given as:
[tex]\rm P=\dfrac{0.267\;mol\;\times\;82.057\;cm^3.atm/mol.K\;\times\;303\;K}{5980.8\;cm^3} \\P=843.6\;mm\;Hg[/tex]
The pressure of the solvent is 843.6 mm Hg.
The mole fraction of solvent is:
[tex]\rm Mole\;fraction=\dfrac{solvent\;moles}{total\;moles}\\\\ Mole\;fraction=\dfrac{0.267}{0.793}\\\\ Mole\;fraction=0.337[/tex]
According to Raoult's law, the vapor pressure is given as:
[tex]\rm Vapor\;pressure=Pressure\;solvent\;\times\;mole\;fraction\\Vapor\;pressure=843.6\;mm\;Hg\;\times\;0.337\\Vapor\;pressure=284.29\;mm\;Hg[/tex]
The vapor pressure of the solution is 284.29 mm Hg.
Learn more about vapor pressure, here:
https://brainly.com/question/25356241
