Question

The vapor pressure of diethyl eth (ether) is 463.57 mm Hg at 25°C. A nonvolatile, nonelectrolyte that dissolves in diethyl ether is DDT. Calculate the vapor pressure of the solution at 25°C when 10.73 grams of DDT, C14H,Cls. are dissolved in 237.2 grams of diethyl ether. diethyl ether = CH3CH2OCH2CH3

Answer 1

Solution -

This example based on vapour pressure lowering due to additon of DDT.

Vapour pressure lowering ,

P₁= X₁P

here,

P₁ = Vapours pressure of solution after DDT addition.

P= Vapour pressure of pure diethylether = 463.57 mmHg

X₁  = mole fraction of solvent.

let's see molar mass of DDT and Diethylether from its molecular formula,

#molar mass of diethylether= C₄H₁₀O

= (12.01 x4) +(10x1.007)+(16 x 1)

= 74.12 g/mol

#molar mass of DDT = C₁₄H₉Cl₅

_{= (12.01 x 14) + (9 x 1.007 ) + (35.45 x 5)}

_{= 354.49 g/mol}

now we have to calculate mole fraction of solution by using  mass and its calculated molar mass .

Amount of DDT =10.73 g,

Moles of DDT (n) = mass (g) / molar mass of DDT

=( 10.73 g /354.49 g/mol)

= 0.0303 mol

Amount of diethylether = 237.2 g

Similarly,

moles of diethylether (n) = mass (g) / molar mass of diethylether

= (237.2 g / 74.12 g/mol )

= 3.200 moles

Now we have to calculate mole fraction of diethylether ,

X_C4H10O = (3.2 mol ether/ ( 3.2 mol +0.0303 mol )

= 0.99

Now we will put mole fraction value into above formula,

P_{ether/DDT Sol. = 0.99 x 463.57 mm Hg}

_{= 459.22 mm Hg}