Question

A mixture of water and acetone at 756 mm boils at 70.0°C. The vapor pressure of acetone is

Answer 1

Given :

A mixture of water and acetone at 756 mm boils at 70.0°C.

The vapor pressure of acetone is  1.54 atm at 70.0°C, while the vapor pressure of water is 0.312 atm at the same temperature.

To Find :

The percentage composition of the mixture.

Solution :

By Raoult's law :

$P=x_{acetone}P^o_{acetone}+x_{water}P^o_{water}\\\\x_{acetone}1.58+x_{water}0.312=\dfrac{756}{760}=0.995\ atm\\\\1.58x_a+0.312x_w=0.995$......( 1 )

Also , $x_a+x_b=1$      ......( 2 )

Solving equation 1 and 2 , we get :

$x_a=0.54\ and \ x_w=0.46$ .

Mass of acetone ,

$m_a=x_a\times MM_a\\\\m_a=0.54\times 58\\\\m_a=31.32\ g$

Mass of water ,

$m_w=x_w\times MM_w\\\\m_w=0.46\times 18\\\\m_a=8.28\ g$

$\%water =\dfrac{8.28}{8.28+31.32}\times 100\\\\\%water =20.9\%\\\\\%acetone =79.1\%$

Hence , this is the required solution.