Question

Calculate the mole fraction of ethylene glycol in a solution containing 20% of ethylene glycol prepared in water.
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Answer 1

The chemical formula  of Ehylene glycol
                   C2 H6 O2  =  OH - CH2 - CH2 - OH
      molar mass = 2 * 12 + 6* 1+ 16*2 = 62     and     density = 1.113 gm/cm³

chemical formula of  water   :  H2 O
            molecular mass: 16+2 *1 = 18        Density = 1 gm/cm³

case 1)  The solution of glycol is prepared by mixing  water and glycol by mass.
  So in 100 gms of the solution, we have 20 gms of glycol and 80 gm of water.

   number of moles of glycol = mass/molar mass = 20/62 = 10/31
   number of moles of water = 80/18 =  40/9
   total number of moles in 100 grams of solution: N = 10/31 + 40/9  = 1330/279

   Mole fraction of glycol = (10/31) /(1330/279)  = 2790/(1330*31) =0.06767
    mole fraction of water in the solution = 1 - 0.06767 = 

   This can be  calculated directly as :  [20/62] / [20/62 + 80/18]

2)  if the liquids are mixed by volume then:
     In 100 ml of solution we have  20 ml of glycol and 80 ml of water.
    20 ml of glycol has a mass of 20 * 1.113 gm. and 80 ml of water has a mass of 80 gm.

   mole fraction of  glycol in this case : 
            [20*1.113/62]  / [ 20*1.113/62 + 80/18]  = 0.359 / 4.803 = 0.0747
   mole fraction of water in the solution will be  1 - 0.0747 =