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Calculate the molarity of a solution of ethanol in water in which the mole fraction of ethanol is 0.040 (assume the density of water to be one).

Calculate the molarity of a solution of ethanol in water in which the mole fraction of ethanol is 0.040 (assume the density of water to be one).

Grade:12

8 Answers

Naveen Kumar
askIITians Faculty 60 Points
9 years ago
mole fraction=0.04
So if one molof solution contain 0.04 mol of ethanol and (1-0.04)molof water=0.96
So the mass of water=0.96*18 g=17.28g
So the mass of ethanol=0.04*46 g=1.84g
total mass=18.92g
Assuming the density of solution to be 1g/ml, the vlume of the solution=18.92ml
So if18.92ml of solution contain 0.04 mol of ethanol.
So …....1ml...............................0.04/18.92mol....
so 1000ml...............................(0.04/18.92)*1000=molaritty of the solution=2.11M
Satyam Singh
11 Points
6 years ago
Mole fraction of C2H5OH= .................1Let the moles of C2H5OH= XNow density of water = 1 (given)And the weight of 1000ml of water = volume * density (from density = mass/volume)= 1000 x 1=1000gTherefore moles of water = 1000/18= 55.55 mol (18g is molecular mass of water)Also mole fraction of C2H5OH= 0.040 (given)Putting the values in equation 1,we get=0.040=X/X+55.55=0.040X+2.222 = XOR X= 2.3145 molMolarity of solution = 2.314 M
Aniketh
11 Points
6 years ago
1 mole of solution contains 0.040 moles of ethanol》1-0.040=0.960 mole of water(as mole fraction sums upto 1)Mass of water=0.960×18=17.280gm=0.040×100÷17.280(divide by 1000 as we convert g intokgg)m=2.31m
Sumit Mukherjee
11 Points
6 years ago
Mole fraction of ethanol is given that is 0.040 (X)
As in this case ethanol acted as solute
X= n2(ethanol)/n2(ethanol)+n1(no.of moles of water)
As the solution is diluted tus 
1lt of soln=1lt of water
n1(number of moles of water)= 1000g/18=55.5
By putting this in formula
0.040=n2(ethanol)/n2+55.5
By taking reciprocal of this
25=1+55.5/n2
25-1=55.5/n2
24=55.5/n2
n2=2.31
Thus, in 1000g of water contains 2.31 moles of ethanol
Therefore,the molarity of solution is 2.31M.
Marya
13 Points
5 years ago
Molarity means moles of solute (ethanol) in one litre of the solution.
1L of ethanol = 1L of water 
Number of moles of H2O in 1L water = 1000g/18
                                                                  = 55.55moles
For a binary solution, 
x1+x2 = 1
xH2O = 1 – xC2H3OH
           = 1– 0.04
           = 0.96
xH2O = nH2O/nH2O + nC2H5OH
0.96 = 55.55/55.55+nC2H5OH
53.328 + 0.96nC2H5OH = 55.55
0.96nC2H5OH = 55.55 – 53.328
                          = 2.222
      nC2H5OH = 2.222/0.96
                          2.3145mol
    
 
 
           = 0.96
xH2O = nH2O
Ajeet Tiwari
askIITians Faculty 86 Points
3 years ago
Hello Sudhanshu,
mole fraction=0.04
So if one molof solution contain 0.04 mol of ethanol and (1-0.04)molof water=0.96
So the mass of water=0.96*18 g
=17.28g
So the mass of ethanol=0.04*46 g
=1.84g
total mass=18.92g
Assuming the density of solution to be 1g/ml,
the vlume of the solution=18.92ml
So if18.92ml of solution contain 0.04 mol of ethanol.
So 1ml gives 0.04/18.92mol
so 1000ml gives (0.04/18.92)*1000
=molaritty of the solution=2.11M
Thanks
Yash Chourasiya
askIITians Faculty 256 Points
3 years ago
Dear Students

Let consider mole fraction as moles of compounds.

Moles of ethanol = 0.04 mol

Moles of water = 1 - 0.04 = 0.96 mol

Mass of ethanol = 0.04 mol x 46 g/mol = 1.84 g

Mass of water = 0.96 mol x 18 g/mol = 17.3 g

Mass of the solution = 17.3 g + 1.84 g = 19.1g

Assuming density of water to be 1 g/ml,

Volume of solution = mass / density = 19.1 / 1 = 19.1 ml = 0.0191 L

Molarity is the number of moles of solute present in 1 L of solution.
Hence,
Molarity of the solution = 0.040 / 0.0191 = 2.1 M

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya
Anchal Aiswariya Dutta
13 Points
3 years ago
Hello friends, getting this answer has many ways but the main thing is to understand its concept. Once u understand then you can make your one formula. 
Molarity =mole fraction of solute×1000/mole fraction of solvent×m.m of solvent.
Regards, Anchal A

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