Question

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)?

Answer 1

Given :
Mole fraction of ethanol (say e)= 0.040.
Mole fraction of water (say w) = 1-0.040 =0.96
Density of water = 1g/cm³
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Let's first find out molality (m) of the soln using :
m =( 1000×e)/(w×j)
here j is molar mass of solvent (water ; 18g/mole) .
=> m= 40/ 17.28 = 2.314 molal
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2.314 molal solution means :
2.314 moles of solute ( here ethanol) is present in 1 kg of solvent ( here water).

Now we have :
no of moles of ethanol(say n) = 2.314 moles
mass of water = 1Kg = 1000g.
density of water = 1g/cm³
=> Volume of water(say v) = mass/density
= 1000/1 = 1000cm³ = 1000mL = 1L
Now using :
Molarity = n/v
= 2.314/1 = 2.314M
Hence the molarity of solution is 2.314M
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hope it helps!