In a solution of ethanol in water, the mole fraction of ethanol is `0.05` and the density of solution is `1.94 g mL^(-1)`. The molarity of the solution is ___ `M`

Options

A. 9.8
B. 5
C. 4.7
D. 2.5

Answer

2

Explanation

Molarity is number of moles of solute dissolved per litre of solution. Use mole fraction data to find the number of moles of ethanol and use density to find the volume of solution.
`chi_(C_(2)H_(5)OH)=n_(C_(2)H_(5)OH)/n_(soln)=0.05 =5/100`
This implies that if we consider 100 moles of solution then there are 5 moles of `C_(2)H_(5)OH`.
Volume of solution `=("mass of solution")/("density of solution")`
Mass of solution = mass of solute + mass of solvent
Since, `n=("mass")/("molar mass")`
`Mass=(n) ("molar mass")`
Thus
Mass of ethanol = `(n_(C_(2)H_(5)OH))("molar mass"_(C_(2)H_(5)OH))`
`=(5 mol)(46 g//mol)`
`=230 g`
`"Mass of "H_(2)O =(n_(H_(2)O))("molar mass"_(H_(2)O))`
`=(95 mol)(18 g mol^(-1))`
`=1710 g`
Mass of solution `=(230 g)+(1710 g)`
`=1940 g`
Volume of solution `=(1940 g)/(1.94 g//mL)`
`=1000 mL`
`"Molarity "=n_(C_(2)H_(5)OH)/v_(mL)xx(1000 mL)/(1 L)`
`=(5 mol)/(1000 mL)xx(1000 mL)/L`
`=5 mol L^(-1)`