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

Mole fraction of C₂H₅OH `=("Number of moles of ""C"_2"H"_5"OH")/"Number of moles of solution"`

`0.040="n"_("C"_2"H"_5"OH")/("n"_("C"_2"H"_5"OH")+"n"_("H"_2"O"))`     .......(1)

Number of moles present in 1 L water:-

`"n"_("H"_2"O") = (1000 " g")/(18 " g"" mol"^-1)`

`"n"_("H"_2"O") = 55.55 " mol"`

Substituting the value of `"n"_("H"_2"O")` in equation (1),

`"n"_("C"_2"H"_5"OH")/("n"_("C"_2"H"_5"OH")+55.55)=0.040`

`"n"_("C"_2"H"_5"OH") = 0.040 "n"_("C"_2"H"_5"OH") + (0.040)(55.55)`

`0.96" n"_("C"_2"H"_5"OH") = 2.222 " mol"`

`"n"_("C"_2"H"_5"OH") = 2.222/0.96" mol"`

`"n"_("C"_2"H"_5"OH") = 2.314" mol"`

∴ Molarity of solution `=(2.314" mol")/(1 "L")`

= 2.314 M