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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).
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Solution
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
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