`30mL` of `CH_(3)OH (d = 0.780 g cm^(-3))` and `70 mL` of `H_(2)O (d = 0.9984 g cm^(-3))` are mixed at `25^(@)C` to form a solution of density `0.9575 g cm^(-3)`. Calculate the freezing point of the solution. `K_(f)(H_(2)O)` is `1.86 kg mol^(-1)K`. Also calculate its molarity.

Explanation

Weight of `"CH"_(3)"OH"("w"_(1))=30"cm"^(3)xx0.7980" gm"//"cm"^(3)=23.94" gm"`
Weight of solvent `("H"_(2)"O")("w"_(2))=70"cm"^(3)xx0.9984"gm cm"^(3)=69.888"gm"`
`"m"=23.94/32xx1000/69.88=10.7046" molal"`
`thereforeDelta"T"_("F")="K"_("F")xx"i"xx"molality", ("for" "CH"_(3)"OH","i"=1)`
`Delta"T"_("F")=1.86xx10.7046^(@)"C"=19.91^(@)"C"`
Freezing point of the solution`=0-19.91^(@)"C"=-19.91^(@)"C"`
Weight of solution =weight of solute + weight of solvent=23.94+69.888=93.828 gm
`"volume of the solution"=("wt. of the solution")/("density of the solution")=93.828/0.95751=97.99"ml"`
M (molarity)`=23.94/32xx1000/97.99"mol lit"^(-1)=7.63 "M"`