Which of the following is suitable alternative for density of the solution , when molarity ( M) and molality ( m ) of an aqueous solution of urea is same at fixed temperature ? ( Molecular wt. of urea = 60 )

Options

A. `1- ( 3M)/( 5)`
B. `1- ( M )/( 25)`
C. `( 50+3m)/( 50)`
D. `( 25+2m)/( 25)`

Answer

C

Explanation

`("Molarity")/("Molarity")= ( 1000xx W )/( M xx V ) xx ( MxxW_(0))/(1000 xx W ) `
`:.("Molarity")/("Molarity")= ( W_(0))/(V) gm//ml`
Now molarity=molality
`:. ( W_(0))/(V) = 1 gm //ml`
`:. Dm //ml = 1 gm//ml + ( "molarity" xx M)/(1000)`
For urea molecular mass ( M =`60 gm //ml`
`:. d= 1+ ( "molarity"xx 60)/( 1000) :. d =(50 + 3M)/(50)`