how much of cane sugar should be dissolved in 0.300Kg so that resulting solution has same boiling point as that of 3gm of Urea in 0.1Kg of Water

 

The elevation in boiling point for sugar solution is,

                                  ?T_b(sucrose) = (K_b X W_sucrose) / (M_sucrose X W_water )

 

Where, M_sucrose = 342 gm/mole

             W_water = 0.300 kg

 

Similarly, the elevation in boiling point for urea solution is,

                    ?T_b(urea) = (K_b X W_urea ) / (M_urea X W_water )

Where, M_urea = 60 gm/mole

             W_water = 0.1 kg

According to the question, ?T_b(sucrose) = ?T_b(urea)

        

     (K_b X W_sucrose) / (M_sucrose X W_water ) = (K_b X W_urea ) / (M_urea X W_water )

 

Or, W_sucrose / (342 X 0.300 ) = 3  / ( 60 X 0.1 )

  

W_sucrose  = 51.33 gm