The freezing point of solution containing 10 ~mL of non-volatile and non-electrolyte liquid " A " in 500 ~g of water is -0.413^ C . If K_f of water is 1.86 ~K ~kg ~mol ⁻¹ and the molecular weight of A=60 ~g ~mol ⁻¹ , what is the density of the solution in g mL ⁻¹ ? (Assume _ mix V=0 )

Step-by-step solution

Given, Volume of solute =10 ~mL T_f=0-(-0.413)=0.413^ C w( solvent )=500 ~g K_f (water) =1.86 ~K ~kg ~mol ⁻¹ (=w_A ) Molecular weight of (A) or M_B=60 ~g Let mass of solute (A)=w_B aligned & r_f=K_f w_ B M_ B 1000 w_A & 0.413=1.86 w_ B 60 1000 500 & w_ B = 0.413 60 500 1.86 1000 & aligned Mass of solute =6.66 ~g Also, gathered Density (d) of solution = Total mass Total volume = 6.66+500 500+10 = 506.66 510 =0.993 ( ~g ~mL ⁻¹ ) gathered Density (d) of solution =0.993 ~g ~mL ⁻² Hence, option (4) is the correct answer