UPSEE Solved Model Paper 7

Given: Empirical formula of a non-electrolyte = $\mathrm{CH_2O}$ Mass of compound taken = 6 g Concentration of glucose solution = 0.05 M $(\text{Osmotic pressure})_{\text{compound}}$ = $(\text{Osmotic pressure})_{\text{glucose}}$ We have to find !tie molecular formula of the compound Now, the empirical formu!a mass of $\mathrm{CH_2O}$ is: = 12 + 2 × 1 + 16 = 30 Let molar mass of the compound be 'M'. Let osmotic pressure of the compound and glucose be $\pi_1$ and $\pi_2$ respectively and as given: $(\text{Osmotic pressure})_{\text{compound}}$ = $(\text{Osmotic pressure})_{\text{glucose}}$ or, $\pi_1$ = $\pi_2$ Thus, $C_1 R T$ = $C_2 R T$ or, $C_1$ = $C_2$ ... (i) where, $C_1$ = Concentration of solution of compound $C_2$ = Concentration of glucose solution R = Gas constant T = Temperature Now, molarity is given by: Molarity = $\frac{\text{Number of moles}}{\text{Volume of solution (in L)}}$ Number of moles is given by : Mole = $\frac{\text{Mass}}{\text{Molecular mass}}$ Thus, $C_1$ = $\frac{6}{M}$ From equation (i) , we get $\frac{6}{M}$ = 0.05 M = $\frac{6}{0.05}$ = 120 Now, n = $\frac{\text{Molecular mass}}{\text{Empirical formula mass}}$ ... (ii) where, n = Simple whole number Substituting the values in equation (ii). we get n = $\frac{120}{30}$ = 4 Therefore, molecular formula of the compound = $(\mathrm{CH_2O})_n$ = $(\mathrm{CH_2O})_4$ = $\mathrm{C_4H_8O_4}$ Hence, option 'D' is correct.