Solutions and Colligative Properties 2 Question 40
40. $M X_{2}$ dissociates into $M^{2+}$ and $X^{-}$ions in an aqueous solution, with a degree of dissociation $(\alpha)$ of 0.5 . The ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation is
(2014 Adv.)
| 1. (c) | 2. (c) | 3. (c) | 4. (b) |
|---|---|---|---|
| 5. (d) | 6. (c) | 7. (c) | 8. (b) |
| 9. (c) | 10. (d) | 11. (c) | 12. (d) |
| 13. (d) | 14. (b) | 15. (a) | 16. (a) |
| 17. (a) | 18. (a) | 19. (c) | 20. (a) |
| 21. (a) | 22. (b) | 23. (d) | 24. (a) |
| 25. (a) | 26. (a, d) | 27. $(0.05)$ | 28. $(75 %)$ |
| 30. $\left(0.23^{\circ} \mathrm{C}\right)$ | 33. $(23.44 \mathrm{~mm})$ | 34. $(156 \mathrm{~g} / \mathrm{mol})$ | 35. (d) |
| 36. (a) | 37. (b) | 38. $\left(K_{f}\right)$ | 40. (2) |
Show Answer
Solution:
- $M X_{2} \longrightarrow M^{2+}+2 X^{-}$
van’t Hoff factor for any salt can be calculated by using equation $i=1+\alpha(n-1)$
where, $n=$ number of constituent ions
$$ \begin{aligned} & \therefore \quad i\left(M X_{2}\right)=1+\alpha(3-1)=1+2 \alpha \ & \frac{\left(\Delta T_{f}\right){\text {observed }}}{\left(\Delta T{f}\right)_{\text {theoretical }}}=i=1+2 \alpha \ & \therefore \quad i=1+2 \times 0.5 \Rightarrow i=2 \end{aligned} $$
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