Solutions and Colligative Properties - Result Question 15-1
15. Consider separate solution of $0.500 $ $\mathrm{M}$ $ \mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(a q)$, $0.100 $ $\mathrm{M}$ $ \mathrm{Mg}_3\left(\mathrm{PO}_4\right)_2(a q), $0.250$ $ $\mathrm{M} $ $\mathrm{KBr}(a q)$ and $0.125$ M $\mathrm{Na}_3 \mathrm{PO}_4(\mathrm{aq})$ at $25^{\circ} \mathrm{C}$. Which statement is true about these solution, assuming all salts to be strong electrolytes?
(2014 Main)
(a) They all have the same osmotic pressure
(b) $0.100$ $ \mathrm{M}$ $ \mathrm{Mg}_3\left(\mathrm{PO}_4\right)_2(\mathrm{aq})$ has the highest osmotic pressure
(c) $0.125$ $ \mathrm{M}$ $ \mathrm{Na}_3 \mathrm{PO}_4(\mathrm{aq})$ has the highest osmotic pressure
(d) $0.500 $ $\mathrm{M} $ $\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(a q)$ has the highest osmotic pressure
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Answer:
Correct Answer: 15. (a)
Solution:
PLAN: This problem includes concept of colligative properties (osmotic pressure here) and van’t Hoff factor. Calculate the effective molarity of each solution.
$ \text { i.e. effective molarity }=\text { van’t Hoff factor } \times \text { molarity } $
$ 0.5 $ $\mathrm{M} $ $\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(a q) \quad i=1 $
$ \text { Effective molarity }=0.5 $
$ 0.25$ $ \mathrm{M} $ $\mathrm{KBr}(a q) \quad i=2 $
Effective molarity $=0.5 \mathrm{M}$
$ 0.1$ $ \mathrm{M}$ $ \mathrm{Mg}_3\left(\mathrm{PO}_4\right)_2(a q) \quad i=5 $
Effective molarity $=0.5 \mathrm{M}$
$ 0.125$ $ \mathrm{M} $ $\mathrm{Na}_3 \mathrm{PO}_4(a q) \quad i=4 $
Effective molarity $=0.5 \mathrm{M}$
Molarity is same hence, all colligative properties are also same.
NOTE: This question is solved by assuming that the examiner has taken $\mathrm{Mg}_3\left(\mathrm{PO}_4\right)_2$ to be completely soluble. However, in real it is insoluble (sparingly soluble).
BETA
