Sea water contains 29.29 NaCl and 19 MgCl2 by weight of solution.… — Solution | JEE Chemistry

NVAMediumJEE 2023Colligative Properties

Sea water contains $29.29\%$ NaCl and $19\%$ MgCl $_2$ by weight of solution. The normal boiling point of the sea water is:

Answer

Correct answer:113

Standard Method

Given: Sea water contains $29.29\%$ NaCl and $19\%$ MgCl $_2$ by weight of solution.

Find: The normal boiling point of the sea water.

Use elevation in boiling point:

\Delta T_b = iK_bm

From the extracted working,

\Delta T_b = \left(\frac{23 \times 2 \times 1000}{(58.5) \times 57.5} + \frac{3 \times 19.5 \times 1000}{95 \times 57.5}\right) \times 0.52

= \frac{(7.86 + 6.16) \times 0.52}{57.5} \times 100 \simeq 12.66

Therefore, boiling point $\simeq 113^\circ \text{C}$ .

So, the required answer is $113$ .

Using the percentage composition directly as molality is incorrect because boiling point elevation depends on molality, not mass percent. First convert the given percentages into masses of solutes and solvent.
Ignoring the van't Hoff factor is wrong because NaCl and MgCl $_2$ dissociate in solution. Their particle contributions must be counted through the factor $i$ while applying $\Delta T_b = iK_bm$ .
Taking the whole solution mass as solvent mass is incorrect. The solvent mass must exclude the dissolved salts; otherwise the molality is underestimated or overestimated.

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