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<b>Solution:</b>
1. Calculate the van't Hoff factor (i):
MgCl2 dissociates into Mg<sup>2+</sup> and 2Cl<sup>-</sup>, so it dissociates into 3 ions.
The dissociation reaction is: MgCl2 → Mg<sup>2+</sup> + 2Cl<sup>-</sup>
Degree of dissociation (α) = 80% = 0.8
i = 1 + α(n - 1), where n is the number of ions produced.
i = 1 + 0.8 (3 - 1) = 1 + 0.8 * 2 = 1 + 1.6 = 2.6
2. Calculate the effective molality:
Effective molality = i * molality
Effective molality = 2.6 * 1.0 molal = 2.6 molal
3. Calculate the mole fraction of the solute (x_solute):
For a dilute solution, mole fraction of solute ≈ (molality of solute * molar mass of water) / 1000
Molar mass of water (H2O) = 18 g/mol
x_solute = (2.6 * 18) / 1000 = 0.0468
4. Calculate the mole fraction of the solvent (x_solvent):
x_solvent = 1 - x_solute
x_solvent = 1 - 0.0468 = 0.9532
5. Calculate the vapour pressure of the solution (P_solution):
P_solution = x_solvent * P°_water, where P°_water is the vapour pressure of pure water.
P_solution = 0.9532 * 50 mm Hg = 47.66 mm Hg
6. Round to the nearest integer:
P_solution ≈ 48 mm Hg
<b>Therefore, the vapour pressure of the 1.0 molal aqueous solution of MgCl2 at 38°C is approximately 48 mm Hg.</b>
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