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A certain substance X has a normal freezing point of 5.6 °C and a molal freezing point depression constant Kf-7.78 °C-kg·mol-1. A solution is prepared by dissolving some urea ((NH2)2CO) in 550. g of Χ. This solution freezes at-0.9 °C. Calculate the mass of urea that was dissolved. Be sure your answer has the correct number of significant digits.

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Answer:

27.60 g urea

Explanation:

The freezing-point depression is expressed by the formula:

  • ΔT= Kf * m

In this case,

  • ΔT = 5.6 - (-0.9) = 6.5 °C
  • Kf = 7.78 °C kg·mol⁻¹

m is the molality of the urea solution in X (mol urea/kg of X)

First we calculate the molality:

  • 6.5 °C = 7.78 °C kg·mol⁻¹ * m
  • m = 0.84 m

Now we calculate the moles of urea that were dissolved:

550 g X ⇒ 550 / 1000 = 0.550 kg X

  • 0.84 m = mol Urea / 0.550 kg X
  • mol Urea = 0.46 mol

Finally we calculate the mass of urea, using its molecular weight:

  • 0.46 mol * 60.06 g/mol = 27.60 g urea

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