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Dennis_Churaev [7]
2 years ago
9

Assuming complete dissociation of the solute, how many grams of KNO3 must be added to 275 mL of water to produce a solution that

freezes at −14.5 ∘C
Chemistry
1 answer:
iragen [17]2 years ago
5 0

Answer:

108.43 grams KNO₃

Explanation:

To solve this problem we use the formula:

  • ΔT = Kf * b * i

Where

  • ΔT is the temperature difference (14.5 K)
  • Kf is the cryoscopic constant (1.86 K·m⁻¹)
  • b is the molality of the solution (moles KNO₃ per kg of water)
  • and<em> i</em> is the van't Hoff factor (2 for KNO₃)

We <u>solve for b</u>:

  • 14.5 K = 1.86 K·m⁻¹ * b * 2
  • b = 3.90 m

Using the given volume of water and its density (aprx. 1 g/mL) we <u>calculate the necessary moles of KNO₃</u>:

  • 275 mL water ≅ 275 g water
  • 275 g /1000 = 0.275 kg
  • moles KNO₃ = molality * kg water = 3.90 * 0.275
  • moles KNO₃ = 1.0725 moles KNO₃

Finally we <u>convert KNO₃ moles to grams</u>, using its molecular weight:

  • 1.0725 moles KNO₃ * 101.103 g/mol = 108.43 grams KNO₃
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