Respuesta :

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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 i is the van't Hoff factor (2 for KNO₃)

We solve for b:

  • 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 calculate the necessary moles of KNO₃:

  • 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 convert KNO₃ moles to grams, using its molecular weight:

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

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