How many moles of ethylene glycol, C 2 H 6 O 2 , must be added to 1,000 g of water to form a solution that has a freezing point of –10ºC?

How many moles of ethylene glycol, which is c 2h602, must be added to a 1000 grams of water to form a solution that has a freezing point of negative 10 degrees Celsius? Alright. So we're gonna say we have delta t f equals I times k f times molality. And in order to find our change in freezing point, remember that freezing point of the solution equals freezing point of solvent minus delta t f. Now our solvent is water, water, pure water freezes at 0 degrees Celsius. The solution, we're told, freezes at negative 10 degrees Celsius. So the 0 drops out, so negative 10 degrees Celsius equals negative delta t f. Dividing both sides by negative one makes it now 10 degrees Celsius equals change in freezing point. So 10 degrees Celsius goes here. Our solute is ethylene glycol, which is covalent in nature. It's only made of nonmetals. Therefore, it doesn't break up into ions, and your Vonth Van't Hoff factor would be 1. Here, the freezing point constant of water is 1.86 degrees Celsius over molality. We don't know the moles of ethylene glycol, And remember here we put kilograms of our solvent. 1,000 grams is equivalent to 1 kilogram. Alright. So then we're going to say, we're going to solve this, we're going to say 10 equals 1.86 x, Divide both sides by 1.86. So here that's gonna give me x equals 5 point, we're gonna say 4 moles of ethylene glycol, c 2h602. So 5.4 would be our final answer.

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14. Solutions

Freezing Point Depression

General Chemistry

14. Solutions

Freezing Point Depression

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Multiple Choice

How many moles of ethylene glycol, C₂H₆O₂, must be added to 1,000 g of water to form a solution that has a freezing point of –10ºC?

334 moles

5.4 moles

3.2 moles

200 moles

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Verified step by step guidance

Identify the formula for freezing point depression: ΔT_f = i * K_f * m, where ΔT_f is the change in freezing point, i is the van't Hoff factor, K_f is the freezing point depression constant for water, and m is the molality of the solution.

Calculate the change in freezing point (ΔT_f) by subtracting the new freezing point (-10ºC) from the normal freezing point of water (0ºC).

Determine the van't Hoff factor (i) for ethylene glycol, C2H6O2. Since it does not dissociate in solution, i = 1.

Use the known K_f value for water, which is 1.86 ºC kg/mol, and rearrange the formula to solve for molality (m): m = ΔT_f / (i * K_f).

Calculate the number of moles of ethylene glycol needed using the formula: moles = molality * mass of solvent (in kg). Convert 1,000 g of water to kg and use the calculated molality to find the moles of ethylene glycol.