Final answer:
To find the percent composition of ethylene glycol in the original sample, we can use the freezing point depression caused by the solute. By calculating the moles of ethylene glycol and propylene glycol in the solution, we can determine the percent composition of ethylene glycol. The percent composition is approximately 20.5%.
Step-by-step explanation:
To calculate the percent composition of ethylene glycol in the original sample, we need to compare the freezing point depression caused by the ethylene glycol and propylene glycol in the solution. From the given data, we know that the freezing point of the solution is -3.40 ∘C. By using the formula for freezing point depression, we can calculate the moles of solute in the solution and then determine the percent composition of ethylene glycol.
Let's denote the moles of ethylene glycol as 'x' and the moles of propylene glycol as 'y'. The moles of solute can be calculated using the colligative property equation:
ΔT = Kf * (msolute * i)
Where ΔT represents the freezing point depression, Kf is the freezing point depression constant, msolute is the molality of the solution, and i is the van't Hoff factor. Since the van't Hoff factor for ethylene glycol is 1 and for propylene glycol is 2, the equation can be written as:
-3.40 ∘C = Kf * (x/(0.1040 kg) + 2 * y/(0.1040 kg))
By solving this equation, we can find the value of x, which represents the moles of ethylene glycol. Then, we can calculate the percent composition using the formula:
Percent composition of ethylene glycol = (moles of ethylene glycol / total moles of solute) * 100%
The resulting percent composition is approximately 20.5%.