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Question

Calculate the molarity of a solution of ethanol in water in which the mole fraction of ethanol is 0.040.

[Assume the density of water to be one]

Solution
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The mole fraction of ethanol is equal to the ratio of the number of moles of ethanol to the total number of moles present in the solution.

For dilute solutions, 1 L of water (or 1 L of solution) contains 100018=55.55 moles of water.

Let n be the number of moles of ethanol. The mole fraction of ethanol is 0.040.

Hence, 0.040=nn+55.55

n=0.040n+2.222

n=2.22210.040=2.31 moles.

The molarity of the solution is the ratio of the number of moles of solute present in 1 L of solution.

As 1 L of solution contains 2.31 moles of ethanol, the molarity of a solution is 2.31 M.

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