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Calculate the molarity of a solution of ethanol in water in which the mole fraction is 0.040 assume that the density of water to be one?


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June 25, 2013 6:03PM

It depends a bit on what information you are given. However, the principle is the same in all cases, although how you do the specific calculation may vary a bit.

As an example, let's say we have a mixture of 5.00 grams of water and 10.0 grams of ethanol (C2H5OH). What is the mole fraction of the two components?

The first thing we must do is convert the number of grams of each substance into moles. To do that, see the Related Question below:

How do you convert from grams to moles and also from moles to grams?

For water, we have:

5.00 grams ÷ 18.015 grams/mole = 0.2775 moles H2O

For ethanol, we have:

10.0 grams ÷ 46.068 grams/mole = 0.2171 moles C2H5OH

Now we can find the mole ratio, which is defined as follows:

Moles ratio of compound X = number of moles of X ÷ total number of moles in mixture

So the mole ratio of water is: 0.2775 ÷ (0.2775 + 0.2171) = 0.561 or 56.1%

and the mole ratio of ethanol is: 0.2171 ÷ ((0.2775 + 0.2171) = 0.439 or 43.9%

Check your answer! The total mole ratio for all components MUST add up to 1.00:

0.561 + 0.439 = 1.00 Yes!

Note that the weight ratio was 1-to-2 (twice as much ethanol as water by weight), but the mole ratio was completely different.