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Here’s your Shmoop du jour, brought to you by moles, helping you dig into chemistry the [A mole with two dinosaurs fighting]

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dawn of time.

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Let's burrow into the following question…

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Fergie wanted to make lemonade from a mix that consisted primarily of sugar.

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She prepared the lemonade solution by adding 0.50 mol of a sugar mix (solute) with 1.00

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mol of water (solvent).

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What is the mole fraction of the solvent?

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Here are the potential answers.. lot of numbers..

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In order to satisfy Fergie’s craving, we're going to have to find some black eyed peas… [Black eyed peas stirring lemonade]

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But if you just don't have those on hand, math will work just fine, too.

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The question is asking us what mole fraction the solvent is.

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So it might be helpful to know what mole fractions and solvents are before we dive in. [Lots of moles in the ground]

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Well, the question conveniently tells us the solvent is water. [A girl drinking from a bottle of water]

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If only all things in the wonderful world of AP-land were so easy…

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And mole fraction doesn't refer to the unfortunate outcome of moles in The Texas Chainsaw Massacre… [A theatre showing the Texas Chainsaw Massacre on screen]

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What the question actually means by mole fraction is simply what fraction of the total stuff

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is the particular stuff we care about.

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Kind of like if we were at a buffet that only offered two options: chocolate, [People holding plates at a buffet]

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or asparagus-wrapped eggplant.

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So what fraction of the buffet do we care about, or, what fraction of the buffet is

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chocolate?

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Also, where do we find a better buffet…?

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Okay, back to the question…how much total stuff do we have? [Person sitting with feet up watching hoarders on TV]

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Well, we have one mole of water and half a mole of sugar, so that gives us 1.50 total

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moles of things in the mixture.

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Since the question conveniently told us that the water is the solvent, we know that’s [A glass filling with water]

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what we need to know the fraction of.

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Now comes the scary part…

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We're talking math.

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But don't worry, it’s not that terrifying. [A kitten sat with a calculator]

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All we have to do is divide the moles of the solvent by the total moles in the mixture.

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We take 1.00 moles and divide it by 1.50 moles to give a mole fraction of 0.6666666666….

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and let’s just round that to 0.667.

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That means the answer is B.

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But just for kicks and giggles, let's check out the rest of the answers. [Guy kicks friend in his leg]

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Sounds almost as fun as chowing down at the chocolate, asparagus, eggplant buffet. [Man eating at a buffet and face turns green]

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Since a mole fraction is some fraction of the total, it can’t be bigger than 1, which

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rules out answer A.

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Answer D, 0.500, says that half of the mixture would be water, which means there would be [A glass of water and a pile of sugar]

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equal amounts water and sugar.

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But if we look at the amounts we're given, 1 mole is more than 0.5 moles, so the fraction

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should indicate that there is more water than there is sugar.

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Answer D is out.

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Similarly, answer C, 0.333, says that there is less water than sugar, which is also wrong.

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Which leaves us with answer B again.

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Phew. [Girl standing at a lemonade stand]

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Time to wash that answer down with some refreshing lemonade and….

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…Great.

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All we have is eggplant and asparagus. [Eggplant and asparagus appear on a table of lemonade]

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Seriously people, we need a new buffet around here c'mon.

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