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Making 10% Ethanol Solution from 50% Stock Solution?

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bflynn13:
I got this question in a research interview and it kind of rattled me. It's been some time since I worked through one of these:

Given a stock solution of 50% ethanol, what volume of stock solution would you add to 10 mL of water?

I was able to get the correct answer via trial and error, but I'm wondering how to do the math for this in the future. (Correct answer is 2.5 mL added to 10 mL of water to give 1.25 mL of EtOH in 12.5 mL of total solution).

Borek:
Actually whether 2.5 mL is a correct answer depends on what kind of concentration you are given - is it 50% (and 10%) w/w, or w/v? Or even v/v?

In the last case things is a bit easier - assume amount to be added is V (unknown). Then final volume is 10+V, you need 10% of 10+V to be pure ethanol, and you know amount of pure ethanol added is 50% of V. Can be written as an equation in one unknown, simple algebra.

Not that the difference will be huge in other cases, but definitely measurable.

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