If $2.0$ $mu"L"$ of a sample must be diluted by a factor of $50$ , what volume of solvent should be added to accomplish this?

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If $2.0$ $mu"L"$ of a sample must be diluted by a factor of $50$ , what volume of solvent should be added to accomplish this?

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Answer 1 · 2017-12-29T19:46:56

Mix $2.0$ $µ"L"$ of sample with a bit less than $98$ $µ"L"$ of solvent, then add solvent until you reach the $100$ $µ"L"$ mark.

Explanation:

You can use the dilution formula:

$color(blue)(bar(ul(|color(white)(a/a)V_1c_1 = V_2c_2color(white)(a/a)|)))" "$

We can rearrange this formula to get

$V_1 = V_2 × c_2/c_1$

$V_1 = ?; color(white)(mmll)" "" "c_1 = c_1$

$V_2 = "100 µL"; " "" "c_2 = c_1/50$

$V_1 = "100 µL" × (stackrelcolor(blue)(1)color(red)(cancel(color(black)(c_1)))//50)/color(red)(cancel(color(black)(c_1))) = "100 µL" × 1/50 = "2 µL"$

∴ Add a bit less than $98$ $µ"L"$ of solvent to $2$ $µ"L"$ of the sample, then fill up to the mark.

We don't quite add $98$ $µ"L"$ right away because we want to account for any solution volume changes (up/down) due to mixing.

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If $2.0$ $mu"L"$ of a sample must be diluted by a factor of $50$ , what volume of solvent should be added to accomplish this?

1 Answer

Explanation:

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If 2.02.0 mu"L"mu"L" of a sample must be diluted by a factor of 5050, what volume of solvent should be added to accomplish this?

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If $2.0$ $mu"L"$ of a sample must be diluted by a factor of $50$ , what volume of solvent should be added to accomplish this?