Question

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?

Answer 1

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.