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

Answer:

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.