I have a 200 mg/ml ampiciline solution, how much should i add to 300 ml of LB medium to get the final concentration of 40 ug/ml?? How much bacteria (in ml) should i add to 75 ml of medium to dilute the culture 50 times??
You can simply use the dilution law C1V1=C2V2 where C1 is the concentration of your ampiciline solution (i.e. 200 mg/ml), C2 is the final concentration of the diluted ampiciline solution (i.e. 0.04 mg/ml), V2 is the total volume (i.e. 300 ml) and V1 is the is the sought volume to add. So V1 = C2V2/C1.
N.A: V1=0.04*300/200. V1=0.06 ml that’s mean 60 µl. However, if you are not yet prepared your stock solution, I suggest you preparing a new stock with 12 mg/ml (12 g/l) to get a more accurate measured V1 volume (1 ml after calculation).
Concerning your second question, the dilution time D means the total solution (i.e. 75 ml) volume per the added volume (D=Vtotal/Vadd), so Vadd ( bacterial volume in ml) = Vtot/D. N.A: Vadd = 75/50. V add=1.5 ml this means that you should add 1.5 ml of bacteria and complete to 75 ml with your medium.