2 ml of stock antibiotic (64 mg/ml) was diluted into a test tube containing 2 ml of broth (final volume is 4). A series of 2-fold SERIAL DILUTIONS were performed by transferring 2 ml to three other tubes, consecutively (final volumes now 2 ml in each tube). The final concentrations of antibiotic in the four tubes are: 32, 16, 8, and 4.

Question

2 ml of stock antibiotic (64 mg/ml) was diluted into a test tube containing 2 ml of broth (final volume is 4). A series of 2-fold SERIAL DILUTIONS were performed by transferring 2 ml to three other tubes, consecutively (final volumes now 2 ml in each tube). The final concentrations of antibiotic in the four tubes are: 32, 16, 8, and 4.

Next, 2 ml of water were added to each each tube individually (not a serial dilution). What is the final concentration of antibiotics in the tubes?

Answer 1

Make a table and everything would be clear.

stock totVol concentration
2 4 32 (2*64/4=32)
2 8 16 (2*64/8=16)
2 16 8
2 32 4

Now if 2 mL of water are added to each, then concentration would be:

stock totVol concentration
2 6 32 (2*64/6=21.3)
2 10 16 (2*64/10=12.8)
2 18 8 ...
2 34 4 ...

Complete the above table to get the concentrations (mg/mL)

Answer 2

To determine the final concentration of antibiotics in each tube after adding 2 ml of water to each tube, we need to consider the dilution factor.

Let's start with the first tube, which contains 2 ml of the stock antibiotic (64 mg/ml) diluted into 2 ml of broth, resulting in a total volume of 4 ml. The initial concentration can be calculated as follows:

Initial concentration = (initial antibiotic volume * initial antibiotic concentration) / final volume
= (2 ml * 64 mg/ml) / 4 ml
= 128 mg/ml

Now, after the serial dilutions, the volume in each tube is 2 ml. The dilution factor for each transfer is 2-fold, which means that the concentration will be halved after each dilution.

To find the concentration in each tube after serial dilutions, we can apply the following calculations:

Tube 1: 32 mg/ml (half of 64 mg/ml)
Tube 2: 16 mg/ml (half of 32 mg/ml)
Tube 3: 8 mg/ml (half of 16 mg/ml)
Tube 4: 4 mg/ml (half of 8 mg/ml)

So, after the serial dilutions, the concentrations in the four tubes are 32, 16, 8, and 4 mg/ml, respectively.

Now, 2 ml of water is added to each tube individually. This means that the total volume in each tube will increase from 2 ml to 4 ml (2 ml from the original tube volume + 2 ml from the added water).

To calculate the final concentration in each tube after adding water, we can use the following equation:

Final concentration = (initial concentration * initial volume) / final volume
= (initial concentration * 2 ml) / 4 ml

Applying this equation to each tube, we find the final concentrations after adding water as follows:

Tube 1: (32 mg/ml * 2 ml) / 4 ml = 16 mg/ml
Tube 2: (16 mg/ml * 2 ml) / 4 ml = 8 mg/ml
Tube 3: (8 mg/ml * 2 ml) / 4 ml = 4 mg/ml
Tube 4: (4 mg/ml * 2 ml) / 4 ml = 2 mg/ml

So, the final concentrations of antibiotics in the tubes after adding 2 ml of water are: 16 mg/ml, 8 mg/ml, 4 mg/ml, and 2 mg/ml in Tube 1, Tube 2, Tube 3, and Tube 4, respectively.