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?
16,8,4,2
To find the final concentration of antibiotics in each tube after adding 2 ml of water, we need to consider the dilution factor for each tube.
Let's go through the calculations step by step:
1. Tube 1: The original stock solution of antibiotic has a concentration of 64 mg/ml. It was diluted into a final volume of 4 ml. Therefore, the total amount of antibiotic in the stock solution is 64 mg/ml * 2 ml = 128 mg. When this stock solution is mixed with 2 ml of water, the final volume becomes 4 ml + 2 ml = 6 ml.
To find the final concentration, we divide the total amount of antibiotic (128 mg) by the final volume (6 ml):
Final concentration = 128 mg / 6 ml = 21.33 mg/ml
2. Tube 2: For the second tube, we take 2 ml from tube 1, which has a concentration of 32 mg/ml due to the first dilution. The volume remains constant at 2 ml. When 2 ml of water is added, the final volume becomes 2 ml + 2 ml = 4 ml.
Similarly, for tube 2, the final concentration of antibiotics can be calculated:
Final concentration = 32 mg/ml / 4 ml = 8 mg/ml
3. Tube 3: For tube 3, we take 2 ml from tube 2, which has a concentration of 16 mg/ml due to the second dilution. The volume remains constant at 2 ml. When 2 ml of water is added, the final volume becomes 2 ml + 2 ml = 4 ml.
Calculating the final concentration for tube 3:
Final concentration = 16 mg/ml / 4 ml = 4 mg/ml
4. Tube 4: Finally, for tube 4, we take 2 ml from tube 3, which has a concentration of 8 mg/ml due to the third dilution. The volume remains constant at 2 ml. When 2 ml of water is added, the final volume becomes 2 ml + 2 ml = 4 ml.
Calculating the final concentration for tube 4:
Final concentration = 8 mg/ml / 4 ml = 2 mg/ml
So, the final concentrations of antibiotics in the four tubes, after adding 2 ml of water to each individually, are as follows:
Tube 1: 21.33 mg/ml
Tube 2: 8 mg/ml
Tube 3: 4 mg/ml
Tube 4: 2 mg/ml