Question

1. calculate the volume in ml of a 20.5 mg/ml kanamycin needed to make 500 ml of lb with a final concentration of kanamycin at 23μg/ml. report the answer to one decimal place.

Explanation:

Step1: Convert units

First, convert $20.5\ mg/mL$ to $\mu g/mL$. Since $1\ mg = 1000\ \mu g$, then $20.5\ mg/mL=20.5\times1000 = 20500\ \mu g/mL$.

Step2: Use the dilution - formula

The dilution formula is $C_1V_1 = C_2V_2$, where $C_1$ is the initial concentration, $V_1$ is the initial volume, $C_2$ is the final concentration, and $V_2$ is the final volume.
We know that $C_1 = 20500\ \mu g/mL$, $C_2=23\ \mu g/mL$, and $V_2 = 500\ mL$.
We need to solve for $V_1$. Rearranging the formula gives $V_1=\frac{C_2V_2}{C_1}$.

Step3: Substitute values and calculate

Substitute the values into the formula: $V_1=\frac{23\ \mu g/mL\times500\ mL}{20500\ \mu g/mL}$.
$V_1=\frac{11500}{20500}\ mL\approx5.6\ mL$.

Answer:

$5.6$