Question

calculate the mass in grams to prepare a stock solution of 500μg/ml of ampicillin in 10 ml of sterilized di water
first convert 500μg to grams =
calculation:

write the calculation to prepare a ten - fold dilution (1/10) of ampicillin to get a 50μg/ml concentration in a final volume of 500μl of sterilized di water.

Explanation:

Step1: Calculate mass in stock - solution (in $\mu g$)

$m = C\times V$, where $C = 500\ \mu g/mL$ and $V = 10\ mL$, so $m = 500\ \mu g/mL\times10\ mL = 5000\ \mu g$.

Step2: Convert mass in stock - solution from $\mu g$ to $g$

$m_g=\frac{m}{10^{6}\ \mu g/g}$, substituting $m = 5000\ \mu g$, we get $m_g=\frac{5000\ \mu g}{10^{6}\ \mu g/g}=0.005\ g$.

Step3: Calculate mass in final diluted solution

$m_f = C_f\times V_f$, where $C_f = 50\ \mu g/mL$ and $V_f = 0.5\ mL$, so $m_f = 50\ \mu g/mL\times0.5\ mL = 25\ \mu g$.

Step4: Calculate volume of stock - solution for dilution

Using $C_sV_s = C_fV_f$, solve for $V_s$: $V_s=\frac{C_fV_f}{C_s}$, with $C_s = 500\ \mu g/mL$, $C_f = 50\ \mu g/mL$, and $V_f = 0.5\ mL$, we get $V_s = 0.05\ mL = 50\ \mu L$.

Step5: Calculate volume of diluent

$V_d=V_f - V_s$, substituting $V_f = 500\ \mu L$ and $V_s = 50\ \mu L$, we get $V_d = 450\ \mu L$.

Answer:

1. For preparing the stock - solution:

• First, convert $\mu g$ to $g$. We know that $1\ g = 10^{6}\ \mu g$. So, if the concentration of the stock - solution is $C = 500\ \mu g/mL$ and the volume $V = 10\ mL$.
• The mass $m$ (in $\mu g$) of ampicillin in the stock - solution is $m = C\times V=500\ \mu g/mL\times10\ mL = 5000\ \mu g$.
• To convert $\mu g$ to $g$, we use the conversion factor. Let $m_g$ be the mass in grams. Then $m_g=\frac{5000\ \mu g}{10^{6}\ \mu g/g}=0.005\ g$.

1. For preparing the ten - fold dilution:

• We want a final volume $V_f = 500\ \mu L$ and a final concentration $C_f = 50\ \mu g/mL$. First, convert the final volume to $mL$: $V_f = 500\ \mu L=0.5\ mL$.
• The mass of ampicillin in the final solution $m_f = C_f\times V_f=50\ \mu g/mL\times0.5\ mL = 25\ \mu g$.
• Let the volume of the stock - solution (with concentration $C_s = 500\ \mu g/mL$) be $V_s$. Using the dilution formula $C_sV_s = C_fV_f$.
• We can solve for $V_s$: $V_s=\frac{C_fV_f}{C_s}=\frac{50\ \mu g/mL\times0.5\ mL}{500\ \mu g/mL}=0.05\ mL = 50\ \mu L$.
• The volume of diluent (sterilized DI water) $V_d=V_f - V_s=500\ \mu L - 50\ \mu L = 450\ \mu L$.