Question
To make 100mL of 5mg/mL using a stock solution of 50mg/mL, how much stock solution is needed?
A. 100mL stock solution
B. 10mL stock solution
C. 90mL stock solution
D. 1000mL stock solution
Answers
GPT-4o mini
To make a solution of 5 mg/mL from a stock solution of 50 mg/mL, we can use the dilution equation:
\[
C_1V_1 = C_2V_2
\]
Where:
- \(C_1\) is the concentration of the stock solution (50 mg/mL)
- \(V_1\) is the volume of the stock solution needed
- \(C_2\) is the concentration of the diluted solution (5 mg/mL)
- \(V_2\) is the volume of the diluted solution (100 mL)
We can rearrange the equation to solve for \(V_1\):
\[
V_1 = \frac{C_2 V_2}{C_1}
\]
Substituting the known values:
\[
V_1 = \frac{(5 \, \text{mg/mL})(100 \, \text{mL})}{50 \, \text{mg/mL}}
\]
\[
V_1 = \frac{500 \, \text{mg}}{50 \, \text{mg/mL}} = 10 \, \text{mL}
\]
Thus, you need 10 mL of the stock solution.
The correct answer is **B. 10 mL stock solution**.
\[
C_1V_1 = C_2V_2
\]
Where:
- \(C_1\) is the concentration of the stock solution (50 mg/mL)
- \(V_1\) is the volume of the stock solution needed
- \(C_2\) is the concentration of the diluted solution (5 mg/mL)
- \(V_2\) is the volume of the diluted solution (100 mL)
We can rearrange the equation to solve for \(V_1\):
\[
V_1 = \frac{C_2 V_2}{C_1}
\]
Substituting the known values:
\[
V_1 = \frac{(5 \, \text{mg/mL})(100 \, \text{mL})}{50 \, \text{mg/mL}}
\]
\[
V_1 = \frac{500 \, \text{mg}}{50 \, \text{mg/mL}} = 10 \, \text{mL}
\]
Thus, you need 10 mL of the stock solution.
The correct answer is **B. 10 mL stock solution**.