Question

a pharmacy technician dilutes a 1 g vial of cefazolin (ancef) to 100 mg/ml. which of the following is the amount of solution the technician should use to compound a 500 mg dose?
2.5 ml
10 ml
0.5 ml
5 ml

Explanation:

Step1: Convert units to be consistent

We know that \(1\space g = 1000\space mg\), but the concentration is given as \(100\space mg/mL\). We need to find the volume for \(500\space mg\) dose. The formula for volume \(V\) when we know mass \(m\) and concentration \(C\) (where \(C=\frac{m}{V}\)) is \(V=\frac{m}{C}\).

Step2: Plug in the values

Here, \(m = 500\space mg\) and \(C = 100\space mg/mL\). So \(V=\frac{500\space mg}{100\space mg/mL}\)

Step3: Calculate the volume

\(\frac{500}{100}=5\space mL\)? Wait, no, wait. Wait, the concentration is \(100\space mg\) per \(mL\), so to get \(500\space mg\), we do \(500\div100 = 5\)? Wait, no, wait, let's check again. Wait, the vial is \(1\space g = 1000\space mg\) diluted to \(100\space mg/mL\), so the total volume of the solution is \(1000\space mg\div100\space mg/mL = 10\space mL\), but we need \(500\space mg\) dose. So using \(C=\frac{m}{V}\), so \(V=\frac{m}{C}\), \(m = 500\space mg\), \(C = 100\space mg/mL\), so \(V=\frac{500}{100}=5\space mL\)? Wait, no, wait, maybe I made a mistake. Wait, no, let's re - express:

Concentration \(C = 100\space mg\) per \(1\space mL\). So if we need \(500\space mg\), then the volume \(V\) is such that \(100\space mg/mL\times V=500\space mg\). Solving for \(V\), we get \(V=\frac{500\space mg}{100\space mg/mL}=5\space mL\)? Wait, but let's check the options. Wait, the options are 2.5 mL, 10 mL, 0.5 mL, 5 mL. Wait, maybe I messed up the concentration. Wait, the vial is \(1\space g = 1000\space mg\), and it's diluted to \(100\space mg/mL\), so the total volume of the solution is \(1000\space mg\div100\space mg/mL = 10\space mL\). But we need \(500\space mg\) of the drug. Since the concentration is \(100\space mg\) per \(mL\), then for \(500\space mg\), the volume is \(500\div100 = 5\space mL\). Wait, but let's do it again.

The formula for volume in pharmacy calculations (when using concentration \(C\) in \(mg/mL\), mass \(m\) in \(mg\)) is \(Volume (mL)=\frac{Mass (mg)}{Concentration (mg/mL)}\)

Given \(m = 500\space mg\), \(C = 100\space mg/mL\)

So \(Volume=\frac{500}{100}=5\space mL\)

Wait, but let's check the options. The last option is 5 mL. So that's the answer.

Answer:

\(5\space mL\) (the option with "5 mL")