A physician order a 25 mgof 1L drug, IM. Add 2ml of diluent to yeild 100mg/2ml. How many ml will you give?
To find out how many ml you will give, you need to calculate the volume of the dilution needed to achieve the desired concentration.
Given:
Desired concentration: 100 mg/2 ml
Ordered dose: 25 mg
Diluent volume: 2 ml
Step 1: Calculate the concentration of the original drug.
Let V1 be the original volume (unknown) and C1 be the original concentration.
Using the dilution equation: C1 * V1 = C2 * V2
C1 * V1 = 100 mg/2 ml * 1 L
C1 * V1 = 50,000 mg/L
C1 = 50,000 mg/L / V1
Step 2: Calculate the volume of the original drug necessary to obtain the ordered dose.
25 mg = C1 * V_dose
25 mg = (50,000 mg/L / V1) * V_dose
V1 * V_dose = 50,000 mg/L / 25 mg = 2,000 L
V1 = 2,000 L / V_dose
Step 3: Calculate the volume you will give.
V_given = V1 + V_diluent
V_given = (2,000 L / V_dose) + 2 ml
Now you can substitute the values into the formula to find the volume you will give.