Problem

The doctor orders morphine sulfate $13.2 \mathrm{mg}$ subcutaneously every 4 hours as needed for pain for a female weighing 73 pounds. The recommended maximum dose for a child is 0.1 to $0.2 \mathrm{mg} / \mathrm{kg} / \mathrm{dose}$. Morphine sulfate is available in $22 \mathrm{mg}$ per $1 \mathrm{~mL}$. How many milliliters would be drawn for this dosage? After calculating the dosage, determine if the dosage is therapeutic. If it is not, what is the correct therapeutic dosage? For this dosage $\square \mathrm{mL}$ would be drawn. (Type an integer or a decimal.)

Solution

Step 1 :First, convert the weight from pounds to kilograms since the recommended dosage is given in mg/kg. We know that 1 pound is approximately 0.453592 kg. So, the weight in kg is \(73 \times 0.453592 = 33.112216 \, \text{kg}\).

Step 2 :Next, calculate the volume of morphine sulfate to be drawn by dividing the ordered dosage by the concentration. So, the volume is \(\frac{13.2}{22} = 0.6 \, \text{mL}\).

Step 3 :Then, calculate the dosage in mg/kg by dividing the ordered dosage by the weight in kg. So, the dosage is \(\frac{13.2}{33.112216} = 0.3986444157044639 \, \text{mg/kg}\).

Step 4 :Check if the dosage is therapeutic by comparing it with the recommended dosage. The dosage is not therapeutic as it is greater than the maximum recommended dosage of 0.2 mg/kg.

Step 5 :Finally, calculate the correct therapeutic dosage. The correct therapeutic dosage is the minimum recommended dosage of 0.1 mg/kg times the weight in kg. So, the correct dosage is \(0.1 \times 33.112216 = 3.3112215999999997 \, \text{mg}\).

Step 6 :And the correct volume to be drawn for this dosage is \(\frac{3.3112215999999997}{22} = 0.1505100727272727 \, \text{mL}\).

Step 7 :Final Answer: For the ordered dosage, \(0.6 \, \text{mL}\) would be drawn. However, the dosage is not therapeutic. The correct therapeutic dosage is approximately \(3.31 \, \text{mg}\), for which approximately \(0.15 \, \text{mL}\) would be drawn. Therefore, the answer is \(\boxed{0.6}\).

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Source: https://solvelyapp.com/problems/17760/

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