Question

section 3.4 dosages and concentrations
objective 1 - compare dosages and concentrations
objective 2 - understand density
objective 1 - compare dosages and concentrations
guided practice activity #8 - dosages and concentrations
common conversions

1. medicine is ordered at 0.048 g and comes mixed in solution at 25 mg/100 ml. how many ml should be administered?
2. a doctor orders 2.3 g of rocephin to be taken by a 15 lb. 6 oz. infant every 8 hours. the recommended dosage is 75 - 100 mg/kg per day. is the ordered amount within the recommended range?

Explanation:

Step1: Convert grams to milligrams

Since \(1\ g = 1000\ mg\), for the first problem, \(0.048\ g=0.048\times1000 = 48\ mg\).

Step2: Set up a proportion

The concentration is \(25\ mg/100\ ml\). Let \(x\) be the volume in \(ml\). We have the proportion \(\frac{25\ mg}{100\ ml}=\frac{48\ mg}{x}\).
Cross - multiply: \(25x = 48\times100\).

Step3: Solve for \(x\)

\(x=\frac{48\times100}{25}\).
\(x = 192\ ml\).

Step4: Convert the infant's weight to kilograms (for the second problem)

First, convert \(15\ lb\ 6\ oz\) to ounces. \(15\ lb=15\times16 = 240\ oz\), so total ounces \(=240 + 6=246\ oz\).
Since \(1\ oz\approx28.3495\ g\) and \(1\ kg = 1000\ g\), the weight in kilograms: \(w=\frac{246\times28.3495}{1000}\approx6.97\ kg\).

Step5: Calculate the recommended dosage range per day

The lower limit: \(75\ mg/kg\times6.97\ kg = 522.75\ mg\).
The upper limit: \(100\ mg/kg\times6.97\ kg=697\ mg\).
The ordered amount per day: Since it is ordered every \(8\) hours (\(3\) times a day), \(2.3\ g\times3 = 6.9\ g=6900\ mg\) (this is wrong, we should convert \(2.3\ g\) per dose to \(mg\) per dose: \(2.3\ g = 2300\ mg\) per dose. Per day (3 doses): \(2300\times3=6900\ mg\) (error in previous thought, correct way: convert weight correctly. \(1\ lb = 0.453592\ kg\), \(15\ lb=15\times0.453592 = 6.80388\ kg\), \(6\ oz=\frac{6}{16}\ lb = 0.375\ lb\), \(0.375\ lb\times0.453592\ kg/lb\approx0.170\ kg\), total weight \(w = 6.80388+0.170\approx6.97\ kg\). Ordered dose per day: \(2.3\ g\times3 = 6.9\ g=6900\ mg\). Recommended: lower \(75\times6.97 = 522.75\ mg\), upper \(100\times6.97 = 697\ mg\). The ordered amount (\(6900\ mg\)) is not within the range.

Answer:

1. \(192\ ml\)
2. No, the ordered amount is not within the recommended range.