QuestionA child weighing 32 lb needs acetaminophen. Calculate mg in 1/2 tsp and check if it's safe based on 25-35 mg/kg/day.

Studdy Solution

STEP 1

Assumptions1. The child's weight is32 lb. The recommended dose of acetaminophen is25-35 mg/kg/day3. Acetaminophen is supplied as325 mg/10 mL4.1 teaspoon is approximately5 mL5. The physician's order is for1/ tsp every4 hours as needed for fever

STEP 2

First, we need to convert the child's weight from pounds to kilograms since the recommended dose is in mg/kg. We can do this using the conversion factor1 kg =2.20462 lb.
$Weight_{kg} = Weight_{lb} /2.20462$

STEP 3

Now, plug in the given value for the child's weight to calculate the weight in kilograms.
$Weight_{kg} =32\,lb /2.20462$

STEP 4

Calculate the child's weight in kilograms.
$Weight_{kg} =32\,lb /2.20462 \approx14.515\,kg$

STEP 5

Next, we need to find out how many mg of acetaminophen are in a1/2 teaspoon. We can do this by first finding out how many mg are in1 mL, and then multiplying by the volume of a1/2 teaspoon.
$Acetaminophen_{mg/mL} = Acetaminophen_{mg} / Volume_{m}$

STEP 6

Now, plug in the given values for the acetaminophen and volume to calculate the amount of acetaminophen per mL.
$Acetaminophen_{mg/mL} =325\,mg /10\,m$

STEP 7

Calculate the amount of acetaminophen per mL.
$Acetaminophen_{mg/mL} =325\,mg /10\,m =32.5\,mg/mL$

STEP 8

Now that we have the amount of acetaminophen per mL, we can find out how many mg are in a1/2 teaspoon. Since1 teaspoon is approximately5 mL, a1/2 teaspoon is2.5 mL.
$Acetaminophen_{1/2\,tsp} = Acetaminophen_{mg/mL} \times Volume_{1/2\,tsp}$

STEP 9

Plug in the values for the acetaminophen per mL and the volume of a/2 teaspoon to calculate the amount of acetaminophen in a/2 teaspoon.
$Acetaminophen_{/2\,tsp} =32.5\,mg/mL \times2.5\,m$

STEP 10

Calculate the amount of acetaminophen in a/2 teaspoon.
$Acetaminophen_{/2\,tsp} =32.5\,mg/mL \times2.5\,m =81.25\,mg$

STEP 11

Now, we need to check if this is a safe dose. The recommended dose is25-35 mg/kg/day, and the physician's order is for/ tsp every4 hours as needed for fever. This means the child could potentially receive6 doses in a day. $Total\,daily\,dose = Acetaminophen_{/\,tsp} \times Number\,of\,doses$

STEP 12

Plug in the values for the acetaminophen in a/2 teaspoon and the number of doses to calculate the total daily dose.
$Total\,daily\,dose =81.25\,mg \times6$

STEP 13

Calculate the total daily dose.
$Total\,daily\,dose =81.25\,mg \times6 =487.5\,mg$

STEP 14

Now, we need to compare this with the recommended daily dose for the child's weight. The recommended dose is25-35 mg/kg/day.
$Recommended\,daily\,dose = Weight_{kg} \times Recommended\,dose_{mg/kg/day}$

STEP 15

Plug in the values for the child's weight and the recommended dose to calculate the recommended daily dose.
$Recommended\,daily\,dose =14.515\,kg \times25\,mg/kg/day\, to\,35\,mg/kg/day$

STEP 16

Calculate the recommended daily dose.
$Recommended\,daily\,dose =14.515\,kg \times25\,mg/kg/day\, to\,35\,mg/kg/day =362.875\,mg/day\, to\,508.025\,mg/day$

STEP 17

Compare the total daily dose with the recommended daily dose. If the total daily dose is within the range of the recommended daily dose, then it is a safe dose.
The total daily dose of487.5 mg is within the recommended range of362.875 mg/day to508.025 mg/day, so it is a safe dose.

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