Question

Using conversion factors, solve each of the following clinical problems: a. You have used 250 L of distilled water for a dialysis patient. How many gallons of water is that? b. A patient needs $0.024\mathrm{g}$ of a sulfa drug. There are $8-\mathrm{mg}$ tablets in stock. How many tablets should be given? c. The daily dose of ampicillin for the treatment of an ear infection is $115\mathrm{mg}/\mathrm{kg}$ of body weight. What is the daily dose for a 34-lb child?

Short answer

a. 66.043 gallonsb. 3 tabletsc. 1774 mg

Step-by-step solution

Convert Liters to Gallons

To convert 250 liters of distilled water to gallons, use the conversion factor: 1 liter = 0.264172 gallons. Multiply 250 by 0.264172.$$250\text{ L}\times 0.264172\frac{\text{gallons}}{\text{L}}=66.043\text{ gallons}$$

Convert Grams to Tablets

To find how many 8-mg tablets are needed for a 0.024 g sulfa drug dose, first convert grams to milligrams (1000 mg = 1 g). Then divide the total milligrams by the mg per tablet.$$0.024\text{ g}\times 1000\frac{\text{mg}}{\text{g}}=24\text{ mg}$$$$\frac{24\text{ mg}}{8\text{ mg/tablet}}=3\text{ tablets}$$

Convert Pounds to Kilograms

To calculate the daily dose of ampicillin, first convert the child's weight from pounds to kilograms. Use the conversion factor: 1 lb = 0.453592 kg.$$34\text{ lbs}\times 0.453592\frac{\text{kg}}{\text{lbs}}=15.4221\text{ kg}$$

Calculate Daily Dose

Now, multiply the child's weight in kilograms by the dosage in mg/kg to get the daily dose.$$115\text{ mg/kg}\times 15.4221\text{ kg}=1773.5415\text{ mg}$$Round to a suitable precision, such as 1774 mg.

Key concepts

Conversion Factors

Understanding conversion factors is fundamental in clinical problem-solving in chemistry. A conversion factor is a ratio that represents the relationship between two different units. It is used to convert one unit to another without changing the quantity's value. For instance, knowing that 1 liter is equal to 0.264172 gallons, allows you to convert 250 liters of distilled water into gallons easily.
To perform the conversion, you multiply the quantity you have (250 liters) by the conversion factor (0.264172 gallons per liter). So the calculation looks like: a) 250 L x 0.264172 (gallons/L) = 66.043 gallonsUsing conversion factors is crucial in healthcare settings. It ensures accurate dosing, which can significantly impact patient outcomes. Always remember:

• Identify the units you want to convert.
• Find the appropriate conversion factor.
• Multiply the quantity by the conversion factor.

Dosage Calculation

Dosage calculation ensures that patients receive the correct amount of medication. In clinical settings, medications might be available in different forms or concentrations. Let's understand how to calculate dosage using conversion factors. For instance, a patient needs 0.024 g of a sulfa drug, but the tablets available are 8 mg each.
You first need to convert grams to milligrams since 1 gram = 1000 milligrams. Like so:b) 0.024 g x 1000 (mg/g) = 24 mgNext, you find out how many tablets are needed. Each tablet contains 8 mg, so:24 mg / 8 mg (per tablet) = 3 tabletsTop tips for dosage calculations include:

• Always convert to the same unit before dividing or multiplying.
• Check the concentration of the medication.
• Double-check your work to prevent errors.

Unit Conversion

Unit conversion is essential in healthcare for accurately measuring and administering treatments. Units could be in weight (pounds to kilograms), volume (liters to gallons), or dosage (grams to milligrams). For example, to calculate the daily dose of ampicillin for a child weighing 34 pounds, you first convert pounds to kilograms.
The conversion factor is 1 lb = 0.453592 kg.c) 34 lbs x 0.453592 (kg/lb) = 15.4221 kgNow, multiply the child's weight in kilograms by the recommended dosage in mg/kg:115 mg/kg x 15.4221 kg = 1773.5415 mgAfter rounding, the daily dose is approximately 1774 mg.
For effective unit conversion:

• Always ensure the initial and final units match.
• Use accurate conversion factors.
• Check your work for precision and accuracy.