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Chapter 2: Problem 25

A pharmacy technician is asked to prepare an antibiotic IV solution that will contain 500. mg of cephalosporin for every 100 . \(\mathrm{mL}\) of normal saline solution. The total volume of saline solution will be 1 L. How many grams of the cephalosporin will be needed for this IV solution?

Short Answer

Expert verified
5 grams

Step by step solution

01

- Convert Total Volume to Milliliters

Convert the total volume from liters to milliliters. Since 1 liter (L) is equivalent to 1000 milliliters (mL), the total volume will be 1000 mL.
02

- Set Up Proportion

Set up a proportion to determine how many milligrams of cephalosporin are needed for 1000 mL of saline solution. Given that 500 mg of cephalosporin are required for every 100 mL of saline, this can be written as: \( \frac{500 \text{ mg}}{100 \text{ mL}} = \frac{x \text{ mg}}{1000 \text{ mL}} \)
03

- Solve the Proportion for x

Cross-multiply and solve for the variable x (the amount of cephalosporin in milligrams needed for 1000 mL): \( 500 \text{ mg} \times 1000 \text{ mL} = 100 \text{ mL} \times x \text{ mg} \). Simplify to get: \( 500,000 = 100x \). Divide both sides by 100: \( x = \frac{500,000}{100} \). This simplifies to: \( x = 5000 \text{ mg} \).
04

- Convert Milligrams to Grams

Convert the amount of cephalosporin needed from milligrams to grams. Since 1000 milligrams (mg) is equivalent to 1 gram (g), \( 5000 \text{ mg} = \frac{5000}{1000} = 5 \text{ g} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Unit Conversion
Unit conversion is a fundamental skill in chemistry and pharmacy calculations. It involves converting measurements from one unit to another, ensuring consistency in the quantities used. In this problem, we converted liters to milliliters and milligrams to grams.
To convert a larger unit to a smaller unit (liters to milliliters), multiply by the conversion factor:
  • 1 L = 1000 mL
Similarly, convert milligrams to grams by dividing:
  • 1000 mg = 1 g
Mastering these conversions simplifies your calculations and helps in maintaining accuracy.
Proportions
Proportions help us find an unknown quantity by setting up equivalent ratios. In this exercise, we used proportions to determine the required amount of cephalosporin for a given volume of saline solution.
We set up the proportion using the known ratio of cephalosporin to saline:
  • \(\frac{500 \text{ mg}}{100 \text{ mL}} = \frac{x \text{ mg}}{1000 \text{ mL}} \)
This equation shows us that the ratio of cephalosporin to saline remains constant. Cross-multiplying and solving for the unknown variable (x) allows us to maintain this proportion across different volumes.
Dimensional Analysis
Dimensional analysis, or the factor-label method, is a powerful tool in chemistry for converting units and solving problems involving measurements. It checks that units cancel appropriately in calculations.
For example, we started with a volume in liters and needed to convert it to milliliters:
  • \(1 \text{ L} \times \frac{1000 \text{ mL}}{1 \text{ L}} = 1000 \text{ mL}\)
Next, we determined the amount of cephalosporin through setting proportions and solved for the desired unit, milligrams, before converting to grams through dimensional analysis:
  • \(5000 \text{ mg} \times \frac{1 \text{ g}}{1000 \text{ mg}} = 5 \text{ g}\)
Ensuring proper dimensional alignment is crucial in pharmacy calculations.
Pharmacy Calculations
Pharmacy calculations are vital in preparing accurate medicinal dosages. They often involve unit conversion, proportions, and dimensional analysis. Let's walk through the steps as applied in this exercise:
  • Convert total saline volume from liters to milliliters: 1 L = 1000 mL
  • Set up a proportion for cephalosporin adding to 1000 mL of saline. Given \(\frac{500 \text{ mg}}{100 \text{ mL}} = \frac{x \text{ mg}}{1000 \text{ mL}}\).
  • Solve for x by cross-multiplying and dividing: x = 5000 mg.
  • Convert 5000 mg to grams: 5000 mg ÷ 1000 = 5 g
Accurate pharmacy calculations ensure patients receive the correct medication strength. This exercise helps build these essential skills.

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Most popular questions from this chapter

Dark-roasted coffee contains increased amonts of Nmethylpyridinium, or NMP, a ringed compound that is not present in green unroasted coffee beans. This compound seems to decrease the stomach acid production normally associated with drinking coffee. In coffee made from dark-roasted coffee, the concentration of NMP is \(31.4 \mathrm{mg} / \mathrm{L}\). How many milligrams of NMP would you consume if you drank \(2.00\) large cups of dark-roasted coffee? (One coffee cup contains \(10.0\) fluid ounces of liquid.)

Jodi, a sculptor, has prepared a mold for casting a bronze figure. The figure has a volume of \(225 \mathrm{~mL}\). If bronze has a density of \(7.8 \mathrm{~g} / \mathrm{mL}\) and Jodi likes to use \(90.0 \%\) of the bronze melted (she sometimes spills), how many ounces of bronze does Jodi need to melt in the preparation of the bronze figure?

A \(35.0-\mathrm{mL}\) sample of ethyl alcohol (density \(0.789 \mathrm{~g} / \mathrm{mL}\) ) is added to a graduated cylinder that has a mass of \(49.28 \mathrm{~g}\). What will be the mass of the cylinder plus the alcohol?

A \(25.27\)-g sample of pure sodium was prepared for an experiment. How many \(\mathrm{mL}\) of sodium is this? (Density of sodium is \(0.97 \mathrm{~g} / \mathrm{mL}\).)

Forgetful Freddie placed \(25.0 \mathrm{~mL}\) of a liquid in a graduated cylinder with a mass of \(89.450 \mathrm{~g}\) when empty. When Freddie placed a metal slug with a mass of \(15.454\) g into the cylinder, the volume rose to \(30.7 \mathrm{~mL}\). Freddie was asked to calculate the density of the liquid and of the metal slug from his data, but he forgot to obtain the mass of the liquid. He was told that if he found the mass of the cylinder containing the liquid and the slug, he would have enough data for the calculations. He did so and found its mass to be \(125.934 \mathrm{~g}\). Calculate the density of the liquid and of the metal slug.
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