Problem 24 - Calculate With Confidence

Question

Calculate the dosages as indicated. Use the labels where provided. Order: Magnesium sulfate \(3 \mathrm{~g} / \mathrm{hr}\). Available: \(25 \mathrm{~g}\) of \(50 \%\) magnesium sulfate in \(300 \mathrm{~mL}\) D5W. What rate in \(\mathrm{mL} / \mathrm{hr}\) would be needed to administer the required dose?

Step-by-Step Solution

Answer

The rate needed is 36 mL/hr.

Step 1: Understand the Concentration

The solution available is 25g of magnesium sulfate in 300 mL of D5W. A 50% solution means there are 25g in 300 mL. This concentration can be calculated as 25g per 300mL.

Step 2: Calculate Concentration Per mL

To find out how much magnesium sulfate is in 1 mL, divide the total grams of magnesium sulfate by the total volume in mL.\[\text{Concentration} = \frac{25 \text{ g}}{300 \text{ mL}} = \frac{1}{12}\text{ g/mL}\]

Step 3: Set Up the Proportion for Desired Dosage

You need to administer 3 g/hr. Use the concentration to find how many mL/hr are required to deliver the dosage:Let \( x \) be the volume in mL/hr.\[\frac{1}{12} \text{ g/mL} \times x \text{ mL/hr} = 3 \text{ g/hr}\]

Step 4: Solve the Proportion

Solve for \( x \) by multiplying both sides by 12.\[x = 3 \times 12 = 36 \text{ mL/hr}\]

Step 5: Final Check

Verify that with this rate, the dosage of magnesium sulfate delivered is correct:\(36 \text{ mL/hr} \times \frac{1}{12} \text{ g/mL} = 3 \text{ g/hr}\). The calculation confirms the administration of the correct dosage.

Key Concepts

Mediction Concentration

Medication concentration refers to the amount of a substance (often a drug) present within a given volume of liquid. In medical settings, it is expressed as grams per milliliter (g/mL). Understanding and calculating concentration is crucial because it directly affects how we prepare dosages.

In the exercise example, we have magnesium sulfate where 25 grams are dissolved in 300 mL of D5W solution. This is described as a 50% solution. To comprehend this better, think about how every milliliter contains a fraction of those total 25 grams.

When you want to determine concentration in terms of per milliliter, you need to divide the total weight of the substance by the volume it is in. This is written using the formula:

• \[\text{Concentration} = \frac{\text{Total grams of solute}}{\text{Total volume in mL}}\]

For our magnesium sulfate, it comes out as 25 grams divided by 300 milliliters, or roughly 0.0833 g/mL. Formation of this mental picture is helpful because it sets the basis for accurate dosage determination.

Proportion Method

The proportion method is a powerful mathematical technique used to solve problems where two ratios are set to be equal. This is extremely useful for dosage calculations because it allows us to determine how much volume (e.g., mL/hr) is necessary to administer a specific amount of drug (e.g., g/hr), based on the known concentration.

Let's say you need to administer 3 grams of magnesium sulfate every hour. By using proportion, we link the concentration per milliliter to the desired grams per hour. Here's how you set it up:

• \[\frac{1}{12} \text{ g/mL} \times x\text{ mL/hr} = 3 \text{ g/hr}\]

In this equation, the unknown is \(x\), which represents the volume needed per hour. By solving \(x\), we find out how much fluid needs to be administered to meet the order. Calculating this involves cross-multiplying and solving the proportion so that you can effectively convert the desired drug amount into its corresponding fluid volume. It’s a great skill that supports precise medication administration.

Rate Calculation

Rate calculation in medical contexts often requires you to determine how quickly or slowly a medication should be administered to achieve the intended therapeutic effect.

With our example problem, you're given a required dose of 3 g/hr and need to find the correct rate in mL/hr to achieve this, using the proportion setup you’ve carried out.

Once you have your equation from the proportion method, solving it gives you:

• \[x = 3 \times 12 = 36 \text{ mL/hr}\]

This result means that administering the medication at a rate of 36 mL per hour will ensure exactly 3 grams of magnesium sulfate are delivered to the patient each hour. Understanding rate calculations ensures that medications are given safely and as intended, keeping patients safe while receiving effective treatment.