Question

Calculate the dosages as indicated. Use the labels where provided. Order: \(2 \mathrm{~g} / \mathrm{hr}\) of \(50 \%\) magnesium sulfate. The solution available is \(25 \mathrm{~g}\) of \(50 \%\) magnesium sulfate in \(300 \mathrm{~mL}\) D5W. What flow rate in \(\mathrm{mL} / \mathrm{hr}\) would be needed to administer the required dose?

Short answer

48 mL/hr

Step-by-step solution

Understand the Problem

We need to determine how many mL/hr of a solution (containing 25g of 50% magnesium sulfate in 300mL) is required to deliver 2g of magnesium sulfate per hour.

Calculate Magnesium Sulfate Concentration in Solution

The solution contains 25g of 50% magnesium sulfate in 300mL. Since it's a 50% solution, this means 12.5g of magnesium sulfate (50% of 25g) is in 300mL. Thus, the concentration is \( \frac{12.5 \, \text{g}}{300 \, \text{mL}} \).

Determine the Amount in Grams per mL

Divide the total grams of magnesium sulfate (12.5g) by the total volume (300mL) to find grams per mL: \( \frac{12.5 \, \text{g}}{300 \, \text{mL}} = 0.0417 \, \text{g/mL} \).

Calculate Required Flow Rate

To administer 2g/hr, divide the required dose (2g) by the concentration (0.0417g/mL): \( \frac{2 \, \text{g/hr}}{0.0417 \, \text{g/mL}} \approx 48 \, \text{mL/hr} \).

Review and Verify

Verify the calculations: 48 mL/hr at 0.0417 g/mL delivers \(48 \, \text{mL/hr} \times 0.0417 \, \text{g/mL} = 2 \, \text{g/hr} \), confirming the flow rate is correct.

Key concepts

Understanding Flow Rate

Flow rate plays a crucial role in medical dosage calculations. It refers to the volume of fluid that moves over a certain period, often measured in milliliters per hour (mL/hr). In medical settings, maintaining the correct flow rate ensures that patients receive the precise amount of medication needed.
In this context, we're looking at administering a specific dose of a medication continuously over a set time. To determine the right flow rate, one must consider both the desired dosage and the concentration of the medication in the solution.

• Example: If you need to deliver 2 grams of magnesium sulfate each hour, you need to set the solution's flow rate correctly based on its concentration.
• Importance: Achieving the right flow rate prevents overdosing or underdosing, ensuring patient safety.

Understanding Magnesium Sulfate

Magnesium sulfate is a medication used to treat various conditions, including seizures in eclampsia and preventing premature labor. Its administration often requires careful dosage management due to its potent effects on the body.
Magnesium sulfate solutions are typically prepared in specific concentrations, such as the 50% solution described. This percentage indicates the proportion of magnesium sulfate in the solution, making it essential for calculating the exact amount needed for treatment.

• Composition: A 50% solution means that every 100 mL contains 50 grams of magnesium sulfate.
• Application: It’s often administered intravenously in hospital settings.
• Monitoring: Healthcare providers must monitor magnesium levels carefully, as high levels can be harmful.

Grasping Concentration

Concentration in medical solutions is a measure of how much solute (such as magnesium sulfate) is present per amount of solvent (like water). It is typically expressed in terms of grams per milliliter (g/mL) in medical dosing.
A 50% magnesium sulfate solution implies that nearly half of the weight of the solution is made up by magnesium sulfate. To find the exact concentration in terms of g/mL, you divide the amount of solute by the total solution volume.

• Calculation: In the given exercise, the solution contains 12.5 g of magnesium sulfate in 300 mL, making its concentration 0.0417 g/mL.
• Usage: Knowing the concentration helps in determining the volume of solution needed to provide a specific dose.
• Practice: Always ensure you check and double-check calculations to maintain accuracy in dosing.