Problem 34 - Calculate With Confidence

Question

Calculate the dosages as indicated. Use the labels where provided. A client is receiving lidocaine \(1 \mathrm{~g}\) in \(500 \mathrm{~mL}\) D5W at a rate of \(20 \mathrm{~mL} / \mathrm{hr}\). Calculate the following: a. \(\mathrm{mg} / \mathrm{hr}\) b. \(\mathrm{mg} / \mathrm{min}\)

Step-by-Step Solution

Answer

a. 40 mg/hr b. 0.67 mg/min

Step 1: Understand the Problem

We are given that a client receives lidocaine in a concentration of \(1 \text{ g}\) in \(500 \text{ mL}\) of a solution labeled D5W. This solution is infused at a rate of \(20 \text{ mL/hr}\). Our task is to find how many milligrams of lidocaine the client receives per hour and per minute.

Step 2: Convert Grams to Milligrams

Since the dosages are needed in milligrams, convert the gram amount to milligrams: \[ 1 \text{ g} = 1000 \text{ mg} \] Therefore, there are \(1000 \text{ mg}\) of lidocaine in \(500 \text{ mL}\) of solution.

Step 3: Calculate mg/mL

Calculate the concentration of lidocaine per mL in the solution. Divide the total milligrams of lidocaine by the total volume of the solution to get the concentration:\[ \text{Concentration} = \frac{1000 \text{ mg}}{500 \text{ mL}} = 2 \text{ mg/mL} \]

Step 4: Calculate mg/hr

To determine the dosage in mg/hr, multiply the concentration of lidocaine by the rate of infusion in mL/hr:\[ \text{Dosage in mg/hr} = 2 \text{ mg/mL} \times 20 \text{ mL/hr} = 40 \text{ mg/hr} \]

Step 5: Calculate mg/min

Convert the hourly dosage to a per minute dosage by dividing by 60 (since there are 60 minutes in an hour):\[ \text{Dosage in mg/min} = \frac{40 \text{ mg/hr}}{60} = \frac{2}{3} \text{ mg/min} \approx 0.67 \text{ mg/min} \]

Key Concepts

Lidocaine Dosage

When administering lidocaine to a patient, it's crucial to calculate the dosage accurately to ensure safety and effectiveness. Lidocaine is often used as a numbing medication and in some cases for treating irregular heartbeats. For this exercise, you need to determine how much lidocaine in milligrams is given to a patient per hour and per minute.
This problem is straightforward if you follow a step-by-step approach. To start with, you will convert the lidocaine amount from grams to milligrams. In this situation, the lidocaine provided is 1 gram. Thus, we will first perform this basic conversion:

• 1 gram = 1000 milligrams

The next step would be calculating how much of this total milligram amount is administered per hour and per minute to the patient, based on the given infusion rate.

Concentration Calculation

To make accurate dosage calculations, knowing the concentration of lidocaine in the solution is vital. In this scenario, the solution has 1 gram of lidocaine in 500 mL of D5W (5% dextrose in water). You've already converted this gram amount into milligrams. Now, calculate the concentration in terms of mg/mL:

• Total lidocaine = 1000 mg
• Total solution volume = 500 mL
• Concentration = \( \frac{1000 \text{ mg}}{500 \text{ mL}} = 2 \text{ mg/mL} \)

This means that each milliliter of solution contains 2 mg of lidocaine. Such concentration values are crucial and often used for subsequent calculations regarding infusion and dosage.

Infusion Rate

The infusion rate essentially tells you how fast the medication is administered to the patient. It's often measured in milliliters per hour for practical medical routines. In this case, the medication is being infused at 20 mL per hour.
To find the dosage in milligrams per hour (mg/hr), you multiply the concentration (mg/mL) by the infusion rate (mL/hr):

• Concentration = 2 mg/mL
• Infusion rate = 20 mL/hr
• Dosage (mg/hr) = 2 \( \times \) 20 = 40 mg/hr

Next, converting the hourly dosage into a per-minute dosage is straightforward:

• Dosage (mg/min) = \( \frac{40 \text{ mg/hr}}{60} \approx 0.67 \text{ mg/min} \)

This is crucial for making real-time adjustments in medical situations to maintain appropriate dosing.