An 85 lb dog is receiving a CRI of 500 mL of normal saline containing 50 mg of drug at a dosage of 0.005 mg/kg/min. What is the drip rate in gtt/sec if the CRI is being administered with a standard administration set (15gtt/mL) over 30 minutes (to the nearest whole number)?

To calculate the drip rate in drops per second (gtt/sec), follow these steps:

### Step 1: Convert the dog's weight from pounds to kilograms
1 lb ≈ 0.453592 kg  
\[ 85 \, \text{lb} \times 0.453592 \, \frac{\text{kg}}{\text{lb}} = 38.555 \, \text{kg} \]

### Step 2: Calculate the total drug dosage per minute
The dosage rate is given as 0.005 mg/kg/min. Multiply this by the dog's weight in kg to find the dosage in mg per minute:

\[
0.005 \, \frac{\text{mg}}{\text{kg} \cdot \text{min}} \times 38.555 \, \text{kg} = 0.1928 \, \text{mg/min}
\]

### Step 3: Calculate the total drug dosage over 30 minutes
The drug is administered over 30 minutes, so the total amount of drug given is:

\[
0.1928 \, \text{mg/min} \times 30 \, \text{min} = 5.784 \, \text{mg}
\]

### Step 4: Check the concentration of the drug in the saline
The CRI contains 50 mg of the drug in 500 mL of saline. Therefore, the concentration of the drug is:

\[
\frac{50 \, \text{mg}}{500 \, \text{mL}} = 0.1 \, \text{mg/mL}
\]

### Step 5: Calculate the total volume of fluid required
Since 5.784 mg of the drug is required, and the concentration is 0.1 mg/mL, the volume of fluid that must be given is:

\[
\frac{5.784 \, \text{mg}}{0.1 \, \frac{\text{mg}}{\text{mL}}} = 57.84 \, \text{mL}
\]

### Step 6: Calculate the total number of drops to be administered
The standard administration set delivers 15 drops (gtt) per mL. Therefore, the total number of drops is:

\[
57.84 \, \text{mL} \times 15 \, \frac{\text{gtt}}{\text{mL}} = 867.6 \, \text{gtt}
\]

### Step 7: Calculate the drip rate in drops per second
The CRI is to be administered over 30 minutes, which is:

\[
30 \, \text{min} \times 60 \, \frac{\text{sec}}{\text{min}} = 1800 \, \text{sec}
\]

Now, divide the total number of drops by the total time to get the drip rate in drops per second:

\[
\frac{867.6 \, \text{gtt}}{1800 \, \text{sec}} \approx 0.48 \, \frac{\text{gtt}}{\text{sec}}
\]

### Final Answer:
The drip rate is approximately **0.48 gtt/sec**.

---

Would you like any more details or have any questions? Here are some related problems to expand your understanding:

1. What would the drip rate be if the dog weighed 100 lb instead?
2. How would the drip rate change if the CRI was administered over 1 hour instead of 30 minutes?
3. What would happen to the drip rate if a 60 gtt/mL administration set was used instead of 15 gtt/mL?
4. If the concentration of the drug was increased to 100 mg/500 mL, how would this affect the drip rate?
5. What would the total volume of fluid be if the dosage was increased to 0.01 mg/kg/min?

**Tip**: When solving dosage and administration rate problems, always ensure units are consistent and convert them as needed!

Learn how to calculate the drip rate (gtt/sec) for an 85 lb dog receiving a continuous rate infusion (CRI) of 500 mL normal saline with 50 mg of drug at a dosage of 0.005 mg/kg/min. This detailed solution involves unit conversion, dosage, and drip rate calculations, ideal for veterinary or nursing professionals.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation