Final answer:
To calculate the amount of fentanyl required, use the formula C₁V₁ = C₂V₂. Given that the doctor ordered a fentanyl CRI at 4ug/Kg/hour and the dog weighs 40 kg, calculate the required fentanyl dose per hour and convert it to milligrams. Use the formula C₁V₁ = C₂V₂ to calculate the volume of fentanyl with a concentration of 0.05 mg/ml that must be added to 1000 ml of 0.9% sodium chloride.
Step-by-step explanation:
To calculate the amount of fentanyl required, we need to use the formula: C₁V₁ = C₂V₂. In this case, C₁ is the concentration of fentanyl, V₁ is the volume of fentanyl needed, C₂ is the concentration of sodium chloride, and V₂ is the total volume of sodium chloride solution.
Given that the doctor ordered a fentanyl CRI (constant rate infusion) at 4ug/Kg/hour, and the dog weighs 40 kg, we can calculate the required fentanyl dose per hour: 4ug/Kg/hour * 40 kg = 160 ug/hour. We also have the concentration of fentanyl, which is 0.05 mg/ml, so we need to convert the required dose from micrograms to milligrams: 160 ug = 0.16 mg.
Next, we consider the total volume of sodium chloride solution, which is 1000 ml. We will use the formula C₁V₁ = C₂V₂ to calculate the volume of fentanyl needed. Rearranging the formula, we have V₁ = (C₂V₂) / C₁. Plugging in the values, we have V₁ = (0.05 mg/ml * 1000 ml) / 0.16 mg = 312.5 ml of fentanyl with a concentration of 0.05 mg/ml must be added to 1000 ml of 0.9% sodium chloride.