Final answer:
The total calories provided by the parenteral solution, consisting of 65 grams of protein, 200 grams of dextrose, and a 20% fat emulsion at 7 ml per hour over 24 hours, is 1362.4 calories.
Step-by-step explanation:
To calculate the total calories provided by the parenteral solution consisting of 65 grams of protein, 200 grams of dextrose (glucose), and a 20% fat emulsion at 7 ml per hour over a 24-hour period, we'll use the standard caloric values for each macronutrient:
- Protein: 4 calories per gram
- Carbohydrates (dextrose): 4 calories per gram
- Fat: 9 calories per gram
First, we'll convert the 20% fat emulsion rate from ml per hour to grams, as 1 ml of the emulsion contains 0.2 grams of fat. Then, we multiply the amount of each nutrient by its respective caloric value:
- Proteins: 65g × 4 cal/g = 260 calories
- Dextrose: 200g × 4 cal/g = 800 calories
- Fat: (7 ml/hr × 24 hrs × 0.2 g/ml) × 9 cal/g
The total grams of fat infused over 24 hours is 7 ml/hr × 24 hrs × 0.2 g/ml = 33.6 grams of fat.
The calories from fat are thus 33.6g × 9 cal/g = 302.4 calories.
Finally, we add the calories from protein, dextrose, and fat to obtain the total calories:
260 + 800 + 302.4 = 1362.4 total calories
This parenteral solution provides a total of 1362.4 calories over a 24-hour period.