A patient receives 3.2 L of intravenous (IV) glucose solution. If 100. mL of the solution contains 5.0 g of glucose (carbohydrate), how many kilocalories did the patient obtain from the glucose solution?

Verified step by step guidance

1. Step 1: Determine the total volume of the glucose solution in milliliters. Since the patient receives 3.2 L, convert this to milliliters using the conversion factor 1 L = 1000 mL. The total volume is 3.2 × 1000 = 3200 mL.
2. Step 2: Calculate the total mass of glucose in the solution. Use the given ratio that 100 mL of solution contains 5.0 g of glucose. Set up a proportion: (5.0 g / 100 mL) = (x g / 3200 mL). Solve for x to find the total mass of glucose.
3. Step 3: Determine the energy content of glucose. Recall that glucose provides 4 kilocalories (kcal) per gram. Multiply the total mass of glucose obtained in Step 2 by 4 kcal/g to calculate the total energy in kilocalories.
4. Step 4: Ensure unit consistency and verify calculations. Check that all units (mL, g, kcal) are correctly converted and consistent throughout the problem.
5. Step 5: Interpret the result. The final value represents the total kilocalories the patient obtained from the glucose solution, which is useful for understanding the energy provided by the IV solution.

Key Concepts

Caloric Content of Carbohydrates

Carbohydrates provide energy, with each gram yielding approximately 4 kilocalories. Understanding this conversion is essential for calculating the total energy provided by glucose in the IV solution.

Volume to Mass Conversion

To determine the total amount of glucose in the IV solution, one must convert the volume of the solution (in liters) to mass (in grams). This involves knowing the concentration of glucose in the solution, which is given in grams per 100 mL.

Unit Conversion

In this context, converting between milliliters and liters, as well as grams to kilocalories, is crucial. Proper unit conversion ensures accurate calculations and understanding of the total caloric intake from the glucose solution.