A patient receives 3.4 L of glucose solution intravenously (IV). If 100. mI of the solution contains 5.5 g of glucose (carbohydrate), how many kcals did the patient obtain from the glucose solution
Express the energy to two significant figures and include the appropriate units.
To find the amount of glucose in the IV solution, we can use unit analysis:
100 mL of solution contains 5.5 g of glucose.
1 L = 1000 mL, so 1 L of solution contains (5.5 g/100 mL) * (1000 mL/1 L) = 55 g of glucose.
Therefore, the patient receives 3.4 L * 55 g/L = 187 g of glucose.
There are 4 kcal/g in glucose, so the patient obtains 187 g * 4 kcal/g = 748 kcal from the glucose solution.
Rounded to two significant figures, the patient obtains 750 kcal.
To calculate the energy obtained from the glucose solution, follow these steps:
Step 1: Find the number of moles of glucose in 100 mL of the solution.
To do this, divide the mass of glucose (5.5 g) by the molar mass of glucose (180.16 g/mol):
Number of moles = 5.5 g / 180.16 g/mol = 0.0305 mol
Step 2: Find the number of moles of glucose in 3.4 L of the solution.
There are 1000 mL in 1 L, so the number of moles in 3.4 L is:
Number of moles = 0.0305 mol/100 mL × 3.4 L = 0.1037 mol
Step 3: Calculate the energy in kilocalories (kcals) obtained from the glucose solution.
Each mole of glucose provides the body with 4 kcals of energy. So, the total energy obtained from the glucose solution is:
Energy = 0.1037 mol × 4 kcals/mol = 0.415 kcals
Therefore, the patient obtained approximately 0.415 kcals of energy from the glucose solution.