Final answer:
The molarity of dextrose in D5W is 5.71 M, which means there are 5.71 kcal per L in D5W.
Step-by-step explanation:
D5W is a 5.0% by mass solution of dextrose (C6H12O6) in water. The density of D5W is 1.029 g/mL. To find the kcal per L in D5W, we need to calculate the molarity of dextrose in the solution. To do this, we need to convert the mass percentage of dextrose to molarity. We can use the formula: M = (mass of solute / molar mass of solute) / (volume of solution / 1000). Given that the molar mass of dextrose is 180.16 g/mol and the density of D5W is 1.029 g/mL, we can calculate the molarity of dextrose in the solution, which will give us the kcal per L.
- Calculate the mass of dextrose in 1 L of D5W solution: mass = volume x density = 1 L x 1.029 g/mL = 1.029 g
- Calculate the molarity of dextrose: M = (mass / molar mass) / (volume / 1000) = (1.029 g / 180.16 g/mol) / (1 L / 1000 mL) = 5.71 M
- Since 1 M dextrose solution contains 1 kcal/L, the D5W solution, which has a molarity of 5.71 M, will contain: kcal/L = 5.71 x 1 = 5.71 kcal/L