A typical IV used in hospitals is dextrose 5\(\%\) in water (called D5W). This solution is injected into veins through an IV to replace lost fluids and to provide carbohydrates. Injectable medicines are also delivered to the body using the D5W IV. D5W contains 5.0 g dextrose monohydrate $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \cdot \mathrm{H}_{2} \mathrm{O}\right)\( per 100.0 \)\mathrm{mL}$ of solution. Assuming a density of 1.01 \(\mathrm{g} / \mathrm{cm}^{3}\) , calculate the molarity and molality of D5W.

From the molecular formula (C6H12O6·H2O), we obtain the molar mass as follows: Molar mass of dextrose monohydrate = 6 × (mass of C) + 12 × (mass of H) + 6 × (mass of O) + 2 × (mass of H) + 1 × (mass of O) Considering mass of C = 12.01 g/mol, mass of H = 1.01 g/mol, and mass of O = 16.00 g/mol. Plugging in the values we get: Molar mass = 6 × 12.01 + 12 × 1.01 + 6 × 16.00 + 2 × 1.01 + 1 × 16.00 Molar mass = 72.06 + 12.12 + 96.00 + 2.02 + 16.00 Molar mass = 198.2 g/mol

In order to calculate the molarity of the D5W solution, we first need to find out how many moles of dextrose monohydrate are present in the solution. With the mass of dextrose monohydrate (5.0 g) given and the molar mass (198.2 g/mol) calculated, we can calculate the moles as follows: Moles of dextrose monohydrate = mass / molar mass Moles of dextrose monohydrate = 5.0 g / 198.2 g/mol Moles of dextrose monohydrate = 0.0252 mol Now, we can find molarity using the formula: Molarity (M) = moles of solute / volume of solution (in liters) First, convert the volume of the solution from mL to L: 100.0 mL = 0.1 L Now calculate the molarity: Molarity (M) = 0.0252 mol / 0.1 L Molarity (M) = 0.252 mol/L

In order to find the molality, we need to find the mass of the solvent (water) in the solution. We already know the mass of dextrose monohydrate in the solution (5.0 g) and we can find the total mass of the solution using its density. Given density = 1.01 g/cm³ and volume = 100 mL, let's calculate the mass of the solution: Total mass of the solution = density × volume Total mass of the solution = 1.01 g/cm³ × 100 cm³ (recall 1 mL = 1 cm³) Total mass of the solution = 101 g Now, we can find the mass of the solvent (water): Mass of water = total mass of the solution - mass of dextrose monohydrate Mass of water = 101 g - 5.0 g Mass of water = 96 g Now, we can find molality using the formula: Molality (m) = moles of solute / mass of solvent (in kg) First, convert the mass of the solvent from g to kg: 96 g = 0.096 kg Now calculate the molality: Molality (m) = 0.0252 mol / 0.096 kg Molality (m) = 0.262 mol/kg Thus, the molarity of the D5W solution is 0.252 mol/L, and its molality is 0.262 mol/kg.