✨ VIPSolutions

Let's solve each part step by step with explanations: --- ### 6a. Calculate the number of dextrose molecules per liter in 5% dextrose in water. #### **Step 1: Determine the mass of dextrose in 1 liter** - A 5% (w/v) solution means 5 grams of dextrose in 100 mL of water. - So, in 1 liter (1000 mL): \( 5 \text{ g} \times 10 = 50 \text{ g (dextrose per liter)} \) **Explanation:** We multiplied by 10 because 1 L = 1000 mL and 1000/100 = 10. --- #### **Step 2: Convert grams to moles** - Molar mass of dextrose (glucose, C₆H₁₂O₆) ≈ **180 g/mol** - Moles of dextrose per liter: \( \frac{50 \text{ g}}{180 \text{ g/mol}} = 0.278 \text{ mol/L} \) **Explanation:** We use the formula: moles = mass / molar mass. --- #### **Step 3: Calculate the number of molecules** - 1 mole = \( 6.022 \times 10^{23} \) molecules - Number of molecules per liter: \( 0.278 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 1.67 \times 10^{23} \text{ molecules} \) **Explanation:** We multiply the number of moles by Avogadro's number to get the number of molecules. --- **Final Answer for 6a:** There are approximately **\( 1.67 \times 10^{23} \) dextrose molecules per liter** in a 5% dextrose solution. --- ### 6b. Is this solution hypotonic, isotonic, or hypertonic? Explain. #### **Step 1: Understand isotonicity** - An isotonic solution has the same osmolarity as blood plasma (~0.9% NaCl or ~300 mOsm/L). **Explanation:** Isotonic solutions do not cause cells to shrink or swell. --- #### **Step 2: Compare 5% dextrose to isotonic solutions** - 5% dextrose is considered **isotonic** when administered, but it becomes **hypotonic** after dextrose is metabolized (since only water remains). **Explanation:** Initially, 5% dextrose has similar osmolarity to plasma, but as cells take up and metabolize glucose, only water is left, diluting the blood. --- **Final Answer for 6b:** **5% dextrose in water is considered isotonic when administered intravenously, but it acts as a hypotonic solution after metabolism of dextrose.** This is because the initial osmolarity matches that of plasma, but as the glucose is used up, only water remains, making the solution hypotonic relative to cells.

**6a.** There are approximately **\(1.67 \times 10^{23}\)** dextrose molecules per liter in 5% dextrose solution. **6b.** The solution is **initially isotonic** with blood plasma but becomes **hypotonic** after dextrose metabolism.