A patient needs 100. g of glucose in the next 12 h. How many liters of a 5% (m/v) glucose solution must be given?

Verified step by step guidance

1. Step 1: Understand the problem. We need to find out how many liters of a 5% (m/v) glucose solution are required to provide 100 g of glucose over 12 hours.
2. Step 2: Recall that a 5% (m/v) solution means there are 5 grams of solute (glucose) in every 100 mL of solution.
3. Step 3: Set up a proportion to find the volume of solution needed. If 5 g of glucose is in 100 mL, then 100 g of glucose will be in X mL. The proportion is: $\frac{5\text{ g}}{100\text{ mL}}=\frac{100\text{ g}}{X\text{ mL}}$.
4. Step 4: Solve the proportion for X to find the volume in milliliters. Cross-multiply and divide to isolate X.
5. Step 5: Convert the volume from milliliters to liters, knowing that 1 liter = 1000 milliliters.

Key Concepts

Concentration (m/v)

Mass/volume (m/v) concentration expresses the mass of solute per 100 mL of solution. A 5% (m/v) glucose solution means there are 5 grams of glucose in every 100 mL of solution. Understanding this concept is crucial for calculating how much solution is needed to deliver a specific mass of glucose.

Volume Calculation

To determine the volume of solution required, one must use the formula: Volume = Mass / Concentration. In this case, the mass of glucose needed is 100 g, and the concentration of the solution is 5 g per 100 mL. This calculation will yield the total volume of the glucose solution necessary to meet the patient's needs.

Time Factor

The time factor in this scenario indicates that the glucose must be administered over a specific duration (12 hours). This aspect is important for understanding the rate of administration, which can affect how the solution is delivered, ensuring that the patient receives the required amount of glucose safely and effectively within the given timeframe.