You need 500. mL of a 5.0% (m/v) glucose solution. If you have a 25% (m/v) glucose solution on hand, how many milliliters do you need?

Verified step by step guidance

1. Step 1: Understand the problem. You are tasked with preparing 500. mL of a 5.0% (m/v) glucose solution using a 25% (m/v) glucose solution. This is a dilution problem, where you will use the dilution equation: $C_1{V}_1=C_2{V}_2$, where $C_1$ and $V_1$ are the concentration and volume of the stock solution, and $C_2$ and $V_2$ are the concentration and volume of the diluted solution.
2. Step 2: Assign the known values to the variables in the dilution equation. The stock solution has a concentration of $C_1=\; 25\%$ (m/v), and you need to find the volume of this stock solution, $V_1$. The diluted solution has a concentration of $C_2=\; 5.0\%$ (m/v) and a volume of $V_2=\; 500.$ mL.
3. Step 3: Rearrange the dilution equation to solve for $V_1$, the volume of the stock solution needed. The equation becomes: $V_1=\; (C_2{V}_2)/C_1$.
4. Step 4: Substitute the known values into the rearranged equation. This gives: $V_1=\; (5.0\%\; \times \; 500.\; mL)\; /\; 25\%$. Ensure that the units and percentages are consistent throughout the calculation.
5. Step 5: Perform the calculation to determine the value of $V_1$. This will give you the volume of the 25% (m/v) glucose solution required to prepare the desired 5.0% (m/v) glucose solution.

Key Concepts

Mass/Volume Percentage (m/v)

Mass/volume percentage (m/v) is a concentration unit that expresses the mass of solute in grams per 100 mL of solution. For example, a 5.0% (m/v) glucose solution contains 5 grams of glucose in 100 mL of solution. Understanding this concept is crucial for calculating how much of a concentrated solution is needed to achieve a desired concentration.

Dilution Principle

The dilution principle states that the concentration of a solution can be altered by adding more solvent or mixing it with another solution. The relationship can be expressed using the formula C1V1 = C2V2, where C1 and V1 are the concentration and volume of the initial solution, and C2 and V2 are the concentration and volume of the final solution. This principle is essential for determining how to prepare solutions of specific concentrations.

Volume Calculation

Volume calculation involves determining the amount of liquid required to achieve a specific concentration. In this context, it requires calculating how many milliliters of a higher concentration solution (25% m/v) are needed to create a lower concentration solution (5% m/v) in a total volume of 500 mL. Mastery of volume calculations is vital for accurate solution preparation in laboratory settings.