Determine the final volume, in milliliters, of each of the following:
b. a 2.0% (m/v) LiCl solution prepared from 50.0 mL of a 10.0% (m/v) LiCl solution

Verified step by step guidance

1. Step 1: Understand the problem. You are tasked with determining the final volume of a 2.0% (m/v) LiCl solution that is prepared by diluting a 10.0% (m/v) LiCl solution. This is a dilution problem, and the relationship between the initial and final concentrations and volumes can be expressed using the dilution equation: $C{i}_{}V{i}_{}=C{f}_{}V{f}_{}$, where $C{i}_{}$ and $V{i}_{}$ are the initial concentration and volume, and $C{f}_{}$ and $V{f}_{}$ are the final concentration and volume.
2. Step 2: Write down the known values. From the problem, the initial concentration $C{i}_{}$ is 10.0% (m/v), the initial volume $V{i}_{}$ is 50.0 mL, and the final concentration $C{f}_{}$ is 2.0% (m/v). The final volume $V{f}_{}$ is what we need to calculate.
3. Step 3: Rearrange the dilution equation to solve for the final volume $V{f}_{}$. The equation becomes: $V{f}_{}=\frac{C{i}_{}V{i}_{}}{C}$.
4. Step 4: Substitute the known values into the rearranged equation. Replace $C{i}_{}$ with 10.0%, $V{i}_{}$ with 50.0 mL, and $C{f}_{}$ with 2.0%. The equation becomes: $V{f}_{}=\frac{10.0\times 50.0}{2.0}$.
5. Step 5: Perform the calculation to find the final volume $V{f}_{}$. Ensure that the units are consistent and the result is expressed in milliliters (mL).

Key Concepts

Mass/Volume Percent (m/v)

Mass/volume percent (m/v) is a concentration unit that expresses the mass of solute in grams per 100 mL of solution. For example, a 2.0% (m/v) solution of LiCl means there are 2 grams of LiCl in every 100 mL of the solution. Understanding this concept is crucial for calculating the final volume of a solution when diluting or mixing different concentrations.

Dilution Principle

The dilution principle states that when a solution is diluted, the amount of solute remains constant, while the volume of the solution increases. This can be mathematically represented by the equation C1V1 = C2V2, where C is concentration and V is volume. This principle is essential for determining the final volume of a solution after mixing or diluting a more concentrated solution.

Concentration Calculation

Concentration calculation involves determining the amount of solute in a given volume of solution. In this context, it requires calculating the amount of LiCl in the initial 50.0 mL of a 10.0% solution and then using that amount to find the final volume needed to achieve a 2.0% concentration. This calculation is fundamental for preparing solutions with desired concentrations in laboratory settings.