What is the concentration of a NaCl solution, in (m/v)%, prepared by diluting 65 mL of a saturated solution, which has a concentration of 37 (m/v)%, to 480 mL?

Verified step by step guidance

1. Understand the problem: We are tasked with finding the new concentration of a NaCl solution in (m/v)% after diluting a given volume of a saturated solution to a larger volume. The key concept here is the dilution formula, which states that the amount of solute remains constant before and after dilution.
2. Write the dilution formula: \( C_1 V_1 = C_2 V_2 \), where \( C_1 \) is the initial concentration (37 (m/v)%), \( V_1 \) is the initial volume (65 mL), \( C_2 \) is the final concentration (what we are solving for), and \( V_2 \) is the final volume (480 mL).
3. Rearrange the formula to solve for \( C_2 \): \( C_2 = \frac{C_1 V_1}{V_2} \). This equation allows us to calculate the final concentration after dilution.
4. Substitute the known values into the formula: \( C_2 = \frac{(37 \text{ (m/v)%})(65 \text{ mL})}{480 \text{ mL}} \). Ensure that the units for volume are consistent (both in mL).
5. Simplify the expression to calculate \( C_2 \). The result will give the final concentration of the NaCl solution in (m/v)% after dilution.

Key Concepts

Concentration (m/v)%

Concentration expressed as mass/volume percentage (m/v)% indicates the mass of solute in grams per 100 mL of solution. For example, a 37 (m/v)% NaCl solution contains 37 grams of NaCl in 100 mL of solution. This measurement is crucial for understanding how much solute is present in a given volume of solvent.

Dilution

Dilution is the process of reducing the concentration of a solute in a solution, typically by adding more solvent. The dilution equation, C1V1 = C2V2, relates the initial concentration and volume (C1 and V1) to the final concentration and volume (C2 and V2). This concept is essential for calculating the new concentration after mixing solutions.

Saturated Solution

A saturated solution is one in which the maximum amount of solute has been dissolved at a given temperature, resulting in an equilibrium between dissolved and undissolved solute. In this context, the initial saturated solution of NaCl at 37 (m/v)% serves as the starting point for dilution, influencing the final concentration of the diluted solution.