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. Identify the initial concentration of the NaCl solution, which is given as 37% (m/v). This means there are 37 grams of NaCl in 100 mL of solution.
2. Calculate the amount of NaCl in the initial 65 mL of the saturated solution using the formula: \( \text{mass of NaCl} = \text{concentration} \times \text{volume} / 100 \).
3. Determine the total volume of the diluted solution, which is given as 480 mL.
4. Use the formula for dilution: \( C_1V_1 = C_2V_2 \), where \( C_1 \) and \( V_1 \) are the initial concentration and volume, and \( C_2 \) and \( V_2 \) are the final concentration and volume.
5. Solve for the final concentration \( C_2 \) by rearranging the dilution formula: \( C_2 = \frac{C_1V_1}{V_2} \).

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 solution.

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)% provides a starting point for calculating the concentration after dilution, as it indicates the solute's maximum solubility.