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 per 100 mL of solution.
2. Calculate the mass 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 480 mL.
4. Use the mass of NaCl calculated in step 2 and the total volume from step 3 to find the new concentration using the formula: \( \text{new concentration} = (\text{mass of NaCl} / \text{total volume}) \times 100 \).
5. Express the final concentration as a percentage (m/v) by ensuring the units are consistent and the formula is applied correctly.

Key Concepts

Concentration Units

Concentration can be expressed in various units, including mass/volume percent (m/v)%, which indicates the mass of solute per 100 mL of solution. Understanding this unit is crucial for calculating the concentration of solutions, especially when diluting or mixing different concentrations.

Dilution Principle

Dilution involves reducing the concentration of a solution by adding more solvent. The dilution equation, C1V1 = C2V2, relates the initial concentration and volume to the final concentration and volume, allowing for the calculation of the new concentration after dilution.

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. Knowing the concentration of a saturated solution is essential for determining how much solute is present before dilution.