A bottle of 12.0 M hydrochloric acid has only 35.7 mL left in it. What will the HCl concentration be if the solution is diluted to 250.0 mL?

Verified step by step guidance

1. Identify the initial concentration \( C_1 \) and initial volume \( V_1 \) of the hydrochloric acid solution. Here, \( C_1 = 12.0 \text{ M} \) and \( V_1 = 35.7 \text{ mL} \).
2. Determine the final volume \( V_2 \) after dilution, which is given as \( 250.0 \text{ mL} \).
3. Use the dilution formula \( C_1 \times V_1 = C_2 \times V_2 \) to find the final concentration \( C_2 \).
4. Rearrange the formula to solve for \( C_2 \): \( C_2 = \frac{C_1 \times V_1}{V_2} \).
5. Substitute the known values into the equation: \( C_2 = \frac{12.0 \text{ M} \times 35.7 \text{ mL}}{250.0 \text{ mL}} \) and simplify to find \( C_2 \).

Key Concepts

Molarity

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. It is commonly used in chemistry to express the concentration of a solution. In this case, the initial concentration of hydrochloric acid is given as 12.0 M, indicating that there are 12 moles of HCl in every liter 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, M1V1 = M2V2, relates the initial and final molarities (M1 and M2) and volumes (V1 and V2) of the solution. This principle is essential for calculating the new concentration after adding solvent to the original solution.

Conservation of Mass

The principle of conservation of mass states that mass is neither created nor destroyed in a chemical reaction or physical process. In the context of dilution, this means that the total amount of solute remains constant before and after dilution. Therefore, the number of moles of HCl before dilution must equal the number of moles after dilution, allowing for the calculation of the new concentration.