You can purchase hydrochloric acid in a concentrated form that is 37.0% HCl by mass and that has a density of 1.20 g>mL. Describe exactly how to prepare 2.85 L of 0.500 M HCl from the concentrated solution.

Verified step by step guidance

1. Calculate the moles of HCl needed using the formula: \( \text{Moles of HCl} = \text{Volume (L)} \times \text{Molarity (M)} \).
2. Determine the mass of HCl in the concentrated solution using the percentage by mass: \( \text{Mass of HCl} = \text{Mass of solution} \times 0.37 \).
3. Calculate the volume of the concentrated solution needed using its density: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).
4. Use the dilution equation \( M_1V_1 = M_2V_2 \) to find the volume of concentrated HCl needed, where \( M_1 \) and \( V_1 \) are the molarity and volume of the concentrated solution, and \( M_2 \) and \( V_2 \) are the molarity and volume of the diluted solution.
5. Measure the calculated volume of concentrated HCl and dilute it with water to a total volume of 2.85 L.

Key Concepts

Molarity (M)

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L). To prepare a solution of a specific molarity, one must calculate the amount of solute needed based on the desired volume and molarity, which is crucial for diluting concentrated solutions.

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. Understanding this concept is essential for accurately preparing solutions from concentrated stock.

Density and Mass Percent

Density is the mass of a substance per unit volume, often expressed in grams per milliliter (g/mL). Mass percent indicates the mass of solute in a given mass of solution. For hydrochloric acid, knowing its density and mass percent allows one to calculate the mass of HCl in a specific volume of concentrated solution, which is necessary for preparing the desired diluted solution.