Question

Describe how to prepare \(1.00 \mathrm{~L}\) of \(0.646 \mathrm{M} \mathrm{HCl}\) solution, starting with a \(2.00 \mathrm{M} \mathrm{HCl}\) solution.

Short answer

To prepare a \(1.00 \mathrm{~L}\) of \(0.646 \mathrm{M} \mathrm{HCl}\) solution, one would need to take \(0.323 \mathrm{L}\) (or \(323 \mathrm{mL}\)) of the \(2.00 \mathrm{M} \mathrm{HCl}\) solution and then dilute it with water until the total volume of the solution becomes \(1.00 \mathrm{L}\).

Step-by-step solution

Identify the known values

In this case, we know the initial molarity \(M1 = 2.00 \mathrm{M}\), final molarity \(M2 = 0.646 \mathrm{M}\) and final volume \(V2 = 1.00 \mathrm{L}\). The initial volume \(V1\) for the more concentrated solution is what we need to find.

Apply the dilution formula

Apply the formula \(M1V1 = M2V2\) by substituting the known values into it. This would look like \(2.00 \mathrm{M} * V1 = 0.646 \mathrm{M} * 1.00 \mathrm{L}\)

Solve for \(V1\)

To get the volume \(V1\), you would then divide both sides of the equation by \(2.00 \mathrm{M}\). This yields: \(V1 = (0.646 \mathrm{M} * 1.00 \mathrm{L}) / 2.00 \mathrm{M}\)

Calculate the Volume

After performing the division, the resulting volume \(V1\) is therefore the amount of the \(2.00 \mathrm{M} \mathrm{HCl}\) solution required to make \(1.00 \mathrm{L}\) of a \(0.646 \mathrm{M} \mathrm{HCl}\) solution.

Key concepts

Solution Preparation

Preparing a solution involves taking a concentrated solution and diluting it to achieve a desired concentration. This process often requires precise measurements to ensure accuracy. It is essential to have a clear understanding of the concentration before starting.
One begins this process by determining the initial and final concentrations and volumes. In the given example, you start with a concentrated hydrochloric acid ( HCl ) solution with a molarity of 2.00 M, and the goal is to prepare 1.00 L of a less concentrated solution with a molarity of 0.646 M.
Accurate measurements of volume are crucial during this process. It is common practice to use a pipette to measure liquid volumes precisely. Once the correct amount of concentrated solution has been measured, it is then diluted with a solvent, usually water, to reach the desired concentration. Proper safety measures, including the use of gloves and goggles, should be taken when handling chemicals.

Concentration

Concentration describes the amount of solute present in a given volume of solution. It is crucial for determining the properties and behavior of the solution. In chemistry, concentration can be expressed in various ways, but molarity is one of the most commonly used.
Molarity (M) is defined as the number of moles of solute per liter of solution. When preparing solutions, adjusting concentration involves adding or removing solvent to change this ratio.

• If you increase the amount of solvent, the concentration decreases, which is called dilution.
• Conversely, reducing the volume of solvent increases the concentration, known as concentration.

Understanding concentration allows chemists to predict how substances will interact in reactions, making it a critical concept in solution chemistry.

Molarity Formula

The molarity formula is essential for calculating how to dilute a solution correctly. It provides a relationship between the volume and concentration of two solutions.
The formula is expressed as: \(M1 \times V1 = M2 \times V2\)
In this equation:

• \(M1\) is the molarity of the concentrated solution.
• \(V1\) is the volume of the concentrated solution needed.
• \(M2\) is the molarity of the diluted solution.
• \(V2\) is the final volume of the diluted solution.

By rearranging this equation, one can solve for any of the unknown variables. This formula helps ensure precise solution preparation, providing accurate results crucial for experimentation and analysis. For example, when given all variables except \(V1\), one can rearrange to solve for \(V1\) and find the amount of the concentrated solution to use.

Chemical Solutions

Chemical solutions are homogeneous mixtures of two or more substances. They involve a solute, often a solid or gas, dissolved in a solvent, usually a liquid.
For example, in an HCl solution, HCl gas is the solute, and water is the solvent.
Properties of chemical solutions, such as conductivity, reactivity, and boiling or freezing points, depend heavily on their concentration. Precise control over these properties is vital in fields ranging from industrial processes to medical applications.

• In medical settings, precise concentrations of solutions are crucial for effective treatment.
• In labs, consistency and reliability of chemical reactions often rely on exact solution concentrations.

Understanding how to calculate and manipulate these properties is key for success in chemistry and many fields that rely on chemical solutions.