Question

If you were to prepare exactly \(1.00 \mathrm{L}\) of a \(5 \mathrm{M} \mathrm{NaCl}\) solution, you would not need exactly 1.00 L of water. Explain.

Short answer

To prepare a 1 L solution of 5 M NaCl, we would not need exactly 1 L of water because adding the 292.2 g of NaCl to the water will increase its volume. If we started with exactly 1 L of water, the final volume will be more than 1 L, making the concentration less than 5 M. Instead, we should add the 292.2 g of NaCl to an amount of water less than 1 L and then add more water gradually until the final volume reaches 1 L, ensuring a 5 M concentration.

Step-by-step solution

Understanding Molarity

Molarity (M) is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per liter of solution. So, when preparing a solution, we need to consider the masses of both the solute (in this case, NaCl) and the solvent (water).

Calculate the mass of NaCl required

To prepare a 5 M NaCl solution, we need 5 moles of NaCl per 1 liter of solution. To calculate the mass of NaCl required, we use the molar mass of NaCl. The molar mass of NaCl: Sodium (Na): 22.99 g/mol Chloride (Cl): 35.45 g/mol Molar mass of NaCl = 22.99 + 35.45 = 58.44 g/mol Since we need 5 moles of NaCl, we can calculate the mass as follows: Mass of NaCl = 5 moles × 58.44 g/mol = 292.2 g Thus, we need 292.2 g of NaCl to prepare 1 liter of a 5 M NaCl solution.

Understanding the final volume of the solution

When preparing a solution, we must remember that adding a solute to a solvent will increase the volume of the solution. In this case, when we add 292.2 g of NaCl to water, it will dissolve and slightly increase the volume of the water.

Explain why we don't need exactly 1 L of water

When preparing a 5 M NaCl solution, our goal is to achieve a final volume of 1 L with the correct concentration of the solute. We know that adding 292.2 g of NaCl to the water will increase its volume, so if we were to start with exactly 1 L of water, the final volume would be more significant than 1 L, and the solution will not have the desired 5 M concentration. To prepare a 1 L solution of 5 M NaCl correctly, we should add the 292.2 g of NaCl to an amount of water that is less than 1 L, then add more water gradually until the final volume of the solution reaches 1 L. This way, the concentration will be precisely 5 M, and the final volume will be 1 L.

Key concepts

NaCl Solution

A solution is a homogeneous mixture composed of two or more substances. When we talk about a NaCl solution, we are referring to a mixture in which sodium chloride (NaCl) is dissolved in a solvent, typically water.
NaCl, also known as common table salt, is an ionic compound consisting of positively charged sodium ions and negatively charged chloride ions.
When NaCl is added to water, it dissociates into its ions due to the polar nature of water, which means the ions are evenly distributed throughout the solution. This even distribution is the hallmark of a solution.
One key point to remember is that while NaCl is a solute, water acts as the solvent, the substance in which the solute is dissolved, playing a critical role in the formation of homogeneous solutions.

Solute Concentration

Solute concentration is a measure of how much solute is present in a given amount of solution. Molarity (M) is one of the most common units for expressing concentration and is defined as moles of solute per liter of solution.
In the case of a NaCl solution with a molarity of 5 M, it means there are 5 moles of NaCl dissolved in every one liter of the final solution.
The concentration is crucial because it indicates the strength of the solution and determines how the solution behaves in chemical reactions and physical processes.

• A higher concentration implies more solute in the same volume, making the solution more potent.
• A lower concentration means less solute for the same volume, resulting in a more diluted solution.

Accurate solute concentration is vital because many chemical processes depend on specific concentrations to work correctly, like reactions in scientific research or industrial applications.

Solution Preparation

Preparing a solution involves mixing the right amounts of solute and solvent to achieve the desired concentration and volume.
When preparing a NaCl solution, it's essential to consider that adding a solid solute, such as NaCl, to water increases the total volume of the solution.
To achieve a target concentration and final volume, especially for higher molarity solutions, you generally start by adding the solute to a smaller amount of water. Here’s why:

• The solute itself occupies some space, so its addition increases the volume.
• If you begin with too much water, adding the solute will cause the total volume to exceed your target.

A practical method is to dissolve the solute first in less than the final desired volume of water, and then add water to reach the precise final volume after dissolution.
By careful measurement and adjustment, you ensure that the final solution has the intended molarity, making the solution preparation an exercise in precision and understanding of how solute and solvent interact.