Question

Explain the difference in meaning between the following two solutions: "50. g of NaCl dissolved in 1.0 L of water" and "50. g of NaCl dissolved in enough water to make \(1.0 \mathrm{L}\) of solution." For which solution can the molarity be calculated directly (using the molar mass of \(\mathrm{NaCl}\) )?

Short answer

The difference between the two solutions is that the first one has 50 g of NaCl dissolved in exactly 1.0 L of water, while the second one has 50 g of NaCl dissolved in enough water to make a total volume of 1.0 L. Molarity can be calculated directly for the second solution using the formula \( M = \frac{n}{V} \), with the given mass (50 g) and the molar mass of NaCl (\(58.44 \, g \, mol^{-1}\)), resulting in a molarity of 0.856 mol L\(^{-1}\). For the first solution, the final volume after dissolution is unknown, so we cannot directly calculate its molarity.

Step-by-step solution

Understanding the difference between the two solutions

The first solution description says "50. g of NaCl dissolved in 1.0 L of water." It means that we take 50 grams of NaCl and dissolve it in exactly 1.0 L of water. The final volume of the solution will be more than 1.0 L , as the solute increases the total volume, along with water. The second solution description says "50. g of NaCl dissolved in enough water to make 1.0 L of solution." In this case, we dissolve 50 grams of NaCl in a certain amount of water, and after dissolving the salt, we continue to add water until the total volume reaches 1.0 L. Here, the final volume of the solution is exactly 1.0 L.

Understanding molarity

Molarity is defined as the number of moles of solute per liter of solution. It is represented by the formula: \[ M = \frac{n}{V} \] Where: - \( M \) is molarity (in moles per liter / mol L\(^{-1}\)), - \( n \) is the number of moles of solute, - \(V\) is the volume of the solution (in liters).

Determining which solution allows for direct molar concentration calculations

To calculate the molarity of a solution, we need to know the number of moles of solute and the total volume of the solution. The molar mass of NaCl is approximately \(58.44 \, g \, mol^{-1}\). We can calculate the number of moles of NaCl in both cases using the given mass (50 g) and the molar mass of NaCl: \[ n = \frac{50 \, g}{58.44 \, g \, mol^{-1}} = 0.856 \, mol \, of \, NaCl \] Thus, the number of moles of NaCl in both solutions is the same: 0.856 mol. However, only in the second solution, we know the exact volume: 1.0 L. Therefore, we can calculate the molarity for the second solution directly: \[ M = \frac{0.856 \, mol}{1.0 \, L} = 0.856 \, mol \, L^{-1} \] For the first solution, since we do not know the final volume after dissolving 50 g of NaCl in 1.0 L of water, we cannot directly calculate its molarity. In conclusion, the molarity can be calculated directly for the second solution, where "50 g of NaCl is dissolved in enough water to make 1.0 L of solution" with a molarity of 0.856 mol L\(^{-1}\).

Key concepts

Solutions

In chemistry, a solution is a homogeneous mixture composed of two or more substances. In our everyday life, they frequently appear in liquid form, but solutions can also exist as solids or gases. When forming a solution, a solute (the substance being dissolved) combines with a solvent (the substance doing the dissolving). For instance, when salt is dissolved in water, salt is the solute and water is the solvent.
It is important to understand the nature and properties of a solution, as these impact how concentrations are determined and used in calculations. Depending on how the solution is prepared, the concentration, also known as molarity, can be calculated more directly in certain scenarios.

NaCl (Sodium Chloride)

Sodium chloride, commonly known as table salt, is a chemical compound with the formula NaCl. It consists of one sodium ion (Na⁺) and one chloride ion (Cl⁻). Sodium chloride is known for its high solubility in water, making it a common choice for experiments in chemistry to demonstrate solubility and concentration concepts.
In the context of solutions, the amount of NaCl used, often measured in grams, needs to be converted into moles utilizing its molar mass. This conversion allows us to calculate concentrations and understand interactions within the solution.

Moles and Molar Mass

The concept of moles is central to chemistry, providing a way to quantify the amount of substance present. A mole is a unit that represents 6.022 x 10^23 particles, i.e., Avogadro's number. Molar mass is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). It is found by summing the atomic masses of the constituent elements as listed on the periodic table.
For NaCl, the molar mass is approximately 58.44 g/mol. This is the value used to convert from grams to moles in concentration calculations. With 50 g of NaCl, you can convert this mass into moles using the formula: \[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{50 \text{ g}}{58.44 \text{ g/mol}} = 0.856 \text{ mol} \]
This calculation is crucial for figuring out how the amount of solute affects the molarity of a solution.

Volume of Solution

When making solutions, measuring the volume accurately is vital. The final volume reflects the amount of solute and solvent combined, influencing the molarity of the solution. When NaCl is dissolved in a specific amount of water, the final volume can differ depending on how the solution is prepared.
In the exercise, two scenarios are presented: one where the NaCl is dissolved in 1.0 L of water, potentially resulting in a larger total volume after the solute is added, and the other where NaCl is dissolved until the total final volume is precisely 1.0 L. The latter is a more controlled preparation, allowing direct calculation of molarity.

Calculation of Concentration

Concentration, specifically molarity, tells us how much solute is present in a given volume of solution. Molarity (M) is calculated using the formula: \[ M = \frac{n}{V} \] where \( n \) is the number of moles of solute and \( V \) is the volume of the solution in liters.
Given the two methods of preparing a solution mentioned in the exercise, only the second scenario allows for direct calculation of molarity. Here, the total volume is fixed at 1.0 L after the NaCl has been fully dissolved and the solution has been topped up with water. This yields a straightforward calculation: \( M = \frac{0.856 \text{ mol}}{1.0 \text{ L}} = 0.856 \text{ mol/L} \). In this controlled environment, molarity can be accurately determined from the known quantities, providing clarity and ease in further chemical analyses.