Question

An aqucous \(\mathrm{NaCl}\) solution is made using 112 \(\mathrm{g}\) of \(\mathrm{NaCl}\) diluted to a total solution volume of 1.00 \(\mathrm{L}\) . Calculate the molarity, molality, and mass percent of the solution. (Assume a density of 1.08 \(\mathrm{g} / \mathrm{mL}\) for the solution.)

Short answer

The molarity of the solution is 1.92 M, the molality is 1.98 m, and the mass percent is 9.67%.

Step-by-step solution

Determine the Moles of NaCl

To find the molarity and molality, calculate the moles of NaCl by using the formula: moles = mass (g) / molar mass (g/mol). The molar mass of NaCl is the sum of the atomic masses of sodium (22.99 g/mol) and chlorine (35.45 g/mol), which equals 58.44 g/mol.

Calculate the Molarity

Molarity (M) is defined as moles of solute per liter of solution. Use the formula: Molarity (M) = moles of NaCl / volume of solution (L). The volume of the solution is given as 1.00 L.

Calculate the Molality

Molality (m) is defined as moles of solute per kilogram of solvent. To find the mass of the solvent, first calculate the mass of the solution and then subtract the mass of NaCl.Mass of solution = volume * density. Mass of solvent = mass of solution - mass of NaCl.Use the formula: Molality (m) = moles of NaCl / mass of solvent (kg).

Calculate the Mass Percent

Mass percent is calculated by the formula: mass percent = (mass of solute / mass of solution) * 100%. Use the mass of NaCl and the mass the solution you calculated in the previous steps.

Key concepts

Molarity

Molarity is a crucial concept in chemistry that helps understand the concentration of a solution. Skipping straight to the math might be a common approach, but let's break down what molarity truly means. It refers to the number of moles of solute (the substance being dissolved) present in one liter of solution. The formula for calculating molarity is straightforward:
\( M = \frac{moles \, of \, solute}{volume \, of \, solution \, (L)} \)
In the context of our exercise, after determining the moles of sodium chloride (NaCl), you divide that number by the total volume of the aqueous solution in liters. As the solution volume is already provided as 1.00 L, the molarity is immediately obtained after finding the moles of NaCl. Remember, the density information plays no part in this molarity calculation.

Molality

While molarity counts the solute's moles per liter of solution, molality counts them per kilogram of solvent. This is useful because molality isn't affected by changes in temperature, making it important for boiling point elevation and freezing point depression studies. The molality formula is:
\( m = \frac{moles \, of \, solute}{mass \, of \, solvent \, (kg)} \)
To calculate molality, you need to first determine the mass of the solvent. You do this by subtracting the mass of NaCl from the total mass of the solution. The total mass of the solution can be found by multiplying its volume by the given density. Once you have the mass of the solvent, simply divide the moles of NaCl by this mass (in kilograms) to find the molality. In our exercise, since the solution's density is provided, you would convert the volume to grams (using density), subtract the mass of NaCl, and then convert this value to kilograms for the calculation.

Mass Percent

Mass percent is another way to express concentration, indicating the mass of the solute compared to the total mass of the solution, multiplied by 100 to get a percentage. The formula for mass percent is:
\( \text{mass percent} = \left( \frac{mass \, of \, solute}{mass \, of \, solution} \right) \times 100\% \)
For the given exercise, you first find the total mass of the solution using the provided density and solution volume. Then you divide the mass of NaCl (solute), by the total mass of the solution, and multiply by 100 to convert it into a percentage. This figure will tell you how much NaCl, by mass, is in the solution. It's a simple and intuitive way to understand solution concentration without depending on volume, crucial when working in various conditions, like changes in pressure or temperature.

Moles Calculation

Understanding how to calculate moles is foundational in chemistry, as moles link the microscopic world of atoms and molecules to the macroscopic world we can measure. The mole concept allows chemists to count particles by weighing them. Moles calculation involves the formula:
\( \text{moles} = \frac{mass \, (g)}{molar \, mass \, (g/mol)} \)
To perform moles calculation for NaCl in our exercise, divide the provided mass of NaCl by its molar mass (the sum of the atomic masses of sodium and chlorine). In practical terms, you're seeing how many 'packets' of NaCl fit into the mass you have. Molar mass effectively acts as the 'price tag' for one mole of particles, and the mass you have indicates 'how much you've spent' on NaCl particles.