Question

It is desired to prepare exactly $100.$ mL of sodium chloride solution. If $2.71\mathrm{g}$ of $\mathrm{NaCl}$ is weighed out, transferred to a volumetric flask, and water added to the 100 -mL mark, what is the molarity of the resulting solution?

Short answer

The molarity of the sodium chloride solution is $0.464mol/L$.

Step-by-step solution

1. Convert mass of NaCl to moles.

First, we need to convert the given mass of NaCl (2.71 g) to moles using its molar mass. The molar mass of NaCl is 58.44 g/mol (22.99 g/mol for Na and 35.45 g/mol for Cl). Moles of NaCl = mass of NaCl / molar mass of NaCl $Mole{s}_{NaCl}=\frac{2.71g}{58.44g/mol}$

2. Calculate the number of moles of NaCl.

Now, we can calculate the number of moles of NaCl: $Mole{s}_{NaCl}=\frac{2.71g}{58.44g/mol}=0.0464mol$

3. Convert the volume of the solution to liters.

The volume of the solution is given in milliliters (100 mL). To convert this to liters, simply divide the value by 1000: Volume in Liters = Volume in mL / 1000 $V_L=\frac{100mL}{1000}=0.1L$

4. Calculate the molarity of the NaCl solution.

Now, we can find the molarity (M) of the NaCl solution using the formula: M = moles of solute / volume of solution in liters $M_{NaCl}=\frac{Mole{s}_{NaCl}}{V_L}$ Plug in the values calculated in steps 2 and 3: $M_{NaCl}=\frac{0.0464mol}{0.1L}=0.464mol/L$ Thus, the molarity of the sodium chloride solution is 0.464 mol/L.

Key concepts

Understanding Molar Mass

Molar mass is a key concept when working with chemical solutions. It's the mass of one mole of a substance, usually expressed in grams per mole (g/mol). For sodium chloride (NaCl), the molar mass is calculated by summing the atomic masses of sodium (Na) and chlorine (Cl). Sodium has an atomic mass of approximately 22.99 g/mol, and chlorine is about 35.45 g/mol. Therefore, the molar mass of NaCl is 58.44 g/mol.
This value helps in converting grams to moles, allowing us to understand how many NaCl molecules we're dealing with when preparing a solution.

Understanding Moles and Molarity

Molarity is a measure of the concentration of a solute in a solution, given as moles per liter (mol/L). To calculate molarity, you need to know the number of moles of solute and the volume of the solution in liters.
Start by converting the mass of the solute to moles using its molar mass. For instance, if you have 2.71 g of NaCl, you divide by its molar mass (58.44 g/mol) to find the moles:

• Moles of NaCl = $\frac{2.71\text{g}}{58.44\text{g/mol}}=0.0464\text{mol}$

Once you have the moles, convert the solution volume from milliliters to liters, then use the formula for molarity:

• Molarity (M) = $\frac{\text{moles of solute}}{\text{volume in liters}}$

This tells you how concentrated the solution is.

The Role of Volumetric Flasks

A volumetric flask is an essential tool for accurately preparing a solution of specific volume and concentration. It is designed to contain a precise volume when filled to the mark on its neck.
When preparing a 100 mL solution, you first add the measured solid solute to the flask. Then, you add distilled water up to the 100 mL mark. Swirling or gently inverting the flask ensures that the solute mixes thoroughly with the water, resulting in a uniform solution.
Using a volumetric flask ensures precision and accuracy, which is vital for chemical experiments and reactions that require specific concentrations.

Step-by-Step Solution Preparation

Preparing a solution involves a few straightforward steps, often using a volumetric flask for precision. Here's how to do it:

• Weigh the exact amount of solute needed, in this case, 2.71 g of NaCl.
• Transfer the solute into a clean, dry volumetric flask.
• Add distilled water to the flask gradually, swirling to dissolve the solute.
• Continue adding water until the bottom of the meniscus is at the 100 mL line.

After these steps, your NaCl solution is ready with a precise concentration, crucial for experiments requiring specific molarities like the 0.464 mol/L NaCl solution here.