Question

An experiment calls for \(125 \mathrm{~mL}\) of \(0.105 \mathrm{M} \mathrm{NaCl}\) solution. What mass of \(\mathrm{NaCl}\) is required? What mass of \(\mathrm{NaCl}\) would be required for \(1.00 \mathrm{~L}\) of the same solution?

Short answer

To prepare 125 mL of a 0.105 M NaCl solution, \(0.105 \times (125 \times 0.001) = 0.013125\) moles of NaCl are needed. The mass of NaCl required is \(0.013125 \times 58.44 \approx 0.767 \mathrm{~g}\). For 1.00 L of the same solution, \(0.105 \times 1.00 = 0.105\) moles of NaCl are needed. The mass of NaCl required is \(0.105 \times 58.44 \approx 6.14 \mathrm{~g}\).

Step-by-step solution

Calculate moles of NaCl for 125 mL solution

Firstly, we need to find out how many moles of NaCl are needed to prepare 125 mL of a 0.105 M NaCl solution. To do this, use the molarity formula and convert the volume from mL to L: 0.105 moles/L = moles of NaCl/(125 mL × 0.001 L/mL) moles of NaCl = 0.105 moles/L × (125 mL × 0.001 L/mL)

Calculate mass of NaCl for 125 mL solution

Next, we need to calculate the mass of NaCl required for the 125 mL solution. Use the molar mass of NaCl (58.44 g/mol), and multiply it with the moles of NaCl found in Step 1: mass of NaCl (for 125 mL) = moles of NaCl × 58.44 g/mol

Calculate moles of NaCl for 1.00 L solution

Now, find out how many moles of NaCl are needed to prepare 1.00 L of the same 0.105 M NaCl solution using the molarity formula: 0.105 moles/L = moles of NaCl/1.00 L moles of NaCl = 0.105 moles/L × 1.00 L

Calculate mass of NaCl for 1.00 L solution

Finally, we need to calculate the mass of NaCl required for the 1.00 L solution. Use the molar mass of NaCl (58.44 g/mol), and multiply it with the moles of NaCl found in Step 3: mass of NaCl (for 1.00 L) = moles of NaCl × 58.44 g/mol

Key concepts

Understanding Moles

In chemistry, the concept of a mole is fundamental for measuring amounts of a substance. A mole is defined as the amount of any chemical substance that contains as many elementary entities, such as atoms, molecules, or ions, as there are atoms in 12 grams of pure carbon-12. This equates to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities.

When dealing with solutions, knowing the number of moles of solute (the dissolved substance) helps in understanding its concentration and behavior in the solvent. The formula for molarity (M) is \(M = \frac{\text{moles of solute}}{\text{liters of solution}}\).

In the exercise given, we are calculating the moles of \(\text{NaCl}\) required for specific volumes of solutions with a molarity of \(0.105 \text{ M}\).

• For \(125 \text{ mL}\), converting to liters gives \(0.125 \text{ L}\), thus moles of \(\text{NaCl} = 0.105 \text{ moles/L} \times 0.125 \text{ L} = 0.013125 \text{ moles}\).
• For \(1.00 \text{ L}\), it directly requires \(0.105 \text{ moles of NaCl}\).

Understanding these calculations enables us to accurately prepare solutions of desired concentrations.

Mass Calculations in Solution Preparation

To prepare a solution of a given molarity, we need to know the mass of solute required. This is calculated using the molar mass, which expresses mass per mole of a substance.

The molar mass of sodium chloride \(\text{(NaCl)}\) is \(58.44 \text{ g/mol}\). This molar mass helps convert moles of \(\text{NaCl}\) to the mass needed for the solution.

• For the \(125 \text{ mL}\) solution with \(0.013125 \text{ moles of NaCl}\):
  \[\text{Mass of NaCl} = 0.013125 \text{ moles} \times 58.44 \text{ g/mol} \approx 0.767 \text{ grams}\]
• For \(1.00 \text{ L}\) of solution with \(0.105 \text{ moles of NaCl}\):
  \[\text{Mass of NaCl} = 0.105 \text{ moles} \times 58.44 \text{ g/mol} = 6.136 \text{ grams}\]

These calculations show the precise amount of sodium chloride needed to achieve the required solution concentrations.

Steps in Solution Preparation

Preparing a solution involves careful measurement and mixing of the solute with the solvent. Here are simple steps to successfully prepare a solution with a specific molarity:

1. **Calculate the Moles Needed:** Use the desired molarity and volume to calculate how many moles of the solute are required.

2. **Measure the Mass of Solute:** Utilize the molar mass to convert the moles calculated into mass, which is easily measurable on a scale.

For instance, when preparing a \(0.105 \text{ M NaCl}\) solution:

• For \(125 \text{ mL}\), we measure \(0.767 \text{ grams}\) of \(\text{NaCl}\).
• For a liter, measure \(6.136 \text{ grams}\).

3. **Dissolve the Solute:** Add the measured mass of \(\text{NaCl}\) to a volume of water less than the total desired volume. Stir until completely dissolved.

4. **Dilute to Final Volume:** Once the solute is dissolved, add the remaining solvent to reach the total required volume (e.g., \(125 \text{ mL}\) or \(1.00 \text{ L}\)).

By following these steps, you can ensure that your solution is prepared accurately for successful use in experiments.