Question

A student wants to prepare \(1.00 \mathrm{L}\) of a \(1.00-M\) solution of NaOH (molar mass \(=40.00 \mathrm{g} / \mathrm{mol}\) ). If solid NaOH is available, how would the student prepare this solution? If \(2.00 \mathrm{M}\) NaOH is available, how would the student prepare the solution? To help ensure three significant figures in the NaOH molarity, to how many significant figures should the volumes and mass be determined?

Short answer

To prepare a 1.00 L of 1.00-M NaOH solution using solid NaOH, the student should weigh out 40.0 g of NaOH, dissolve it in approximately 800 mL of water, and then add more water until the total volume reaches 1.00 L. To prepare the solution using a 2.00 M NaOH solution, measure 0.500 L of the 2.00 M solution, mix it with water until the total volume is 1.00 L. The volumes and mass should be determined with at least three significant figures to ensure accurate molarity.

Step-by-step solution

1. Calculating the mass of solid NaOH required

To prepare a 1.00 L solution of 1.00-M NaOH, we first need to calculate the mass of solid NaOH required. Using the molar mass of NaOH (40.00 g/mol), we can find the mass as follows: Mass of NaOH = (Molarity × Volume) × Molar mass Mass of NaOH = (1.00 mol/L × 1.00 L) × 40.00 g/mol Mass of NaOH = 40.0 g

2. Preparing the 1.00-M NaOH solution from solid NaOH

To prepare the 1.00 L of 1.00-M NaOH solution using solid NaOH, the student should: 1. Measure out 40.0 g of solid NaOH. 2. Dissolve the 40.0 g of solid NaOH in approximately 800 mL of water in a 1 L volumetric flask or beaker. 3. Once the NaOH has dissolved, carefully add water to the flask or beaker until the 1 L mark is reached. 4. Stir the solution to ensure homogeneity.

3. Calculating the dilution ratio for preparing 1.00-M NaOH from 2.00-M NaOH solution

To prepare a 1.00 L of 1.00-M NaOH solution using the 2.00 M NaOH solution, we can use the formula: M1 × V1 = M2 × V2 where M1 is the initial molarity (2.00 M), V1 is the initial volume, M2 is the final molarity (1.00 M), and V2 is the final volume (1.00 L). Solving for V1, we get: V1 = M2 × V2 / M1 V1 = (1.00 mol/L × 1.00 L) / 2.00 mol/L V1 = 0.500 L

4. Preparing the 1.00-M NaOH solution from 2.00-M NaOH solution

To prepare the 1.00 L of 1.00-M NaOH solution using the 2.00 M NaOH solution, the student should: 1. Measure out 0.500 L of the 2.00 M NaOH solution. 2. Pour the 0.500 L of 2.00 M NaOH solution into a 1 L volumetric flask or beaker. 3. Carefully add water to the flask or beaker until the 1 L mark is reached. 4. Stir the solution to ensure homogeneity.

5. Determining the required number of significant figures for the volumes and mass

To help ensure three significant figures in the NaOH molarity, the volumes and mass should have at least three significant figures. In this case, the mass of solid NaOH is already measured with three significant figures (40.0 g). For volumes, we should measure the 0.500 L with three significant figures, meaning we should use a volumetric flask or graduated cylinder that has markings up to at least 0.001 L increments.

Key concepts

Molarity

Molarity is a central concept when it comes to solution preparation. It defines the concentration of a solution and is expressed in moles of solute per liter of solution. In this context, learning how to calculate molarity is crucial for accurately preparing solutions in the lab.To determine molarity, you use the formula:\[\text{Molarity (M)} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}\]It's important because it allows you to predict how a chemical will behave in solution, make precise calculations, and understand chemical reactions. When preparing a solution with a specific molarity, you need to ensure that you accurately measure both the amount of solute and the volume of the solution.

Significant Figures

Significant figures are essential for precision and accuracy in scientific measurements. They indicate the certainty of a measurement, reflecting the precision of the instrument used. When you're dealing with molarity, ensuring the correct number of significant figures is crucial for maintaining consistency and reliability across experiments. For example, if a concentration is given as 1.00 M, it features three significant figures. Thus, all related measurements, such as volume and mass, should have at least three significant figures to ensure precise calculation and interpretation of results. To measure significant figures accurately:

• Use instruments designed for accurate measurements, like volumetric flasks.
• Avoid rounding errors until the final step of calculations.

Molar Mass

Molar mass is the mass of one mole of a substance and is measured in grams per mole (g/mol). It is a key concept when converting between the amount of a substance and its mass.For instance, in preparing a sodium hydroxide (NaOH) solution, you would use the molar mass to figure out how much of the solid you need to weigh out. The molar mass of NaOH is 40.00 g/mol as given in the problem. Calculating the needed mass involves:\[\text{Mass of NaOH} = \text{Molarity} \times \text{Volume} \times \text{Molar Mass}\]Understanding molar mass helps ensure that you accurately weigh the correct amount of a substance to achieve the desired concentration in a solution.

Dilution

Dilution is an important laboratory technique used to achieve a lower concentration of a solution from a more concentrated one. This is often necessary for experiments where a specific concentration is required, and it's more practical to dilute a stock solution.The dilution equation is given by:\[M_1 \times V_1 = M_2 \times V_2\]Where M\_1 is the molarity of the initial solution, V\_1 is the initial volume, M\_2 is the molarity of the diluted solution, and V\_2 is the final volume. This equation helps calculate how much of the concentrated solution is needed to make a diluted solution of a desired volume and molarity.Steps to perform a dilution:

• Measure the volume of the concentrated solution accurately.
• Add this to a volumetric flask or beaker.
• Gradually add solvent until the desired final volume is reached, ensuring uniform mixing.

Dilution makes it easier to work with solutions in a more manageable concentration, ensuring accurate and reliable results in experiments.