Question

A student wants to prepare 1.00 L of a 1.00-M solution of NaOH (molar mass = 40.00 g/mol). If solid NaOH is available, how would the student prepare this solution? If 2.00 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 1.00 L of a 1.00 M NaOH solution, the student needs to: 1. Using solid NaOH: a. Weigh 40.00 g of solid NaOH. b. Dissolve it in less than 1.00 L of distilled water. c. Transfer the solution to a 1.00 L volumetric flask and add distilled water up to the mark. 2. Using 2.00 M NaOH solution: a. Measure 0.500 L of the 2.00 M NaOH solution. b. Transfer to a 1.00 L volumetric flask and add distilled water up to the mark. To maintain 3 significant figures in the NaOH molarity, ensure that mass and volumes are measured with at least 3 significant figures.

Step-by-step solution

Calculate the mass of NaOH required

The student wants to prepare a 1.00 L solution of 1.00 M NaOH. To find out how many grams of NaOH are needed, we use the following formula: Mass = Molarity × Volume × Molar mass where Molarity = 1.00 M, Volume = 1.00 L, and Molar mass of NaOH = 40.00 g/mol. Calculating the mass of NaOH we get: Mass = (1.00 M) × (1.00 L) × (40.00 g/mol) = 40.00 g

Preparation of the solution

Weigh 40.00 g of solid NaOH and dissolve it in less than 1.00 L of distilled water. Then pour the solution into a 1.00 L volumetric flask and add distilled water to the mark to make 1.00 L of 1.00 M NaOH solution. **Using 2.00 M NaOH solution:**

Calculate the volume of 2.00 M NaOH solution required

To calculate the required volume of the 2.00 M solution, use the following formula: C1 × V1 = C2 × V2 where C1 is the initial concentration (2.00 M), V1 is the volume of the initial solution required, C2 is the final concentration (1.00 M), and V2 is the final volume (1.00 L). Rearranging the formula to solve for V1: V1 = (C2 × V2) / C1 Calculating the volume of the 2.00 M NaOH solution needed, we get: V1 = (1.00 M × 1.00 L) / 2.00 M = 0.500 L

Preparation of the solution

Measure 0.500 L of the 2.00 M NaOH solution and pour it into a 1.00 L volumetric flask. Add distilled water to the mark to make 1.00 L of 1.00 M NaOH solution. Lastly, to ensure three significant figures in the NaOH molarity, the volumes and mass should be determined to at least three significant figures as well.

Key concepts

Molarity

Molarity is an essential concept when preparing solutions in chemistry. It describes the concentration of a solute in a solution. Molarity is expressed as the number of moles of solute per liter of solution. It's symbolized by the letter "M" and is calculated using the formula:\[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}\]In our exercise, we wanted to prepare a 1.00 M solution of NaOH. This means there should be 1 mole of NaOH dissolved in 1 liter of the solution. Knowing the molar mass of NaOH (40.00 g/mol), we calculated that 40.00 grams of NaOH is needed to make a 1.00-liter solution with a molarity of 1.00 M.Key points about molarity:

• Molarity helps in understanding the concentration of a solution.
• It's important in reactions to know how much of reactants are needed.
• Measured in moles of solute per liter of the solution.

Significant Figures

Significant figures play a critical role in ensuring precision and accuracy in scientific measurements and calculations. When we calculate values such as mass or volume, it's important to reflect the degree of accuracy right from measurement. In the context of preparing solutions, ensuring an accurate concentration like our example of NaOH, having three significant figures means that each figure in our measurements (such as 40.00 g for mass or 1.00 L for volume) significantly impacts the result. This precision is crucial for consistency, especially in scientific experiments or manufacturing where even small deviations can lead to errors. Here's why significant figures matter:

• They indicate the precision of a measurement.
• They help maintain consistency across different measurements and calculations.
• Using appropriate significant figures minimizes the error in scientific computations.

For three significant figures, ensure every measurement, like weighing the NaOH and measuring volumes, is recorded and calculated accordingly. This ensures the final molarity is precise and accurate.

Volumetric Flask

A volumetric flask is a valuable piece of lab equipment used for preparing solutions with precise volumes. These flasks are specifically designed for accuracy and are marked with a line indicating a particular volume. When preparing a solution, such as our 1.00 M NaOH solution, after adding the calculated amount of NaOH and dissolving it partially, the solution is transferred to a 1.00 L volumetric flask. To achieve exactly 1.00 L, distilled water is added until the bottom of the meniscus (the curve seen at the top of the liquid) touches the line on the neck of the flask. Benefits of using a volumetric flask:

• Provides high accuracy and precision in measuring solution volumes.
• Ensures consistency and reliability in chemical experiments.
• Helps maintain the desired concentration of solutions.
• Its shape makes it easy to mix solutions thoroughly.

By using the volumetric flask properly, you ensure that the concentration, such as our needed 1.00 M solution, is accurate. This accuracy is vital for consistency and reliability in lab experiments.