Problem 18 - Introductory Chemistry Atoms First

Question

You have 1 L of a \(3.00 \mathrm{M}\) stock solution of \(\mathrm{NaCl}\) and need to prepare \(400.0 \mathrm{~mL}\) of a \(2.00 \mathrm{M}\) solution. Describe how you would do it.

Step-by-Step Solution

Answer

To prepare 400.0 mL of a 2.00 M NaCl solution from a 3.00 M stock solution, first calculate the required volume of the stock solution using the dilution formula \(V_1 = \frac{C_2V_2}{C_1}\), which results in \(V_1 = 266.7 \mathrm{~mL}\). Then, measure 266.7 mL of the 3.00 M stock solution and pour it into a 400.0 mL volumetric flask. Add distilled water until the volume reaches the 400.0 mL mark and mix well. This will yield a 2.00 M NaCl solution.

Step 1: Identify given information

We are given the following information: - Initial concentration (C1): 3.00 M - Final concentration (C2): 2.00 M - Final volume (V2): 400.0 mL Our goal is to find the volume of the stock solution (V1) needed to prepare the desired 2.00 M NaCl solution.

Step 2: Use the dilution formula

We will use the dilution formula, \(C_1V_1 = C_2V_2\), to determine the volume of the stock solution needed.

Step 3: Solve for V1

To find the volume of the stock solution required, we rearrange the formula as follows: \(V_1 = \frac{C_2V_2}{C_1}\) Plugging in the given values: \(V_1 = \frac{(2.00 \mathrm{~M})(400.0 \mathrm{~mL})}{3.00 \mathrm{~M}}\) Calculate the result: \(V_1 = 266.7 \mathrm{~mL}\) So, we will need 266.7 mL of the 3.00 M stock solution to prepare the desired 2.00 M NaCl solution.

Step 4: Prepare the 2.00 M NaCl solution

To prepare the 2.00 M NaCl solution, follow these steps: 1. Measure 266.7 mL of the 3.00 M stock NaCl solution using a graduated cylinder. 2. Pour the measured stock solution into a 400.0 mL volumetric flask or container. 3. Add distilled water to the container until the volume reaches the desired 400.0 mL mark. Make sure to add water slowly and carefully as you approach the 400.0 mL mark. 4. Mix the solution well, ensuring that the NaCl and water are thoroughly combined. This should result in a 400.0 mL solution with a concentration of 2.00 M NaCl. You have now prepared the desired 2.00 M NaCl solution using the 3.00 M stock solution.

Key Concepts

Dilution Formula

Understanding the dilution formula is crucial for scientists and students working with chemical solutions. It is a simple equation that allows you to calculate the volume or concentration of a solution after it has been diluted. The formula is given by:
\[ C_1V_1 = C_2V_2 \]
where:

• \(C_1\) = initial concentration of the stock solution
• \(V_1\) = volume of the stock solution needed
• \(C_2\) = final concentration of the diluted solution
• \(V_2\) = final volume of the diluted solution

By rearranging the formula to solve for the unknown variable, you can determine the amount of solvent you need to add to reach a desired concentration of solute in a new volume. This is an essential process in various fields such as chemistry, biology, and pharmacology, where precise concentrations are necessary for experiments, formulations, and treatments.

Molarity

Molarity, symbolized by M, is a unit of concentration in chemistry that measures the number of moles of a solute per liter of solution. It is a way to express the concentration of a substance within a given volume of liquid, making it important for reagent preparation and chemical reactions.
The formula for molarity is:
\[ M = \frac{moles\underline{\phantom{xxx}}of\underline{\phantom{xxx}}solute}{liters\underline{\phantom{xxx}}of\underline{\phantom{xxx}}solution} \]
In practical applications, molarity affects the outcome of chemical reactions. For instance, if a reaction requires a specific molarity for reactants to fully engage, too low or too high a molarity could lead to an incomplete reaction or waste of materials. For our example, the target molarity of 2.00 M in 400.0 mL gives us the necessary information to determine the required volume of the stock solution using the dilution formula.

Stock Solution

A stock solution is a concentrated solution that serves as a starting point for making diluted solutions of lower concentrations. They are commonly used in laboratories because they can be precisely prepared and standardized. In many cases, stock solutions are stored for ease of use, to save time during experiments, or to reduce the margin of error when making repeated dilutions.
When working with stock solutions, it is important to remember that only the solvent—usually water—is added during dilution; the amount of solute remains the same. Therefore, the solute's moles before and after the dilution are constant—an essential concept to understand when performing volumetric analysis and ensuring accuracy in experimental outcomes.

Volumetric Analysis

Volumetric analysis is a quantitative analytical method that measures the volume of a solution to determine the concentration of a solute. It incorporates techniques such as titration and the use of volumetric flasks, pipettes, and burettes for precise measurement. The accuracy of these measurements is paramount because they directly impact the reliability of the molarity calculations and subsequent chemical reactions or processes.

Steps in Volumetric Analysis

Typically, the procedure includes the preparation of standard solutions, precise measuring of volumes, and stoichiometric calculations based on balanced chemical equations. The heart of volumetric analysis is the careful control and measurement of volumes to ensure that the concentrations of solutions prepared or analyzed are exact, exemplified by the procedure described in our initial problem for diluting a stock NaCl solution.