Problem 17 - Analytical Chemistry

Question

A series of dilute \(\mathrm{NaCl}\) solutions are prepared starting with an initial stock solution of \(0.100 \mathrm{M} \mathrm{NaCl}\). Solution \(\mathrm{A}\) is prepared by pipeting \(10 \mathrm{~mL}\) of the stock solution into a 250 -mL volumetric flask and diluting to volume. Solution \(\mathrm{B}\) is prepared by pipeting \(25 \mathrm{~mL}\) of solution \(\mathrm{A}\) into a 100 -mL volumetric flask and diluting to volume. Solution \(\mathrm{C}\) is prepared by pipeting \(20 \mathrm{~mL}\) of solution \(\mathrm{B}\) into a 500 -mL volumetric flask and diluting to volume. What is the molar concentration of \(\mathrm{NaCl}\) in solutions \(A, B\) and \(C\) ?

Step-by-Step Solution

Answer

Solution A: 0.004 M, Solution B: 0.001 M, Solution C: 0.00004 M.

Step 1: Calculate Molarity of Solution A

Solution A is prepared by taking 10 mL of a 0.100 M NaCl solution and diluting it to a total volume of 250 mL. Use the dilution formula \(C_1V_1 = C_2V_2\) where \(C_1 = 0.100 \text{ M}\) and \(V_1 = 10 \text{ mL}\). Plug these into the formula: \[0.100 \times 10 = C_2 \times 250\]Solving for \(C_2\):\[C_2 = \frac{0.100 \times 10}{250} = 0.004 \text{ M}\]So, the molarity of Solution A is 0.004 M.

Step 2: Calculate Molarity of Solution B

Solution B is prepared by taking 25 mL of Solution A, which has a molarity of 0.004 M, and diluting it to a total volume of 100 mL. Again, use the dilution formula:\[C_1V_1 = C_2V_2\]where \(C_1 = 0.004 \text{ M}\) and \(V_1 = 25 \text{ mL}\). Plug these into the formula: \[0.004 \times 25 = C_2 \times 100\]Solving for \(C_2\):\[C_2 = \frac{0.004 \times 25}{100} = 0.001 \text{ M}\]So, the molarity of Solution B is 0.001 M.

Step 3: Calculate Molarity of Solution C

Solution C is prepared by taking 20 mL of Solution B, which has a molarity of 0.001 M, and diluting it to a total volume of 500 mL. Use the dilution formula:\[C_1V_1 = C_2V_2\]where \(C_1 = 0.001 \text{ M}\) and \(V_1 = 20 \text{ mL}\). Plug these into the formula: \[0.001 \times 20 = C_2 \times 500\]Solving for \(C_2\):\[C_2 = \frac{0.001 \times 20}{500} = 0.00004 \text{ M}\]So, the molarity of Solution C is 0.00004 M.

Key Concepts

Molarity

Molarity is a way to express the concentration of a solution. It tells us how many moles of solute are present per liter of solution. The formula for molarity is:\[ M = \frac{n}{V} \]where:

• \( M \) is the molarity, measured in moles per liter (M).
• \( n \) is the number of moles of the solute.
• \( V \) is the volume of the solution in liters.

To calculate molarity, you need to know both the amount of solute and the total volume of the solution. Understanding dilutions is key to working with molarities. For dilutions, the molarity of the initial solution multiplied by its volume equals the molarity of the final solution multiplied by its volume:\[ C_1V_1 = C_2V_2 \]Every time you move from a more concentrated solution to a diluted one, the number of moles of solute remains constant, while the volume increases.

Volumetric Flask

A volumetric flask is a piece of laboratory glassware used to prepare precise volumes of liquid solutions. It has a narrow neck with a line etched into it, which helps in measuring the exact volume needed. This ensures that the concentration of the prepared solution is accurate. When preparing a solution using a volumetric flask:

• First, a measured amount of solute is added.
• Then, the solution is diluted to the mark with a solvent, usually water.

The design of the volumetric flask is tailored for precision. The volumes are marked at the neck, making it easy to create solutions with an exact concentration. Volumetric flasks come in different sizes, each meant for different volumes. The accuracy in diluting solutions in laboratory settings is crucial for experimental procedures.

Sodium Chloride Solution

A sodium chloride solution, commonly known as a salt solution, is made by dissolving NaCl into water. This solution is important in chemistry due to its simple ionic nature, which makes it a perfect example for studies on conductivity, colligative properties, and more.Key points about sodium chloride solutions:

• Sodium chloride (NaCl) is an ionic compound made of Na\(^+\) and Cl\(^-\) ions.
• When NaCl dissolves in water, it separates into its ions, which conduct electricity.

In dilution exercises, a sodium chloride solution is often used because diluting helps students understand how the relationship between solute, solvent, and concentration is maintained. Each stage of dilution simply adjusts the amount of solvent relative to the amount of solute, keeping the overall quantity of solute constant.