Question

How would you prepare \(275 \mathrm{~mL}\) of \(0.350 \mathrm{M} \mathrm{NaCl}\) solution using an available \(2.00 \mathrm{M}\) solution?

Short answer

To prepare 275 mL of 0.350 M NaCl solution using an available 2.00 M solution, apply the dilution formula \(C1 \cdot V1 = C2 \cdot V2\). Plug in the values: \( (2.00 \mathrm{M}) \cdot V1 = (0.350 \mathrm{M}) \cdot (275 \mathrm{mL}) \). Solve for V1: \( V1 = \frac{(0.350 \mathrm{M}) \cdot (275 \mathrm{mL})}{(2.00 \mathrm{M})} = 48.125 \mathrm{mL} \). Therefore, 48.125 mL of the 2.00 M NaCl solution is required.

Step-by-step solution

Write down the dilution formula

The formula for dilution is: \(C1 \cdot V1 = C2 \cdot V2\) where, C1 = Initial concentration of the stock (concentrated) solution V1 = Volume of the stock solution needed C2 = Final concentration of the diluted solution V2 = Final volume of the diluted solution In this case: C1 = 2.00 M NaCl (stock solution) V1 = Volume needed from the 2.00 M solution (unknown) C2 = 0.350 M NaCl (final desired concentration) V2 = 275 mL (desired final volume)

Plug in the values and solve for V1

Insert the given values into the dilution formula: \( (2.00 \mathrm{M}) \cdot V1 = (0.350 \mathrm{M}) \cdot (275 \mathrm{mL}) \) To find V1, divide both sides of the equation by 2.00 M: \( V1 = \frac{(0.350 \mathrm{M}) \cdot (275 \mathrm{mL})}{(2.00 \mathrm{M})} \)

Calculate V1

Perform the calculation: \( V1 = \frac{(0.350 \mathrm{M}) \cdot (275 \mathrm{mL})}{(2.00 \mathrm{M})} = 48.125 \mathrm{mL} \)

Final answer

To prepare 275 mL of 0.350 M NaCl solution from the 2.00 M solution, 48.125 mL of the 2.00 M NaCl solution is required.

Key concepts

Dilution Formula

The dilution formula is essential when you need to prepare a solution of a certain concentration from a more concentrated stock solution. This formula is expressed as:

• \( C_1 \times V_1 = C_2 \times V_2 \)

Let's break it down:

• \(C_1\): This represents the initial concentration of the more concentrated solution you start with.
• \(V_1\): This is the volume of the initial concentrated solution you need to dilute.
• \(C_2\): This is the desired concentration you wish to achieve after dilution.
• \(V_2\): This represents the total volume of the final diluted solution.

Using this formula involves plugging in the values you know and solving for the unknown. For example, if you have a 2.00 M NaCl solution and want to prepare 275 mL of a 0.350 M solution, you can use the dilution formula to find out how much of the 2.00 M solution is needed.It's a convenient and widely used formula in chemistry for making accurate dilutions.

Concentration Calculation

Concentration refers to how much solute is present in a given amount of solution. It's typically expressed in moles per liter (Molarity, M). Calculating the concentration before and after dilution is crucial to ensure you obtain the desired mixture.For initial calculations, let's say you have a solution at a concentration \(C_1\) of 2.00 M. After adding enough solvent, you aim for this solution to be at a new concentration \(C_2\), such as 0.350 M. Through concentration calculations, you can figure out the necessary volume of the more concentrated solution required to achieve the desired dilution. The equation \(C_1 \times V_1 = C_2 \times V_2\) embodies the concept that, during dilution, while the concentration changes, the total number of moles present remains constant. This means, despite increasing the volume of the solution, the amount of solute stays the same, ensuring the correct concentration after dilution.

Volume Calculation

Volume calculation in solution preparation involves determining either how much of the concentrated solution is required or what volume the final solution should be. Consider the example: you wish to prepare 275 mL of NaCl solution at a concentration of 0.350 M. Volume calculation helps you determine how much of the original 2.00 M stock solution you should use. By rearranging the dilution formula for \(V_1\), you can directly calculate the volume needed:\[V_1 = \frac{C_2 \times V_2}{C_1}\]In this case, it involves substituting the known concentrations and the desired final volume:

• \(C_1 = 2.00 \) M
• \(C_2 = 0.350 \) M
• \(V_2 = 275 \) mL
• \(V_1 = \frac{(0.350 \times 275)}{2.00} = 48.125 \) mL

The volume calculation ensures you correctly mix your solutions to reach the desired concentration, making sure all components are properly balanced. This method is necessary to maintain consistency and accuracy across different solutions.