Question

Suppose \(325 \mathrm{~mL}\) of \(0.150 \mathrm{M} \mathrm{NaOH}\) is needed for your experiment. How would you prepare this if all that is available is a \(1.01 M \mathrm{NaOH}\) solution?

Short answer

To prepare 325 mL of a 0.150 M NaOH solution using a 1.01 M NaOH solution, you need to take 48.76 mL of the 1.01 M NaOH solution and dilute it with water until the volume reaches 325 mL.

Step-by-step solution

Identify the given values

Given values: - Initial concentration (\(C_1\)) = 1.01 M - Final concentration (\(C_2\)) = 0.150 M - Volume of final solution (\(V_2\)) = 325 mL

Calculate the initial volume using the dilution formula

Using the formula \(C_1V_1 = C_2V_2\), we can calculate the volume of the initial solution (\(V_1\)) needed to obtain the desired concentration: \(V_1 = \frac{C_2V_2}{C_1}\) Substitute the given values: \(V_1 = \frac{0.150 \times 325}{1.01}\)

Calculate the result

\(V_1 = \frac{0.150 \times 325}{1.01}\) \(V_1 = 48.76 \ml\)

Conclusion

To prepare 325 mL of a 0.150 M NaOH solution from a 1.01 M NaOH solution, you will need to take 48.76 mL of the 1.01 M NaOH solution and dilute it with water until the volume reaches 325 mL.

Key concepts

Solution Concentration

Understanding the concept of solution concentration is essential for many laboratory procedures, including dilutions. Concentration is a measure of how much solute is contained within a certain volume of solvent. It’s commonly expressed in molarity (M), which is the number of moles of solute per liter of solution.

To give a practical example, let's consider the exercise where someone needs to use a sodium hydroxide (NaOH) solution for an experiment. It’s crucial to have the correct concentration, as this can affect the outcome of the experiment. In this case, our target concentration is 0.150 M, meaning there should be 0.150 moles of NaOH in every liter of solution. To achieve the correct concentration, the starting material is the more concentrated 1.01 M solution of NaOH, which has to be diluted.

Molarity

Molarity is a central concept in chemistry that quantifies the concentration of a solution. The molarity (M) can be determined by the formula \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \].

Considering our example, when preparing a solution, it's crucial to know the molarity because it indicates the strength of that solution. When a researcher is aiming for a specific reaction or result, they must be precise with the amount of each reactant used. The provided exercise involves adjusting the molarity of an existing NaOH solution to reach a different, precise molar concentration. This process involves calculating the volume of the initial concentrated solution (\(V_1\text{ in mL}\text{ or L}\text{, depending on the equation}\text{ format}\text{ used}\text{)\text that must be used.}

Molar Dilution

Molar dilution is a process which involves reducing the concentration of a solution by adding solvent. The key equation used in molar dilution is \[ C_1V_1 = C_2V_2 \], where \(C_1\) and \(V_1\) are the concentration and volume of the initial solution, respectively, and \(C_2\) and \(V_2\) are the desired concentration and volume of the final solution.

In the provided exercise, the task is to dilute a 1.01 M NaOH solution to reach a final concentration of 0.150 M. Using the dilution equation, we determine that 48.76 mL of the original solution, when diluted to a final volume of 325 mL, will result in the desired concentration. This formula provides a quick and simple method for ensuring accurate concentration adjustments in lab settings, allowing for successful experimental outcomes.