Question

Describe how you would prepare \(2.00 \mathrm{~L}\) of each of the following solutions. a. \(0.250 \mathrm{M} \mathrm{NaOH}\) from solid \(\mathrm{NaOH}\) b. \(0.250 \mathrm{M} \mathrm{NaOH}\) from \(1.00 \mathrm{M} \mathrm{NaOH}\) stock solution c. \(0.100 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr} \mathrm{O}_{4}\) from solid \(\mathrm{K}_{2} \mathrm{CrO}_{4}\) d. \(0.100 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr} \mathrm{O}_{4}\) from \(1.75 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4}\) stock solution

Short answer

To prepare the solutions: a. Measure 20 g of solid NaOH, dissolve in 1 L of distilled water, transfer to a 2 L volumetric flask, and fill to the 2 L mark with distilled water. Mix thoroughly. b. Measure 0.500 L of 1.00 M NaOH stock solution, transfer to a 2 L volumetric flask, and fill to the 2 L mark with distilled water. Mix thoroughly. c. Measure the calculated mass of solid K2CrO4, dissolve in 1 L of distilled water, transfer to a 2 L volumetric flask, and fill to the 2 L mark with distilled water. Mix thoroughly. d. Measure the calculated volume of the 1.75 M K2CrO4 stock solution, transfer to a 2 L volumetric flask, and fill to the 2 L mark with distilled water. Mix thoroughly.

Step-by-step solution

Calculate required moles of solute.

First, we need to determine the moles of NaOH required for 2 L of a 0.250 M solution. We can use the formula: Moles = Molarity × Volume Moles = \(0.250 \mathrm{M} \times 2.00 \mathrm{L}\) = 0.500 moles So, we need 0.500 moles of NaOH.

Calculate mass of solid NaOH required.

To find the mass of solid NaOH needed, we can use its molar mass (approximately 40 g/mol): Mass = Moles × Molar mass Mass = \(0.500 \space moles \times 40 \frac{\mathrm{g}}{\mathrm{mol}}\) = 20 g We need 20 g of solid NaOH.

Describe the preparation process.

To prepare 2 L of 0.250 M NaOH solution, perform the following steps: 1. Measure 20 g of solid NaOH using a balance. 2. Dissolve the solid NaOH in approximately 1 L of distilled water in a beaker. 3. Transfer the solution to a 2 L volumetric flask. 4. Add distilled water up to the 2 L mark on the volumetric flask. 5. Mix the solution thoroughly. #b. 0.250 M NaOH from 1.00 M NaOH stock solution#

Calculate volume of stock solution required.

To find the volume of the 1.00 M NaOH stock solution needed, we can use the dilution formula: \(C_{1}V_{1} = C_{2}V_{2}\) Where \(C_{1}\) is the initial concentration (1.00 M), \(V_{1}\) is the volume of the stock solution, \(C_{2}\) is the final concentration (0.250 M), and \(V_{2}\) is the final volume (2 L). Solving for \(V_{1}\), we have: \(V_{1} = \frac{C_{2}V_{2}}{C_{1}} = \frac{0.250 \space \mathrm{M} \cdot 2.00 \space \mathrm{L}}{1.00 \space \mathrm{M}} = 0.500 \space \mathrm{L}\) We need 0.500 L of the 1.00 M NaOH stock solution.

Describe the preparation process.

To prepare 2 L of 0.250 M NaOH solution, perform the following steps: 1. Measure 0.500 L of the 1.00 M NaOH stock solution using a graduated cylinder. 2. Transfer the stock solution to a 2 L volumetric flask. 3. Add distilled water up to the 2 L mark on the volumetric flask. 4. Mix the solution thoroughly. #c. 0.100 M K2CrO4 from solid K2CrO4# Repeat steps 1-3 for K2CrO4, with the corresponding malarity of 0.100 M and molar mass of approximately 194 g/mol.

Describe the preparation process.

To prepare 2 L of 0.100 M K2CrO4 solution, perform the following steps: 1. Measure the calculated mass of solid K2CrO4 using a balance. 2. Dissolve the solid K2CrO4 in approximately 1 L of distilled water in a beaker. 3. Transfer the solution to a 2 L volumetric flask. 4. Add distilled water up to the 2 L mark on the volumetric flask. 5. Mix the solution thoroughly. #d. 0.100 M K2CrO4 from 1.75 M K2CrO4 stock solution# Repeat step 4 for K2CrO4, with the corresponding initial concentration of 1.75 M and final concentration of 0.100 M.

Describe the preparation process.

To prepare 2 L of 0.100 M K2CrO4 solution, perform the following steps: 1. Measure the calculated volume of the 1.75 M K2CrO4 stock solution using a graduated cylinder. 2. Transfer the stock solution to a 2 L volumetric flask. 3. Add distilled water up to the 2 L mark on the volumetric flask. 4. Mix the solution thoroughly.

Key concepts

Molarity Calculations

Molarity is a foundational concept in chemistry, especially when it comes to solution preparation. It measures the concentration of a solute in a solution. To express it in mathematical terms, molarity (\textbf{M}) is defined as the number of moles of a solute per liter of solution. The formula for molarity can be stated as:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
For our example, to prepare a 0.250 M NaOH solution, we first need to identify how many moles of solute are needed for 2.00 L of the solution. By rearranging the molarity formula, we calculated that 0.500 moles of NaOH are required. Understanding how to manipulate this formula is vital for accurately preparing solutions of precise concentrations.

Dilution of Solutions

Dilution is a process by which the concentration of a solute in a solution is decreased by adding more solvent. The key principle to remember is that while the concentration changes, the total amount of solute remains the same. The dilution formula is a helpful tool for such calculations:
\[ C_1V_1 = C_2V_2 \]
Where \(C_1\) and \(V_1\) are the initial concentration and volume, and \(C_2\) and \(V_2\) are the final concentration and volume respectively. When preparing a diluted NaOH solution, for instance, the formula helped us determine the volume of the stock solution needed. By understanding how to apply this formula, you can create solutions of any desired concentration from a more concentrated stock solution.

Molar Mass Usage

The molar mass of a substance is the mass of one mole of that substance. It is a bridge between the mass of a material and the number of moles since it reflects the mass per mole of its constituent atoms, usually expressed in grams per mole (g/mol).
For the preparation of solutions from solid substances, like NaOH or K2CrO4, we need to use the molar mass to convert moles of the solid to the mass that needs to be weighed out. This step is essential since most practical chemistry requires the weighing of substances.
Calculating the mass of NaOH needed, we used its molar mass of approximately 40 g/mol. Similarly, for K2CrO4 with a molar mass around 194 g/mol, the molar mass allowed for accurate measurement of the substance required. Hence, the molar mass is critical in ensuring the prepared solution has the exact concentration specified by the molarity calculations.