Question

A solution is prepared by dissolving \(0.6706 \mathrm{~g}\) oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) in enough water to make \(100.0 \mathrm{~mL}\) of solution. \(\mathrm{A}\) \(10.00-\mathrm{mL}\) aliquot (portion) of this solution is then diluted to a final volume of \(250.0 \mathrm{~mL}\). What is the final molarity of the oxalic acid solution?

Short answer

The final molarity of the oxalic acid solution after dilution is 0.00298 M.

Step-by-step solution

Calculate the initial moles of oxalic acid

To find the initial moles of oxalic acid, use the given mass and the molar mass of oxalic acid. The molecular formula of oxalic acid is \(H_2C_2O_4\), so its molar mass is: Molar mass of oxalic acid = 2 (H) + 2 (C) + 4 (O) = 2(1.01) + 2(12.01) + 4(16.00) = 90.04 g/mol Now, use the mass of oxalic acid to calculate the moles: Moles of oxalic acid = mass of oxalic acid / molar mass of oxalic acid = 0.6706 g / 90.04 g/mol = \(7.45 \times 10^{-3}\) mol

Calculate the initial molarity of the solution

Now that we have the moles of oxalic acid, we can find the initial molarity using the volume of the initial solution. Molarity (M) = moles of oxalic acid / volume in L = \(7.45 \times 10^{-3}\text{ mol} / 0.100\text{ L}\) = 0.0745 M

Use the dilution concept to find the final molarity

When a portion of the initial solution is diluted, the moles of solute in both solutions remain the same. So, we can use the equation: M1V1 = M2V2 where M1 is the initial molarity, V1 is the aliquot volume, M2 is the final molarity, and V2 is the final volume. We know M1, V1, and V2, so we can find M2: \(0.0745 \text{ M} \times 0.010 \text{ L} = M2 \times 0.250 \text{ L}\) Now, solve for M2: M2 = \((0.0745 \times 0.010) / 0.250 \text{ M}\) = 0.00298 M

Final molarity of the oxalic acid solution

The final molarity of the oxalic acid solution after dilution is 0.00298 M.

Key concepts

Solution Preparation

Solution preparation is a fundamental chemistry task that involves dissolving a solute into a solvent to create a homogeneous mixture or solution. When preparing a solution:

• Start by measuring the correct mass of the solute. Use a balance to ensure accuracy.
• Dissolve the solute in a small amount of solvent. This helps ensure that the solute is completely dissolved.
• Transfer the solution to a volumetric container and add more solvent to reach the desired volume.

In the given exercise, 0.6706 grams of oxalic acid is used as the solute. It's dissolved in water, the solvent, to make exactly 100.0 mL of the solution. This careful preparation ensures that the solution has a known concentration, which is crucial for subsequent calculations.

Molecular Formula

The molecular formula of a compound shows the actual number of atoms of each element present in a molecule. For oxalic acid, the molecular formula is \( H_2C_2O_4 \). This means each molecule contains:

• 2 hydrogen atoms
• 2 carbon atoms
• 4 oxygen atoms

The molecular formula is important because it helps determine the molar mass, which is the sum of the atomic masses for all the atoms in a molecule. For oxalic acid, the molar mass is calculated as 90.04 g/mol, which is essential for calculating the number of moles from a given mass. Understanding the molecular formula is crucial to solving many chemistry problems because it forms the basis for stoichiometric calculations.

Dilution

Dilution involves decreasing the concentration of a solution, generally by adding more solvent. It's a common practice in laboratories when a less concentrated solution is needed from a more concentrated solution. The key principle behind dilution is that while the volume changes, the amount of solute remains constant.The formula for dilution calculations is:\[ M_1V_1 = M_2V_2 \]- \( M_1 \) and \( V_1 \) are the molarity and volume of the initial solution- \( M_2 \) and \( V_2 \) are the molarity and volume after dilutionIn the exercise, a 10.00 mL aliquot of the oxalic acid solution is diluted to 250.0 mL. This calculation uses the initial molarity and volumes to find the new, final molarity of the solution, illustrating this principle clearly.

Oxalic Acid

Oxalic acid is an organic compound with the formula \( H_2C_2O_4 \). It is commonly found in plants like rhubarb and is known for being a relatively strong carboxylic acid. It appears as a colorless crystalline solid and is often used in cleaning and bleaching applications.Some key points about oxalic acid:

• Acts as a reducing agent in various chemical processes.
• Can form insoluble complexes with calcium and other metals, which is why it's often used in rust removal.
• It requires careful handling due to its toxic properties and corrosive nature.

In the context of this exercise, knowledge of oxalic acid's physical and chemical properties helps understand its behavior in solution and its practical applications in the laboratory.