Question

What mass of sodium oxalate \(\left(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) is needed to prepare \(0.250 \mathrm{~L}\) of a \(0.100 M\) solution?

Short answer

To prepare \(0.250 \mathrm{~L}\) of a \(0.100 \mathrm{~M}\) sodium oxalate \(\left(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\right)\) solution, you will need \(3.35 \mathrm{~g}\) of sodium oxalate.

Step-by-step solution

Calculate the number of moles of Na2C2O4 needed

First, we need to determine the number of moles of sodium oxalate required for the solution. We can use the formula: moles = molarity × volume where moles represent the amount of solute (Na2C2O4), molarity refers to the concentration of the solution (0.100 M), and volume is the volume of the solution (0.250 L). So we can plug the given values: moles = (0.100 M) × (0.250 L)

Calculate the moles of Na2C2O4

Now we can calculate the moles of sodium oxalate required: moles = (0.1 moles/L) × (0.25 L) moles = 0.025 moles of Na2C2O4

Determine the molar mass of Na2C2O4

To find the mass of sodium oxalate, we will need to determine its molar mass. The molar mass of a compound is the sum of the atomic masses of each element in the compound. In the case of Na2C2O4, we have: - 2 Na atoms with an atomic mass of 22.99 g/mol - 2 C atoms with an atomic mass of 12.01 g/mol - 4 O atoms with an atomic mass of 16.00 g/mol Molar mass of Na2C2O4 = (2 × 22.99) + (2 × 12.01) + (4 × 16.00)

Calculate the molar mass of Na2C2O4

Based on the atomic masses, we can now calculate the molar mass of sodium oxalate: Molar mass of Na2C2O4 = (2 × 22.99) + (2 × 12.01) + (4 × 16.00) = 45.98 + 24.02 + 64.00 = 134.00 g/mol

Calculate the mass of Na2C2O4 required

Now we can determine the mass of sodium oxalate needed by multiplying the moles we calculated in Step 2 by the molar mass we found in Step 4: mass = moles × molar mass mass = (0.025 moles) × (134.00 g/mol)

Find the mass of Na2C2O4 needed

Finally, we can find the mass of sodium oxalate required to prepare the solution: mass = (0.025 moles) × (134.00 g/mol) = 3.35 g So, 3.35 grams of sodium oxalate (Na2C2O4) is needed to prepare 0.250 L of a 0.100 M solution.

Key concepts

Solution Preparation

To prepare a solution, we need to understand the relationship between the solute, solvent, and concentration. This involves dissolving a specific amount of solute into a solvent. For a specific molarity, we need the right amount of solute to make a solution of the desired concentration.

In our exercise, the goal is to prepare a solution with a specific volume and molarity. Hence, we need a calculated amount of sodium oxalate (the solute) dissolved in a given volume of water (the solvent).

• The desired molarity is 0.100 M, indicating there are 0.100 moles of solute per liter of solution.
• The volume of the solution is 0.250 L, which helps us determine the number of moles needed.

When these components mix, they create a homogenous solution with uniform chemical composition.

Mole Calculation

Calculating the number of moles is crucial in determining how much solute is needed for the solution. The formula for moles is given by:\[ \text{moles} = \text{molarity} \times \text{volume} \]This relationship helps us find the moles of sodium oxalate needed to achieve the desired concentration.

• By using the molarity (0.100 M) and the volume (0.250 L), we calculate 0.025 moles required of Na\(_2\)C\(_2\)O\(_4\).
• This step ensures that the solution has the precise concentration needed.

Once you have the moles, you can proceed to determine the physical mass of the solute required.

Molar Mass Calculation

To find the mass of a compound needed, having the molar mass is essential. The molar mass is the sum of the atomic masses of all atoms in the formula of the compound. For sodium oxalate (Na\(_2\)C\(_2\)O\(_4\)), we calculate its molar mass by:

• Adding up the atomic masses of 2 sodium (Na) atoms each of 22.99 g/mol.
• Two carbon (C) atoms each of 12.01 g/mol.
• Four oxygen (O) atoms each of 16.00 g/mol.

Once added, the total molar mass is 134.00 g/mol. To find the actual mass of sodium oxalate required for the solution, multiply this molar mass by the moles calculated:\[\text{mass} = \text{moles} \times \text{molar mass} \]In our context, this gives:\[\text{mass} = 0.025 \; \text{moles} \times 134.00 \; \text{g/mol} = 3.35 \; \text{g}\]This is the mass of sodium oxalate needed to make our desired solution.