Calculate the amount of oxalic acid \(\left(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\right)\) required to obtain \(250 \mathrm{~mL}\) of deci-molar solution.

Understanding how to calculate molarity is fundamental in chemistry as it allows you to quantify the concentration of a solution. Molarity, labeled as M, is defined as moles of solute per liter of solution. This can be expressed with the equation: ewline Molarity (M) = \( \frac{\text{Moles of solute}}{\text{Liters of solution}} \).
To determine how much of a substance is needed to achieve a specific molar concentration, especially when preparing a deci-molar solution—which is simply a solution with the concentration of 0.1 M—one would use the above formula restructured to solve for moles: \( \text{Moles} = \text{Molarity} \times \text{Volume (in liters)} \).
In the exercise, we're asked to calculate the amount of oxalic acid needed to make a deci-molar solution for 250 mL (0.250 liters). We apply the formula to find the moles of oxalic acid required for the target volume.

Example Calculation

To prepare 250 mL of a 0.1 M deci-molar oxalic acid solution, the calculation would be:\( \text{Moles} = 0.1 M \times 0.250 L \),which gives the moles of oxalic acid needed for the 250 mL solution.

Identifying the molar mass of a compound is crucial prior to making solutions. The molar mass is the weight of one mole of a chemical compound and is usually expressed in grams per mole (g/mol).
Determining the molar mass of a compound involves adding up the atomic masses of all atoms present in the compound. For hydrated compounds, like oxalic acid dihydrate \(\mathrm{H}_{2} \mathrm{C}_{2}\mathrm{O}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O}\), we must also include the water molecules in the calculation.

Calculating Molar Mass

The molar mass of oxalic acid dihydrate can be computed as follows:\[ \text{Molar mass} = 2(1.008 \, \text{g/mol}) + 2(12.01 \, \text{g/mol}) + 4(15.999 \, \text{g/mol}) + 4(1.008 \, \text{g/mol}) + 2(18.015 \, \text{g/mol}) \],where we multiply the atomic mass of each element by the number of atoms present in the formula and then sum the totals to get the molar mass of the compound.
Understanding the molar mass is important for the next step, which involves the conversion of moles to grams to determine the mass of the compound needed.

Stoichiometry in solutions is the calculation that links the molarity of the solution to the mass of the solute needed. After determining the number of moles and molar mass, stoichiometry comes into play.
Using the molar mass, we can convert the number of moles required for our solution into grams. This gives us the exact amount of the compound we need to dissolve in solvent to obtain our desired concentration.

Applying Stoichiometry

Continuing from our earlier steps for making the deci-molar oxalic acid solution, we multiply the moles of oxalic acid by its molar mass. The equation will look like this:\( \text{Mass of oxalic acid} = \text{Moles} \times \text{Molar mass} \).
For our specific example, if we previously determined the molar mass of oxalic acid dihydrate to be, say, 126.07 g/mol, we would then calculate the required mass of oxalic acid dihydrate to be mixed in water as follows:\( \text{Mass} = \text{Moles calculated} \times 126.07 \, \text{g/mol} \).
This step is critical to ensure the solution's concentration is accurate. Errors in this step could lead to an incorrect concentration, affecting experimental results or product quality.