Oxalic acid dihydrate has the chemical formula H2C2O4·2H2O. Its molar mass is calculated by adding the molar masses of all its constituent atoms:

$$2\times12.01 \text{ g/mol C} + 2\times 1.01 \text{ g/mol H} + 4\times 16.00 \text{ g/mol O} + 2\times 18.02 \text{ g/mol H2O}$$

The molar mass of oxalic acid dihydrate is 126.07 g/mol.

Step 2: Calculate the number of moles of oxalic acid dihydrate needed

We can use the following formula to calculate the number of moles of solute needed to prepare a solution of a given concentration:

Molarity (M) = Moles of solute / Volume of solution (L)

Rearranging the formula, we get:

Moles of solute = Molarity (M) × Volume of solution (L)

In this case, the desired molarity of the oxalic acid dihydrate solution is 0.50 M and the volume of solution we want to prepare is 200 mL, which is equivalent to 0.2 L.

Moles of oxalic acid dihydrate needed = 0.50 M × 0.2 L = 0.1 mol

Step 3: Calculate the mass of oxalic acid dihydrate needed

Now that we know the number of moles of oxalic acid dihydrate needed, we can calculate the corresponding mass using its molar mass:

Mass of oxalic acid dihydrate needed = Moles of oxalic acid dihydrate × Molar mass of oxalic acid dihydrate

Substituting the values we have:

Mass of oxalic acid dihydrate needed = 0.1 mol × 126.07 g/mol = 12.61 g

Therefore, to prepare 200 mL of 0.50 M oxalic acid solution, we will need 12.61 grams of oxalic acid dihydrate.