The correct answer is option 'D' which is 36.13 x 10^23. Let's break down the calculation to understand why.

1. Oxalic acid dihydrate has the chemical formula C2H2O4 · 2H2O. This means that it contains two carbon atoms, two hydrogen atoms, four oxygen atoms from the oxalic acid, and two additional oxygen atoms from the water molecule.

2. To calculate the number of oxygen atoms in one mole of oxalic acid dihydrate, we need to find the molar mass of the compound and then determine the number of moles of oxygen atoms.

3. The molar mass of oxalic acid dihydrate can be calculated by adding up the molar masses of each element present in the compound. The molar mass of carbon (C) is 12.01 g/mol, the molar mass of hydrogen (H) is 1.01 g/mol, and the molar mass of oxygen (O) is 16.00 g/mol.

4. The molar mass of oxalic acid dihydrate can be calculated as follows:
(2 * molar mass of carbon) + (2 * molar mass of hydrogen) + (4 * molar mass of oxygen) + (2 * molar mass of oxygen from water)
= (2 * 12.01 g/mol) + (2 * 1.01 g/mol) + (4 * 16.00 g/mol) + (2 * 16.00 g/mol)
= 24.02 g/mol + 2.02 g/mol + 64.00 g/mol + 32.00 g/mol
= 122.04 g/mol

5. Now, we can calculate the number of moles of oxygen atoms in 122.04 g of oxalic acid dihydrate. Since the molar mass of oxygen is 16.00 g/mol, the number of moles of oxygen atoms can be calculated as follows:
Number of moles = Mass / Molar mass
= 122.04 g / 16.00 g/mol
= 7.6275 mol

6. Finally, we can determine the number of oxygen atoms in one mole of oxalic acid dihydrate by multiplying the number of moles of oxygen atoms by Avogadro's number, which is 6.022 x 10^23 atoms/mol.
Number of oxygen atoms = Number of moles * Avogadro's number
= 7.6275 mol * 6.022 x 10^23 atoms/mol
= 4.591 x 10^24 atoms

Thus, the correct answer is option 'D', which is 36.13 x 10^23 (rounded to two significant figures).