1. Determine the chemical formula of the phosphate compound:

* Since the question asks for the number of barium atoms in a phosphate compound, we need to know the specific phosphate compound. Common examples include barium phosphate (Ba3(PO4)2) and monobarium phosphate (BaHPO4).

2. Calculate the molar mass of the phosphate compound:

* For Barium Phosphate (Ba3(PO4)2):

* Ba: 137.33 g/mol (x 3) = 411.99 g/mol

* P: 30.97 g/mol (x 2) = 61.94 g/mol

* O: 16.00 g/mol (x 8) = 128.00 g/mol

* Total molar mass: 411.99 + 61.94 + 128.00 = 601.93 g/mol

* For Monobarium Phosphate (BaHPO4):

* Ba: 137.33 g/mol

* H: 1.01 g/mol

* P: 30.97 g/mol

* O: 16.00 g/mol (x 4) = 64.00 g/mol

* Total molar mass: 137.33 + 1.01 + 30.97 + 64.00 = 233.31 g/mol

3. Calculate the moles of the phosphate compound:

* Using Barium Phosphate (Ba3(PO4)2):

* Moles = mass / molar mass = 68.2 g / 601.93 g/mol = 0.113 mol

* Using Monobarium Phosphate (BaHPO4):

* Moles = mass / molar mass = 68.2 g / 233.31 g/mol = 0.292 mol

4. Calculate the moles of barium atoms:

* Using Barium Phosphate (Ba3(PO4)2):

* Since there are 3 moles of barium for every mole of Ba3(PO4)2, we multiply the moles of Ba3(PO4)2 by 3: 0.113 mol * 3 = 0.339 mol Ba

* Using Monobarium Phosphate (BaHPO4):

* Since there is 1 mole of barium for every mole of BaHPO4, the moles of barium are equal to the moles of BaHPO4: 0.292 mol Ba

5. Convert moles of barium to number of atoms:

* Using Avogadro's number (6.022 x 10^23 atoms/mol):

* For Barium Phosphate (Ba3(PO4)2):

* Number of Ba atoms = 0.339 mol Ba * 6.022 x 10^23 atoms/mol = 2.04 x 10^23 atoms

* For Monobarium Phosphate (BaHPO4):

* Number of Ba atoms = 0.292 mol Ba * 6.022 x 10^23 atoms/mol = 1.76 x 10^23 atoms

Therefore, the number of barium atoms in 68.2 g of phosphate depends on the specific phosphate compound:

* For Barium Phosphate (Ba3(PO4)2): 2.04 x 10^23 barium atoms

* For Monobarium Phosphate (BaHPO4): 1.76 x 10^23 barium atoms