1. Find the moles of carbon atoms:

* Avogadro's number tells us there are 6.022 x 10^23 atoms in one mole.

* Divide the number of carbon atoms by Avogadro's number to find the moles of carbon:

(1.773 x 10^17 atoms) / (6.022 x 10^23 atoms/mol) = 2.94 x 10^-7 mol C

2. Find the moles of sodium carbonate (Na2CO3):

* The formula for sodium carbonate shows that there's one carbon atom per molecule of sodium carbonate.

* Since the number of moles of carbon and sodium carbonate are equal in this case, we have 2.94 x 10^-7 mol Na2CO3.

3. Calculate the mass of sodium carbonate:

* Find the molar mass of sodium carbonate:

* Na: 22.99 g/mol (x2 = 45.98 g/mol)

* C: 12.01 g/mol

* O: 16.00 g/mol (x3 = 48.00 g/mol)

* Total molar mass: 45.98 + 12.01 + 48.00 = 105.99 g/mol

* Multiply the moles of sodium carbonate by its molar mass:

(2.94 x 10^-7 mol) x (105.99 g/mol) = 3.12 x 10^-5 g Na2CO3

Therefore, 3.12 x 10^-5 grams of sodium carbonate contain 1.773 x 10^17 carbon atoms.