An empirical formula is the simplest whole-number ratio of elements in a compound. It may or may not be the same as the molecular formula.

If the empirical formula weight (EFW) and the molecular formula weight (MFW) are the same, then the empirical and molecular formulas are the same, which is the case with water. Its empirical and molecular formulas are both #"H"_2"O"#. However, often the MFW is a multiple of the EFW, which means the molecular formula is a multiple of the empirical formula.

For example, the empirical formula for glucose is #"CH"_2"O"#, and its EFW is 30 g/mol. The MFW of glucose is 180 g/mol. So now we divide the MFW by the EFW to find the multiple: #(180"g/mol")/(30"g/mol")=6# . So now the subscripts of the empirical formula are multiplied by 6, giving the molecular formula of #"C"_6"H"_12"O"_6"# for glucose.

In the given question, the EFW of #"CO"_3# is 60 g/mol and the molar mass (MFW) is 120 g/mol, We need to divide the MFW by the EFW to determine the multiple: #(120"g/mol")/(60"g/mol")=2#. So the subscripts in the empirical formula are multiplied times 2 to get the molecular formula #"C"_2"O"_6"# .https://www.youtube.com/watch?v=AFqwtY7m2PI