Theoretical Background:

In order to solve this problem, we need to understand the concept of molar ratios and the stoichiometry of chemical reactions. The molar ratio is the ratio of moles of one substance to another in a balanced chemical equation. Stoichiometry is the calculation of quantitative relationships between reactants and products in a chemical reaction.

Given Data:
- Number of moles of oxygen atom (O) = 1.5

Step 1: Write the balanced chemical equation:

The balanced chemical equation for the formation of BaCO2 can be represented as:

2 Ba + O2 → 2 BaO + CO2

This equation indicates that 2 moles of barium (Ba) react with 1 mole of oxygen (O2) to produce 2 moles of barium oxide (BaO) and 1 mole of carbon dioxide (CO2).

Step 2: Determine the molar ratio:

From the balanced equation, we can see that 1 mole of oxygen (O2) reacts with 2 moles of barium carbonate (BaCO2) to form 2 moles of barium oxide (BaO) and 1 mole of carbon dioxide (CO2).

Therefore, the molar ratio of oxygen to barium carbonate is 1:2.

Step 3: Calculate the number of moles of barium carbonate (BaCO2):

To find the number of moles of barium carbonate, we can use the molar ratio:

Number of moles of barium carbonate (BaCO2) = (Number of moles of oxygen atom) / (Molar ratio)

Number of moles of barium carbonate (BaCO2) = 1.5 moles / 2

Number of moles of barium carbonate (BaCO2) = 0.75 moles

Therefore, there are 0.75 moles of barium carbonate (BaCO2) that contain 1.5 moles of oxygen atom.

Conclusion:

The number of moles of barium carbonate (BaCO2) that contains 1.5 moles of oxygen atom is 0.75 moles.