The balanced chemical equation for the combustion of carbon to form carbon dioxide is:

C + O2 -> CO2

From the equation, we can see that 1 mole of carbon reacts with 1 mole of oxygen to produce 1 mole of carbon dioxide.

To find the mass of carbon dioxide formed, we need to calculate the moles of carbon and oxygen and then use the mole ratio from the balanced equation.

Given:
Mass of carbon = 4.5 kg
Mass of oxygen = 12.5 kg

To calculate the moles of carbon and oxygen, we need to divide their masses by their molar masses.

Molar mass of carbon (C) = 12.01 g/mol
Molar mass of oxygen (O2) = 32.00 g/mol

Moles of carbon = mass of carbon / molar mass of carbon
= 4500 g / 12.01 g/mol
= 374.69 mol

Moles of oxygen = mass of oxygen / molar mass of oxygen
= 12500 g / 32.00 g/mol
= 390.63 mol

From the balanced equation, we can see that the mole ratio of carbon dioxide to carbon is 1:1. Therefore, the moles of carbon dioxide formed will be equal to the moles of carbon.

Moles of carbon dioxide = moles of carbon = 374.69 mol

Finally, to find the mass of carbon dioxide formed, we multiply the moles of carbon dioxide by its molar mass.

Molar mass of carbon dioxide (CO2) = 44.01 g/mol

Mass of carbon dioxide = moles of carbon dioxide * molar mass of carbon dioxide
= 374.69 mol * 44.01 g/mol
= 16,498.83 g
= 16.50 kg

Therefore, the mass of carbon dioxide formed is 16.50 kg.