To determine the formula of MnxOy, we need to use the information provided about the reaction with carbon and the resulting production of CO2 gas.
First, let's calculate the number of moles of CO2 produced. The molar mass of CO2 is approximately 44 g/mol:
Number of moles of CO2 = mass of CO2 / molar mass of CO2 = 13.2 g / 44 g/mol = 0.3 mol
Based on the reaction, we can write the balanced equation as follows:
MnxOy + C -> CO2
From the balanced equation, we can see that one mole of MnxOy produces one mole of CO2. Therefore, the number of moles of MnxOy is also 0.3 mol.
Now, let's determine the molar mass of MnxOy. We'll assume that the molar mass of Mn is approximately 55 g/mol and the molar mass of O is approximately 16 g/mol. Let the subscript x represent the number of Mn atoms and the subscript y represent the number of O atoms in the compound.
Molar mass of MnxOy = (molar mass of Mn * x) + (molar mass of O * y)
Given that 31.6 g of MnxOy contains 0.3 mol, we can set up the following equation:
31.6 g = (55 g/mol * x) + (16 g/mol * y)
We have two variables, x and y, but only one equation. Therefore, we need additional information to solve for x and y.
Please provide additional information if available, such as the molar ratio between Mn and O in MnxOy or any other relevant details.