To solve this problem, we need to use stoichiometry and the given masses to find the molar mass of the metal carbonate, and then use that information to determine the identity of the metal, X.
First, we need to calculate the number of moles of carbon dioxide produced:
- The mass of carbon dioxide produced is 0.855 g.
- Using the molar mass of carbon dioxide (44.01 g/mol), we can calculate the number of moles: 0.855 g / 44.01 g/mol = 0.0194 mol.
Next, we need to use the balanced equation to determine the number of moles of XCO3 that must have reacted to produce this amount of carbon dioxide:
- The balanced equation tells us that 1 mole of XCO3 produces 1 mole of CO2.
- Therefore, the number of moles of XCO3 that reacted is also 0.0194 mol.
Now we can use the mass of the metal carbonate and the number of moles that reacted to calculate the molar mass of XCO3:
- The mass of XCO3 is 2.012 g.
- The number of moles of XCO3 is 0.0194 mol.
- Therefore, the molar mass of XCO3 is: 2.012 g / 0.0194 mol = 103.6 g/mol.
The molar mass of XCO3 is a clue to the identity of the metal, X. Looking at the periodic table, we can see that there are a few metals with molar masses close to 103.6 g/mol, including manganese (54.94 g/mol) and iron (55.85 g/mol). However, these metals typically form oxides that are not solid at room temperature. The oxide formed in this reaction, XO, is a solid, which suggests that X is one of the alkali or alkaline earth metals, which commonly form solid oxides.
The molar mass of XCO3 corresponds to a metal with an atomic mass close to 40 g/mol. This could be either calcium (40.08 g/mol) or strontium (87.62 g/mol). However, since calcium is more abundant and more commonly found in nature, it is likely that X is calcium.
Therefore, the metal carbonate is likely calcium carbonate, CaCO3. The reaction can be written as: CaCO3(s) → CaO(s) + CO2(g).
Note: It is important to check the results of our calculations to ensure that the mass balance is correct. In this case, the mass of the products (0.855 g + mass of XO) must equal the mass of the reactant (2.012 g). We can check this by subtracting the mass of carbon dioxide from the total mass of the products: 2.012 g - 0.855 g = 1.157 g. This is the mass of the metal oxide, XO.