A metal carbonate, XCO3 of mass 2.012 g was heated resulting in the formation of XO, a metal oxide and carbon dioxide with a mass of 0.855 g according to the reaction shown below:
XCO3 (s) → XO (s) + CO2 (g)
(Atomic mass of O-15.999 g/mol; H-1.008 g/mol; C-12.011 g/mol).
123.511g/mol
103.711 g/mol
197.311 g/mol
62.011 g/mol
To solve the problem, we need to use the law of conservation of mass. The total mass of the reactants (XCO3) must equal the total mass of the products (XO and CO2).
We can start by finding the moles of CO2 produced, using its mass and molar mass:
0.855 g CO2 x (1 mol CO2 / 44.01 g CO2) = 0.01944 mol CO2
Since the coefficient of CO2 in the balanced equation is 1, this is also the number of moles of XCO3 that reacted.
Now we can find the molar mass of XCO3 by dividing its mass by the number of moles:
2.012 g XCO3 / 0.01944 mol XCO3 = 103.711 g/mol
Therefore, the metal carbonate XCO3 has a molar mass of 103.711 g/mol.
The correct answer is option B: 103.711 g/mol.
To find the molar mass of X, we need to determine the moles of carbon dioxide (CO2) produced in the reaction.
Given that the mass of CO2 produced is 0.855 g, we can calculate the moles of CO2:
Molar mass of CO2 = 12.011 g/mol (C) + (2 * 15.999 g/mol) (2 oxygen atoms) = 44.01 g/mol
moles of CO2 = mass / molar mass = 0.855 g / 44.01 g/mol = 0.0194 mol
According to the balanced equation, each mole of XCO3 produces 1 mole of CO2. Therefore, there are also 0.0194 mol of XCO3.
Given that the mass of XCO3 is 2.012 g, we can calculate the molar mass of XCO3:
molar mass of XCO3 = mass / moles = 2.012 g / 0.0194 mol = 103.711 g/mol
Therefore, the molar mass of XCO3 is approximately 103.711 g/mol.
To find the molar mass of the metal carbonate, XCO3, we need to use the given information about the mass of the carbonate and the mass of the carbon dioxide produced.
1) Calculate the number of moles of carbon dioxide produced:
The molar mass of carbon dioxide (CO2) is calculated as follows:
(Carbon: 12.011 g/mol + 2 x Oxygen: 15.999 g/mol) = 44.009 g/mol.
Divide the mass of carbon dioxide produced (0.855 g) by its molar mass to find the number of moles:
0.855 g / 44.009 g/mol ≈ 0.0194 mol.
2) Since 1 mole of XCO3 produces 1 mole of carbon dioxide, the number of moles of XCO3 is also approximately 0.0194 mol.
3) Divide the mass of XCO3 (2.012 g) by the number of moles (0.0194 mol) to find the molar mass of XCO3:
2.012 g / 0.0194 mol ≈ 103.711 g/mol.
Therefore, the molar mass of XCO3 (metal carbonate) is approximately 103.711 g/mol. So the correct option is 103.711 g/mol.