A mixture weighing 4.08 g of BaO and unknown carbonate XCO3 was heated...
Given information:
- Mixture containing 4.08 g of BaO and unknown carbonate XCO3.
- Residue obtained after heating the mixture weighs 3.64 g.
- Residue is dissolved in 100 mL of 1 N HCl.
- Excess acid requires 16 mL of 2.5 N NaOH for complete neutralization.
To determine the metal M:
Step 1: Finding the moles of BaO
- The molecular weight of BaO (Ba = 137.33 g/mol, O = 16.00 g/mol) is 153.33 g/mol.
- Moles of BaO = mass / molecular weight = 4.08 g / 153.33 g/mol = 0.0266 mol.
Step 2: Finding the moles of CO2 produced
- BaO reacts with HCl to form BaCl2 and H2O: BaO + 2HCl → BaCl2 + H2O.
- 1 mole of BaO reacts with 2 moles of HCl to produce 1 mole of BaCl2.
- Since HCl is 1 N, it contains 1 mole of HCl in 1 L of the solution.
- Therefore, 100 mL (0.1 L) of 1 N HCl contains 0.1 moles of HCl.
- From the balanced equation, 1 mole of BaO reacts with 2 moles of HCl to produce 1 mole of BaCl2.
- So, 0.0266 moles of BaO will react with 0.0532 moles of HCl.
- This means 0.0532 moles of CO2 (molar ratio is 1:1 with HCl) will be produced.
Step 3: Finding the moles of XCO3
- The excess acid requires 16 mL (0.016 L) of 2.5 N NaOH for complete neutralization.
- From the balanced equation, 2 moles of NaOH react with 1 mole of CO2.
- Therefore, 0.016 L of 2.5 N NaOH contains 0.04 moles of NaOH.
- Since the molar ratio of NaOH to CO2 is 2:1, there must be 0.02 moles of CO2 produced.
- This means that the unknown carbonate XCO3 must have also produced 0.02 moles of CO2.
Step 4: Finding the moles of X
- Since 1 mole of XCO3 produces 1 mole of CO2, there must be 0.02 moles of XCO3.
- From the given information, the residue weighs 3.64 g.
- The molecular weight of XCO3 is equal to the sum of the atomic weights of X and CO3.
- Let's assume the atomic weight of X as M.
- Molecular weight of XCO3 = M + (12.01 + 3(16.00)) = M + 60.01 g/mol.
- Moles of XCO3 = mass / molecular weight = 3.64 g / (M + 60.01 g/mol) = 0.02 moles