If one mole of X2O contains the same number of atoms as 75g of XO3, the molar mass of X2O is?

Method 1 :

1 mole of X₂O contains 3 moles of atoms (2 moles of X atoms and 1 mole of O atoms).
Then, the number of moles atoms in 75 g of XO₃ = 3 mol

1 mole of XO₃ contains 4 moles of atoms (1 mole of X atoms and 3 moles of O atoms).
Then, the number of moles of XO₃ that contains 4 moles of atoms = 3/4 mol = 0.75 mol

The mass of 0.75 mole of XO₃ is 75 g.
Molar mass of XO₃ = (75 g) / (0.75 mol) = 100 g/mol


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Method 2 :

Let M g/mol be the molar mass of XO₃.

Number of moles of atoms in 75 g of XO₃ = (75/M mol) × 4 = 300/M mol
Number of moles of atoms in 1 mole of X₂O = (1 mol) × 3 = 3 mol

Number of moles of atoms in 75 g of XO₃ = Number of moles of atoms in 1 mole of X₂O
300/M = 3
M = 100

Molar mass of XO₃ = 100 g/mol

Method 1 :

1 mole of X₂O contains 3 moles of atoms (2 moles of X atoms and 1 mole of O atoms).
Then, the number of moles atoms in 75 g of XO₃ = 3 mol

1 mole of XO₃ contains 4 moles of atoms (1 mole of X atoms and 3 moles of O atoms).
Then, the number of moles of XO₃ that contains 4 moles of atoms = 3/4 mol = 0.75 mol

The mass of 0.75 mole of XO₃ is 75 g.
Molar mass of XO₃ = (75 g) / (0.75 mol) = 100 g/mol


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Method 2 :

Let M g/mol be the molar mass of XO₃.

Number of moles of atoms in 75 g of XO₃ = (75/M mol) × 4 = 300/M mol
Number of moles of atoms in 1 mole of X₂O = (1 mol) × 3 = 3 mol

Number of moles of atoms in 75 g of XO₃ = Number of moles of atoms in 1 mole of X₂O
300/M = 3
M = 100