Correct Answer - Option 1 : 32 amu
Concept:
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The molecular formula is the formula of a compound that shows its constituent atoms and their number per molecule denoted by subscripts.
- Molecular formula if known can be used to calculate:
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Molecular mass or molar mass.
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Percentage of elements in the compound.
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If the percentage composition and molar mass is known, then it can be used to calculate the empirical formula which represents the formula in the simplest whole-number ratio.
- The empirical formula gives us the Molecular formula as:
\(Molecular\;formula = {\left( {Empirical\;formula} \right)_n}\) where n = largest ratio.
Calculation:
- Let the atomic mass of X be 'a'.
- The mass of 4 atoms of 'a' = 4a.
- The mass of 4 molecules of oxygen = 4 × 6 = 96
- Hence, the mass of the compound X4O6 = 4a + 96
Then, in 4a + 96 gm of compound X4O6, X present = 4a
Then, in 1 g of the compound X4O6, X present = \( {4a\over 4a + 96}\)
Then in 10 g of the compound, X present = \( {4a \times 10\over 4a + 96}\)
Now, it is given that 10.0 g of compound contains 5.62 g of X, so we can say,
\( {{4a \times 10\over 4a + 96}} = 5.62\)
or, 22.8 a + 549.12 = 40 a
Solving the equation, we get a = 32.07 a.m.u.
Hence, the atomic mass of X is 32.07 a.m.u
