Concept:To count individual atoms inside a crystal hydrate, one must establish the total moles of the compound and multiply by both the atomicity of the specific element and Avogadro's constant.
Formula:$$ \text{Atoms} = n \times \text{Atomicity} \times N_A $$
Solution:- First, find the moles of \( \text{FeSO}_4 \cdot 7\text{H}_2\text{O} \):
- Given mass = 278g. Molar mass = 278 g/mol.
- \( n = 278 / 278 = 1 \text{ mole} \).
- Next, determine the atomicity of Oxygen in one molecule of hydrated ferrous sulphate.
- There are 4 oxygen atoms in the sulphate (\( \text{SO}_4 \)) and 7 oxygen atoms in the water of crystallization (\( 7\text{H}_2\text{O} \)). Total = \( 4 + 7 = 11 \) atoms of O per molecule.
- Total O atoms = \( 1 \times 11 \times (6.02 \times 10^{23}) \).
- Result = \( 66.22 \times 10^{23} \), which in standard scientific notation is \( 6.62 \times 10^{24} \) atoms.
Why other options are incorrect:- \( 6.023 \times 10^{23} \): This is the number of complete formula units of ferrous sulphate, not the individual oxygen atoms within them.
- \( 2.408 \times 10^{23} \): Found by miscalculating atomicity (likely assuming only 4 oxygens).
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