The value of n for the chemical reaction is 13.67.
How to find values?
The number of moles of potassium manganate (VII) used:
moles of KMnO₄ = volume of KMnO₄ × molarity of KMnO₄
moles of KMnO₄ = 22.5 cm³ × 0.0150 moldm³
= 0.0003375 mol
The balanced chemical equation for the reaction between ammonium iron (II) sulphate and potassium manganate (VII) is:
5FeSO₄ + 2KMnO₄ + 8H₂SO₄ → K₂SO₄ + 2MnSO₄ + Fe₂(SO₄)₃ + 8H₂O
From the balanced equation, 5 moles of FeSO₄ react with 2 moles of KMnO₄. Therefore, the number of moles of FeSO₄ in the solution is:
moles of FeSO₄ = (moles of KMnO₄ × 5) / 2
moles of FeSO₄ = (0.0003375 mol × 5) / 2
= 0.00084375 mol
The molarity of FeSO₄ in the solution is:
molarity of FeSO₄ = moles of FeSO₄ / (volume of solution / 1000)
molarity of FeSO₄ = 0.00084375 mol / (250 cm³ / 1000)
= 0.003375 mol/dm³
The molar mass of FeSO₄.nH₂O is:
molar mass of FeSO₄.nH₂O = mass of FeSO₄.nH₂O / (molarity of FeSO₄ × volume of solution / 1000)
molar mass of FeSO₄.nH₂O = 8.492 g / (0.003375 mol/dm³ × 250 cm³ / 1000)
= 396.0 g/mol
The molar mass of FeSO₄ is 152 g/mol. Therefore, the value of n is:
n = (molar mass of FeSO₄.nH₂O - 152 g/mol) / 18 g/mol
n = (396.0 g/mol - 152 g/mol) / 18 g/mol
= 13.67
Therefore, the value of n is 13.67.