Metal deficiency defect is shown by \(Fe_{0.93}O\). In the crystal, some \(Fe^{2+}\) cations are missing and loss of positive charge is compensated by the presence of \(Fe^{3+}\) ions. The percentage of \(Fe^{2+}\) ions in the \(Fe_{0.93}O\) crystals is ______ . (Nearest integer)
To determine the percentage of \(Fe^{2+}\) ions in the compound \(Fe_{0.93}O\), consider the defect structure described. In this structure, some \(Fe^{2+}\) ions are absent, resulting in a deficiency that leads to the formation of \(Fe^{3+}\) ions to compensate for charge imbalance.
Let the original number of \(Fe\) atoms per mole in a perfect crystal be 1. The given formula is \(Fe_{0.93}O\), indicating a deficiency of 0.07 per mole of \(Fe\) atoms. This deficiency corresponds to the conversion of some \(Fe^{2+}\) to \(Fe^{3+}\).
Balancing the charges, assume \(x\) is the amount of \(Fe^{3+}\) ions formed. Hence, the deficiency of \(Fe^{2+}\) is exactly \(x\), and \(0.93\ -\ x\) is the amount of \(Fe^{2+}\) ions present.
For charge neutrality, the total positive charge should balance the oxygen's charge, which is 1 mole of \(O^{2-}\):
\(2(0.93\ -\ x) + 3x = 2\)
Solving for \(x\):
\(1.86 - 2x + 3x = 2\)
\(1.86 + x = 2\)
\(x = 0.14\)
Thus, \(0.93 - x = 0.93 - 0.14 = 0.79\) which means 0.79 moles of \(Fe^{2+}\) ions are present per mole of \(Fe\).
