To determine the oxidation number of manganese (Mn) in the permanganate ion (\( \text{MnO}_4^- \)), we can follow a systematic approach based on the known oxidation states of oxygen and the overall charge of the ion.
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Know the oxidation state of oxygen: In most compounds, oxygen has an oxidation state of \(-2\).
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Determine the contribution of oxygen to the ion: In \(\text{MnO}_4^-\), there are four oxygen atoms. Therefore, the total contribution of oxygen to the oxidation state is: \[ 4 \text{(oxygen)} \times (-2 \text{ (oxidation state of oxygen)}) = -8 \]
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Set up the equation for the total charge: The permanganate ion has an overall charge of \(-1\). Let \(x\) be the oxidation number of manganese (Mn). The equation relating the contributions from manganese and oxygen to the overall charge of the ion can be set up as follows: \[ x + (-8) = -1 \]
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Solve for \(x\): \[ x - 8 = -1 \ x = -1 + 8 \ x = +7 \]
Thus, the oxidation number of manganese (Mn) in the permanganate ion \( \text{MnO}_4^- \) is \( +7 \).
In summary, the oxidation number of Mn in \( \text{MnO}_4^- \) is \( +7 \) because the four oxygen atoms contribute a total of \(-8\) to the charge, and to balance that with the overall \(-1\) charge of the ion, Mn must have an oxidation state of \(+7\).