Question

Assign oxidation states to all of the atoms in each of the following: a. \(\mathrm{BiO}^{+}\) b. \(\mathrm{PO}_{4}^{3-}\) c. \(\mathrm{NO}_{2}^{-}\) d. \(\mathrm{Hg}_{2}^{2+}\)

Short answer

a. In \(\mathrm{BiO}^{+}\), Bi has an oxidation state of +3, and O has an oxidation state of -2. b. In \(\mathrm{PO}_{4}^{3-}\), P has an oxidation state of +5, and each O has an oxidation state of -2. c. In \(\mathrm{NO}_{2}^{-}\), N has an oxidation state of +3, and each O has an oxidation state of -2. d. In \(\mathrm{Hg}_{2}^{2+}\), each Hg has an oxidation state of +1.

Step-by-step solution

Recap the rules for assigning oxidation states

The following rules will help us to determine the oxidation states of all atoms in a compound: 1. The oxidation state of an element in its elemental form is 0. 2. The oxidation state of a monatomic ion is equal to its charge. 3. Oxygen usually has an oxidation state of -2 (with some exceptions, like peroxides featuring -1 each). 4. Hydrogen in most compounds has an oxidation state of +1, while in metal hydrides its oxidation state is -1. 5. The sum of the oxidation states of all atoms in a molecule or ion must equal its overall charge. Now let's analyze each compound and identify the oxidation states for each of its atoms.

Assign oxidation states for each element in the given compounds

a. \(\mathrm{BiO}^{+}\) Since Bi is bonded to O, the oxidation state of O is assumed to be -2, according to rule 3. Therefore, for the overall molecule to have a charge of +1, the oxidation state of Bi must be: \[+1 = (+x) + (-2)\] Solving for x, we get the oxidation state of Bi: \[x = +3\] b. \(\mathrm{PO}_{4}^{3-}\) The oxidation state of O is -2, as stated earlier. Since we have 4 O atoms, their combined oxidation state is -8. The overall charge of the ion is -3, so the oxidation state of P must be: \[(-3) = (+x) + (-8)\] Solving for x, we get the oxidation state of P: \[x = +5\] c. \(\mathrm{NO}_{2}^{-}\) Again, O has an oxidation state of -2 (x2 for two O atoms) which sums to -4. The overall charge of the ion is -1. The oxidation state of N must be: \[((-1) - (-4)) = (+x)\] Solving for x, we get the oxidation state of N: \[x = +3\] d. \(\mathrm{Hg}_{2}^{2+}\) Since the overall charge of the ion is +2, the oxidation state of the metals must be equal but opposite to account for the charge. The total oxidation state of the two Hg is +2, so the oxidation state of each Hg is: \[+2/2 = +1\]