Problem 59 - Chemistry: The Central Science

Question

Write a molecular formula for each compound, and indicate the oxidation state of the group \(5 \mathrm{~A}\) element in each formula: (a) phosphorous acid, (b) pyrophosphoric acid, (c) antimony trichloride, (d) magnesium arsenide, (e) diphosphorus pentoxide, (f) sodium phosphate.

Step-by-Step Solution

Answer

The molecular formulas and oxidation states of the Group \(5 \mathrm{~A}\) elements in each compound are: a) Phosphorous acid: \(\mathrm{H_3PO_3}\), oxidation state of P: \(+3\) b) Pyrophosphoric acid: \(\mathrm{H_4P_2O_7}\), oxidation state of P: \(+5\) c) Antimony trichloride: \(\mathrm{SbCl_3}\), oxidation state of Sb: \(+3\) d) Magnesium arsenide: \(\mathrm{Mg_3As_2}\), oxidation state of As: \(-3\) e) Diphosphorus pentoxide: \(\mathrm{P_2O_5}\), oxidation state of P: \(+5\) f) Sodium phosphate: \(\mathrm{Na_3PO_4}\), oxidation state of P: \(+5\)

Step 1: a) Phosphorous acid formula and oxidation state of Phosphorus

The chemical formula for phosphorous acid is \(\mathrm{H_3PO_3}\). To calculate the oxidation state of phosphorus (P) in this compound, let's assign oxidation states to all the elements: $$ H: +1 \\ O: -2 \\ $$ Using the oxidation numbers of hydrogen (+1), oxygen (-2), and knowing that the sum of them must be equal to the overall charge of the molecule (0 for neutral compounds), we can find the oxidation state of P. $$ 3(+1) + x + 3(-2) = 0\\ 3 - 6 + x = 0\\ x = +3 $$ The oxidation state of phosphorus (P) in phosphorous acid is \(+3\).

Step 2: b) Pyrophosphoric acid formula and oxidation state of Phosphorus

The chemical formula for pyrophosphoric acid is \(\mathrm{H_4P_2O_7}\). In order to find the oxidation state of P in this compound, let's assign oxidation states to all the elements: $$ H: +1\\ O: -2\\ $$ Using the oxidation numbers of hydrogen (+1), oxygen (-2), and knowing that the sum of them must be equal to the overall charge of the molecule (0 for neutral compounds), we can find the oxidation state of P. $$ 4(+1) + 2x + 7(-2) = 0 \\ 4 - 14 + 2x = 0 \\ 2x = 10 \\ x = +5 $$ The oxidation state of phosphorus (P) in pyrophosphoric acid is \(+5\).

Step 3: c) Antimony trichloride formula and oxidation state of Antimony

The chemical formula for antimony trichloride is \(\mathrm{SbCl_3}\). In order to find the oxidation state of Sb in this compound, let's assign oxidation states to all the elements: $$ Cl: -1 $$ Using the oxidation numbers of chlorine (-1), and knowing that the sum of them must be equal to the overall charge of the molecule (0 for neutral compounds), we can find the oxidation state of Sb. $$ x + 3(-1) = 0 \\ x - 3 = 0 \\ x = +3 $$ The oxidation state of antimony (Sb) in antimony trichloride is \(+3\).

Step 4: d) Magnesium arsenide formula and oxidation state of Arsenic

The chemical formula for magnesium arsenide is \(\mathrm{Mg_3As_2}\). In order to find the oxidation state of As in this compound, let's assign oxidation states to all the elements: $$ Mg: +2 $$ Using the oxidation numbers of magnesium (+2), and knowing that the sum of them must be equal to the overall charge of the molecule (0 for neutral compounds), we can find the oxidation state of As. $$ 3(+2) + 2x = 0 \\ 6 + 2x = 0 \\ 2x = -6 \\ x = -3 $$ The oxidation state of arsenic (As) in magnesium arsenide is \(-3\).

Step 5: e) Diphosphorus pentoxide formula and oxidation state of Phosphorus

The chemical formula for diphosphorus pentoxide is \(\mathrm{P_2O_5}\). In order to find the oxidation state of P in this compound, let's assign oxidation states to all the elements: $$ O: -2 \\ $$ Using the oxidation numbers of oxygen (-2), and knowing that the sum of them must be equal to the overall charge of the molecule (0 for neutral compounds), we can find the oxidation state of P. $$ 2x + 5(-2) = 0 \\ 2x - 10 = 0 \\ 2x = 10 \\ x = +5 $$ The oxidation state of phosphorus (P) in diphosphorus pentoxide is \(+5\).

Step 6: f) Sodium phosphate formula and oxidation state of Phosphorus

The chemical formula for sodium phosphate is \(\mathrm{Na_3PO_4}\). In order to find the oxidation state of P in this compound, let's assign oxidation states to all the elements: $$ Na: +1 \\ O: -2 \\ $$ Using the oxidation numbers of sodium (+1), oxygen (-2), and knowing that the sum of them must be equal to the overall charge of the molecule (0 for neutral compounds), we can find the oxidation state of P. $$ 3(+1) + x + 4(-2) = 0 \\ 3 - 8 + x = 0 \\ x = +5 $$ The oxidation state of phosphorus (P) in sodium phosphate is \(+5\).