Problem 64 - Chemistry: The Central Science

Question

Write a chemical formula for each compound or ion, and indicate the oxidation state of the group \(5 \mathrm{~A}\) element in each formula: (a) phosphate ion, (b) arsenous acid, (c) antimony(III) sulfide, (d) calcium dihydrogen phosphate, (e) potassium phosphide.

Step-by-Step Solution

Answer

(a) Phosphate ion: chemical formula \(\mathrm{PO_4^{3-}}\), oxidation state of P is +5. (b) Arsenous acid: chemical formula \(\mathrm{H_3AsO_3}\), oxidation state of As is +3. (c) Antimony(III) sulfide: chemical formula \(\mathrm{Sb_2S_3}\), oxidation state of Sb is +3. (d) Calcium dihydrogen phosphate: chemical formula \(\mathrm{Ca(H_2PO_4)_2}\), oxidation state of P is +5. (e) Potassium phosphide: chemical formula \(\mathrm{K_3P}\), oxidation state of P is -3.

Step 1: (a) Phosphate ion

The phosphate ion is composed of one phosphorus atom (a group 5A element) and four oxygen atoms. Its chemical formula is written as \(\mathrm{PO_4^{3-}}\). To determine the oxidation state of phosphorus, we can set up an equation by considering the charge of each atom and the total charge of the ion: \[x + 4(-2) = -3\] Solving for x, we find the oxidation state of phosphorus to be +5.

Step 2: (b) Arsenous acid

Arsenous acid contains one arsenic atom (a group 5A element) and three oxygen atoms, along with three hydrogen atoms. The chemical formula for arsenous acid is \(\mathrm{H_3AsO_3}\). To determine the oxidation state of arsenic, we can set up an equation by considering the charge of each atom and the overall neutrality of the compound: \[3(+1) + x + 3(-2) = 0\] Solving for x, we find the oxidation state of arsenic to be +3.

Step 3: (c) Antimony(III) sulfide

Antimony(III) sulfide contains one antimony atom (a group 5A element) in the +3 oxidation state and two sulfur atoms in the -2 oxidation state. The chemical formula for antimony(III) sulfide is \(\mathrm{Sb_2S_3}\). The oxidation state of antimony is given as +3.

Step 4: (d) Calcium dihydrogen phosphate

Calcium dihydrogen phosphate consists of one calcium atom, two hydrogen atoms, one phosphorus atom (a group 5A element), and four oxygen atoms. The chemical formula for calcium dihydrogen phosphate is \(\mathrm{Ca(H_2PO_4)_2}\). To determine the oxidation state of phosphorus, we can set up an equation by considering the charge of each atom and the overall neutrality of the compound: \[(+2) + 2[(2(+1) + x + 4(-2))] = 0\] Solving for x, we find the oxidation state of phosphorus to be +5.

Step 5: (e) Potassium phosphide

Potassium phosphide is composed of three potassium atoms and one phosphorus atom (a group 5A element). The chemical formula for potassium phosphide is \(\mathrm{K_3P}\). To determine the oxidation state of phosphorus, we can set up the following equation by considering the charge of each atom and the overall neutrality of the compound: \[3(+1) + x = 0\] Solving for x, we find the oxidation state of phosphorus to be -3.

Key Concepts

Chemical Formula

Understanding the chemical formula of a compound is essential in chemistry. It essentially serves as a type of shorthand that provides information about the types and numbers of atoms present in a molecule. For example, water (H_2O) consists of two hydrogen atoms and one oxygen atom.

A chemical formula can also tell you the oxidation states of the atoms in a compound. In the case of the group 5A elements, such as phosphorus in phosphate ions (PO_4^{3-}), you can determine the oxidation state by balancing the charges of the constituent atoms to match the overall charge of the compound or ion. This is pivotal for predicting reactivity and bonding behavior.

Phosphate Ion

The phosphate ion is a polyatomic ion with the formula PO_4^{3-} and is notable for its role in biochemistry, particularly in energy transfer as part of ATP. Phosphates also serve as fertilizers in agriculture due to their importance for plant growth.

In regards to oxidation states, the phosphorus atom in a phosphate ion has an oxidation state of +5. This is calculated by acknowledging that each oxygen has a -2 charge and using algebra to balance the charges, leading to the +5 state for phosphorus in order to result in the overall -3 charge of the ion.

Arsenous Acid

Arsenous acid, or H_3AsO_3, is an arsenic-containing oxyacid. It's less commonly encountered than its counterparts, such as arsenic acid, but it's still important in the context of arsenic chemistry. The oxidation state of arsenic in arsenous acid is +3.

This is found by considering the usual oxidation state of hydrogen as +1 and that of oxygen as -2, and then balancing these with arsenic's oxidation number to achieve the overall neutral charge of the molecule.

Antimony Sulfide

Antimony sulfide (Sb_2S_3) is a compound consisting of antimony and sulfur, where antimony is in the +3 oxidation state. This compound is known for its use in fireproofing materials, and historically as a cosmetic in ancient Egypt.

Here, antimony's oxidation state is understood without the usual algebra since the problem explicitly mentions it as antimony(III) sulfide—implying the +3 state. The formula indicates there are two antimony atoms and three sulfur atoms, with the sulfurs each having a -2 oxidation state.

Calcium Dihydrogen Phosphate

Calcium dihydrogen phosphate (Ca(H_2PO_4)_2) is a chemical compound utilized as a leavening agent in the food industry and as a fertilizer. The oxidation state of phosphorus in this compound is +5, following a similar logic applied in the cases above.

By accounting for the +2 charge of calcium and balancing it with the charges of hydrogen and oxygen atoms bonded to phosphorus, you arrive at the +5 oxidation state for phosphorus to maintain neutrality in the compound.

Potassium Phosphide

Potassium phosphide (K_3P) is a binary ionic compound containing potassium and phosphorus. What makes it interesting is that phosphorus exhibits a -3 oxidation state here. This is in contrast with the previously discussed phosphorus compounds where it had a positive oxidation state.

This negative oxidation state indicates that phosphorus is gaining electrons from potassium, which has a +1 charge. Bearing in mind that the compound as a whole is electrically neutral, the negative three charge from phosphorus balances out the positive charges of the three potassium atoms.