Problem 63 - General Chemistry: Principles and Modern Applications

Question

Write a formula for (a) the chloride of titanium having Ti in the O.S. \(+4 ;\) (b) the sulfate of iron having Fe in the O.S. \(+3 ;(c)\) an oxide of chlorine with Cl in the O.S. \(+7 ;\) (d) an oxoanion of sulfur in which the apparent O.S. of \(S\) is +7 and the ionic charge is \(2-\).

Step-by-Step Solution

Answer

The formulas for the compounds are: (a) \(TiCl_4\), (b) \(Fe_2(SO_4)_3\), (c) \(Cl_2O_7\), and (d) \(S_2O_7^{2-}\).

Step 1: Part (a) - Chloride of Titanium in O.S. +4

The chloride of titanium will be a binary compound consisting of titanium (Ti) and chloride (Cl). Titanium is in oxidation state +4, meaning it has lost 4 electrons, and chloride always has a charge of -1 (gained 1 electron). The formula for the compound will be written by equaling the total positive charge to the total negative charge. Here, \(Ti = +4\) and \(Cl = -1\). So, to equalize the charges, we need 4 chloride ions for each titanium ion, which gives the formula \(TiCl_4\).

Step 2: Part (b) - Sulfate of Iron in O.S. +3

The sulfate of iron includes iron (Fe) and sulfate (SO4) ions. Here, iron is in oxidation state +3 and sulfate ion always carries a charge of -2. Thus, two iron(III) ions will be needed to balance the charges of three sulfate ions. This gives us the iron(III) sulfate formula as \(Fe_2(SO_4)_3\).

Step 3: Part (c) - Oxide of Chlorine in O.S. +7

The oxide of chlorine will contain chlorine(Cl) and oxygen(O). Chlorine in O.S. of +7 means it has lost 7 electrons, and oxygen always has a charge of -2 (gained 2 electrons). To balance the charges, we need seven half oxygen ion for each chlorine ion, which results in the formula \(Cl_2O_7\).

Step 4: Part (d) - Oxoanion of Sulfur in O.S. +7 and ionic charge 2-

An oxoanion of sulfur will contain sulfur(S), oxygen(O) and carry an overall ionic charge of -2. Here, sulfur (S) is in an oxidation state of +7 and oxygen (O) is in an oxidation state of -2. Oxygen is more electronegative than sulfur and will pull electrons towards itself. Sulfur will have its own oxidation state and oxygen will have -2 (-II in traditional notations). In order to balance out the total charge of -2 for the ion, 4 oxygen atoms (-8) and one sulfur atom (+7) will be needed, as \(+7 - 8 = -1\). To balance out the total charge assigned to the ion of -2, results in the formula \(S_2O_7^{2-}\).

Key Concepts

Oxidation States

In chemistry, oxidation states (O.S.) help us understand how atoms form bonds in compounds. The oxidation state is a number assigned to an element in a compound, signifying the number of electrons lost or gained. This concept is crucial for determining the formula of various compounds.
For example, when titanium is in the oxidation state of +4, it means titanium has lost four electrons. This charge needs to be balanced by other atoms in a compound. Cl, the chloride ion, consistently has a charge of -1, indicating that it has gained one electron.
A key point to remember is that oxidation states help balance charges in chemical reactions, allowing for the proper formation of chemical formulas. Understanding this concept allows chemists to predict the bonding behavior of elements in a compound.

Ionic Compounds

Ionic compounds are composed of ions, positive (cations) and negative (anions), that attract each other. The bond is formed due to the electrostatic forces between these opposite charges.
For instance, in titanium chloride, the titanium ion and chloride ions form an ionic compound. Titanium with a +4 charge combines with four chloride ions, each with a -1 charge. Similarly, in the case of iron(III) sulfate, iron ions in the oxidation state of +3 combine with sulfate ions, each having a -2 charge, forming a balanced and stable ionic compound.
Ionic compounds have unique properties such as high melting and boiling points, and they conduct electricity when dissolved in water because the ions are free to move.

Balancing Charges

Balancing charges is fundamental when writing chemical formulas for ionic compounds. This ensures that the compound is electrically neutral. The total positive charge must equal the total negative charge.

• Consider the chloride of titanium: Ti has a +4 charge, requiring four Cl ions with -1 charges each. This forms the compound TiCl₄.
• For iron(III) sulfate, Fe, with a +3 charge, requires matching it with three sulfate ions, each with a -2 charge, to form Fe₂(SO₄)₃.

Balancing charges is an essential principle in chemistry that allows for the prediction and confirmation of chemical formulas of compounds.

Binary Compounds

Binary compounds consist of two different elements. They are simple and fundamental to understanding more complex chemical structures.
Titanium chloride (TiCl₄) is an example of a binary compound, composed of titanium and chlorine. As binary compounds, these serve as basic building blocks in chemistry. They illustrate the principles of bonding and charge balance in a straightforward manner.
Binary compounds are also relevant in naming conventions and help in the simplification of chemical nomenclature.