Problem 79 - Chemistry Matter and Change

Question

Using oxidation numbers, explain why the formula \(\mathrm{NaF}_{2}\) is incorrect.

Step-by-Step Solution

Answer

The formula \(\mathrm{NaF}_{2}\) is incorrect because it does not balance the oxidation numbers to zero. The correct formula is \(\mathrm{NaF}\).

Step 1: Determine Sodium's Oxidation Number

Sodium (Na) is an alkali metal, located in Group 1 of the periodic table. Elements in this group typically have an oxidation number of +1 in their compounds.

Step 2: Determine Fluorine's Oxidation Number

Fluorine (F) is a halogen, located in Group 17 of the periodic table. Halogens typically have an oxidation number of -1 in their compounds.

Step 3: Calculate the Total Oxidation Number for \(\mathrm{NaF}\)

For a stable compound, the sum of oxidation numbers must equal zero. If the formula is \(\mathrm{NaF}_{2}\), this would imply: \(1(\text{Na}) + 2(\text{F}) = 0\). Using known oxidation numbers, substitute into the equation:\[ \text{Na: } +1 \ \text{F: } 2 \times (-1) \ \text{Sum: } +1 + 2(-1) = +1 - 2 = -1 \] The total is -1, which indicates a mismatch because a neutral compound should sum to zero.

Step 4: Identify the Correct Formula

To balance the oxidation number, the correct formula should have one sodium atom and one fluorine atom, resulting in the formula \(\mathrm{NaF}\). This satisfies the requirement that the sum of the oxidation numbers equals zero: \(+1 + (-1) = 0\).

Key Concepts

Chemical Formula

A chemical formula represents the atoms in a chemical compound. It shows the types and numbers of atoms involved, conveying how they come together to form the compound. In

• molecular compounds, the formula indicates the exact number of each type of atom in a single molecule.
• ionic compounds, it represents the simplest ratio of the ions involved.

The formula \[ \text{NaF}_2 \] appears incorrect upon inspection through the lens of oxidation numbers. Sodium (Na) is present once, while fluoride (F) appears twice. Oxidation numbers help to balance the charge by indicating how many electrons an atom tends to lose, gain, or share when it forms a compound. Each type of atom has a characteristic oxidation number depending on its position in the periodic table. In this case, while sodium's expected oxidation number is +1, and fluorine's is -1, the proposed formula leads to a net charge that isn't zero. This is why it's incorrect; the correct formula instead must be \[ \text{NaF} \] where one Na neutralizes with one F.

Ionic Compounds

Ionic compounds consist of positively and negatively charged ions. These ions attract each other to form a neutral compound. Ionic bonds typically form between metals and nonmetals. The metal loses electrons, becoming a cation with a positive charge, while the nonmetal gains those electrons, becoming an anion with a negative charge.
The compound must be neutral overall. This means the total positive charge from the cations must equal the total negative charge from the anions. For instance, when \[ \text{Na} \], a metal from Group 1, pairs with halogen \[ \text{F} \] from Group 17, they form \[ \text{NaF} \] because sodium contributes a +1 charge and fluorine a -1 charge, balancing each other out.
So, ionic compounds such as these obey the principle of charge neutrality, which helps predict the ratio in which ions combine.

Periodic Table Groups

The periodic table is an organized arrangement of elements, based largely on their atomic number and properties. Elements are categorized into groups, or families, which are columns on the table. Elements within the same group often have similar chemical properties due to having the same number of valence electrons.

• Group 1 elements are known as alkali metals, having one electron in their outer shell, usually taking an oxidation number of +1.
• Group 17 elements are halogens, needing one electron to complete their outer shell, often holding an oxidation number of -1.

These group-based properties are fundamental in explaining and predicting behavior in compounds. For the incorrect formula \[ \text{NaF}_2 \], understanding the nature of Group 1 and Group 17 helps clarify why the combination suggested by the formula doesn't satisfy the charge neutrality condition observed in ionic compounds. Sodium, being in Group 1, naturally forms compounds with halides like fluorine from Group 17 in a 1:1 ratio, leading to \[ \text{NaF} \], not \[ \text{NaF}_2 \].