Problem 18 - Chemistry Principles and Practice

Question

Assign the oxidation numbers of all atoms in the following species. (a) \(\mathrm{CaCO}_{3}\) (b) \(\mathrm{HBrO}_{4}\) (c) \(\mathrm{Fe}^{3+}\)

Step-by-Step Solution

Answer

(a) Ca: +2, C: +4, O: -2; (b) H: +1, Br: +7, O: -2; (c) Fe: +3.

Step 1: Understand the Compound

For each compound given, identify the elements and their usual oxidation states. Recall common oxidation numbers: Oxygen is usually -2, hydrogen is usually +1, metals in Group 1 are +1, and Group 2 are +2. Elements in their standard state are 0.

Step 2: Assign Oxidation Numbers in \( \mathrm{CaCO}_{3} \)

Calcium (Ca) is in Group 2, thus it usually has an oxidation number of +2. Oxygen (O) typically has an oxidation number of -2. The compound is neutral, so the sum of oxidation numbers should be zero. For carbonate ion, \( \mathrm{CO}_{3}^{2-} \), sum of oxidation numbers should be -2.

Step 3: Calculation for \( \mathrm{CaCO}_3 \)

In \( \mathrm{CaCO}_3 \), the oxidation number of Ca is +2. \( \mathrm{C} \) is the unknown. The three O have a total charge of \(-2 \times 3 = -6\). Set up the equation: \(+2 + x - 6 = 0\). Solving gives \(x = +4\). Thus, Ca in \( \mathrm{CaCO}_3 \) is +2, C is +4, each O is -2.

Step 4: Assign Oxidation Numbers in \( \mathrm{HBrO}_{4} \)

For \( \mathrm{HBrO}_{4} \), H typically has an oxidation number of +1, and each O is -2. This compound is neutral, so the sum of the oxidation numbers is zero.

Step 5: Calculation for \( \mathrm{HBrO}_{4} \)

The equation is \(1 + x + 4(-2) = 0\) where \(x\) is the oxidation number of Br. Solve for \(x\): \(1 + x - 8 = 0\) gives \(x = +7\). Therefore, H is +1, Br is +7, O is -2.

Step 6: Assign Oxidation Number for \( \mathrm{Fe}^{3+} \)

This is a monoatomic ion, and the oxidation number is the same as its charge. So, the oxidation number of Fe in \( \mathrm{Fe}^{3+} \) is +3.

Key Concepts

Oxidation State Assignment

Understanding how to assign oxidation numbers, also known as oxidation states, is crucial in balancing chemical reactions and identifying redox processes. The oxidation number is a theoretical charge that an atom would have in a molecule or compound if electrons were completely transferred, rather than shared. To determine these numbers accurately, there are some general rules:

• The oxidation number of a free element is always 0.
• For a monoatomic ion, the oxidation number is equivalent to the ion's charge.
• Oxygen typically has an oxidation number of -2, except in peroxides where it's -1, or when combined with fluorine.
• Hydrogen generally has an oxidation number of +1, except when forming hydrides with more electropositive elements.
• The sum of oxidation numbers in a neutral compound must equal 0 while in a polyatomic ion, it must equal the ion's charge.

In the case of \( \mathrm{CaCO}_{3} \), calcium has an oxidation number of +2, oxygen is -2, and using the rules above, carbon is found to be +4 to balance the compound. For \( \mathrm{HBrO}_{4} \), hydrogen is +1, oxygen is -2, and bromine balances the compound at +7. Finally, a monoatomic ion such as \( \mathrm{Fe}^{3+} \) has an oxidation number equal to the ion charge, +3.

Compound Analysis

When analyzing compounds, it is essential to identify the elements involved and understand their typical oxidation states. This method allows us to assign accurate oxidation numbers. This involves looking at the compound's structure and chemistry.Consider \( \mathrm{CaCO}_{3} \):

• Calcium, a Group 2 metal, usually assumes an oxidation state of +2. This is a common attribute for alkaline earth metals.
• Carbon is central in the carbonate ion \( \mathrm{CO}_3^{2-} \), where it's more unusual to assume an oxidation state. It compensates for the 3 oxygen atoms, each -2, totaling -6, balanced by the +4 state of carbon to meet the overall ionic charge requirement of carbonate (-2).

Next, analyze \( \mathrm{HBrO}_{4} \):

• Hydrogen, typically +1, is present as expected.
• Bromine, surprisingly in an \( \mathrm{HBrO}_{4} \) molecule, assumes a +7 state. This balances the strong -8 charge from the four oxygen atoms at -2 each, crucial for maintaining the compound's neutrality.

Understanding how these elements interact helps in assigning appropriate oxidation states, ensuring the chemical validity of your calculations.

Chemical Species

Chemical species refer to atoms, molecules, ions, or radicals identifiable by their unique chemical structure and characteristics. Proper identification and analysis of these species are fundamental to chemistry, particularly when assigning oxidation numbers.Consider the chemical species involving elements like iron or multi-element compounds:

• For monoatomic ions like \( \mathrm{Fe}^{3+} \), the oxidation state is usually obvious as it mirrors the ion's charge, which is +3 in this scenario.
• For more complex entities such as \( \mathrm{CaCO}_{3} \) and \( \mathrm{HBrO}_{4} \), deciphering the oxidation numbers for each atom involves understanding the inherent tendencies of the involved elements and how they form stable bonds within the species.
• These species, regardless of complexity, are governed by the conservation of charge and are most stable when these guidelines are closely followed.

Mastering the analysis of chemical species and their structural makeup helps immensely when determining oxidation states, as this influences their reactivity and interaction in chemical reactions.