Problem 38 - Chemical Principles

Question

Assuming that the oxidation number of aluminum is \(+3\) in both compounds, what is the oxidation number of silicon in (a) clay, \(\mathrm{Al}_{2} \mathrm{Si}_{2} \mathrm{O}_{5}(\mathrm{OH})_{4}\); (b) mica, \(\mathrm{KMg}_{3}\left(\mathrm{Si}_{3} \mathrm{AlO}_{10}\right)(\mathrm{OH})_{2}\) ?

Step-by-Step Solution

Answer

For clay, the oxidation number of silicon is +2. For mica, the oxidation number of silicon is also +2.

Step 1: Analyze the Composition of Clay

Identify the oxidation numbers of all elements except for silicon in the compound Al2Si2O5(OH)4. Aluminum has an oxidation state of +3, oxygen is typically -2, and hydrogen (in hydroxide, OH) is typically +1.

Step 2: Calculate the Oxidation Number of Silicon for Clay

Since the sum of oxidation states must equal zero for a neutral compound, set up the equation based on the oxidation state contributions: 2(Al) + 2(Si) + 5(O) + 4(H) = 0. Given that Al is +3, O is -2, and H is +1, replace these values and solve for Si.

Step 3: Analyze the Composition of Mica

Identify the oxidation numbers of all elements except for silicon in the compound KMg3(Si3AlO10)(OH)2. Potassium (K) has an oxidation state of +1, magnesium (Mg) is +2, aluminum (Al) is +3, oxygen (O) is -2, and hydrogen (in hydroxide, OH) is +1.

Step 4: Calculate the Oxidation Number of Silicon for Mica

Again, the sum of the oxidation states must equal zero for a neutral compound, so set up another equation: (K) + 3(Mg) + 3(Si) + (Al) + 10(O) + 2(H) = 0. Place the known oxidation states into the equation and solve for Si.

Key Concepts

Chemical Composition

Understanding the chemical composition of substances is fundamental in chemistry. It involves identifying the different elements that make up a compound and their respective proportions. For instance, in the compound \( \mathrm{Al}_{2} \mathrm{Si}_{2} \mathrm{O}_{5}(\mathrm{OH})_{4} \) (clay), the elements present are aluminum (Al), silicon (Si), oxygen (O), and hydrogen (H). The subscripts in the chemical formula indicate the number of atoms of each element in one molecule of the compound.

For students struggling with chemical composition, visual aids such as Lewis structures or ball-and-stick models can be very helpful. These graphical representations allow one to picture how atoms are bonded and arranged within a compound. Drawing diagrams can serve as a preliminary step before delving into calculations related to chemical composition, leading to a clearer understanding of the underlying stoichiometry and oxidation states.

Oxidation States

The oxidation state, or oxidation number, is a concept that describes the degree of oxidation of an element in a chemical compound. It is an indicator of the hypothetical charge that an atom would have if all bonds to atoms of different elements were completely ionic.

For example, in \( \mathrm{Al}_{2} \mathrm{Si}_{2} \mathrm{O}_{5}(\mathrm{OH})_{4} \), it is given that aluminum has an oxidation number of +3. Typically, oxygen has an oxidation number of -2, and hydrogen (in hydroxide, OH) is +1. By understanding these common oxidation states, students can deduce the oxidation number of the remaining element, silicon in this case, by ensuring the sum of oxidation numbers in the compound is zero, which reflects its neutral overall charge.

Rule of Thumb for Common Oxidation Numbers:

• Oxygen is usually -2, except in peroxides.
• Hydrogen is usually +1 when bonded to non-metals, and -1 when bonded to metals.
• Alkali metals (group 1) are typically +1, and alkaline earth metals (group 2) are typically +2.
• Transition metals can have various oxidation states.

These rules can serve as a starting point when calculating oxidation numbers for elements in a compound.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It also plays an important role when dealing with the composition of compounds, as it requires understanding the molar ratios and how these relate to the chemical formula.

For instance, the stoichiometric calculation to find the oxidation number of silicon in clay utilizes the known oxidation numbers and proportions of other elements in the compound. By setting up an equation reflecting the stoichiometric relationship (2(Al) + 2(Si) + 5(O) + 4(H) = 0), one can solve for the unknown oxidation number of silicon.

Stoichiometry Tips for Better Understanding:

• Always verify the charges on all atoms and ensure the total charge is balanced.
• Use molar masses to convert between grams and moles when necessary.
• Balance chemical equations to reflect the law of conservation of mass.
• Practice with real-life examples, such as cooking recipes, to relate the concept of proportions to everyday activities.

Grasping the concept of stoichiometry enhances the understanding of how different elements interact and combine to form various compounds, fostering a more holistic comprehension of chemistry.