Problem 20 - Chemistry The Central Science In Si Units

Question

Write a balanced chemical equation for the reaction that occurs when (a) titanium metal reacts with \(\mathrm{O}_{2}(g) ;(\mathbf{b})\) silver(I) oxide decomposes into silver metal and oxygen gas when heated; \((\mathbf{c})\) propanol, \(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{OH}(l)\) burns in air;(d) methyl tert-butyl ether, \(\mathrm{C}_{5} \mathrm{H}_{12} \mathrm{O}(l),\) burns in air.

Step-by-Step Solution

Answer

(a) 2Ti + O_2 → 2TiO_2; (b) 2Ag_2O → 4Ag + O_2; (c) 2C_3H_7OH + 9O_2 → 6CO_2 + 8H_2O; (d) C_5H_{12}O + 8O_2 → 5CO_2 + 6H_2O

Step 1: Writing the Unbalanced Equation for Ti and O2

When titanium (Ti) reacts with oxygen gas (O_2), titanium(IV) oxide (TiO_2) is formed. The unbalanced equation is:\[ \text{Ti} + \text{O}_2 \rightarrow \text{TiO}_2 \]

Step 2: Balance the Equation for Ti and O2

To balance the oxygen atoms, place a coefficient of 2 in front of TiO_2 and a coefficient of 2 in front of Ti:\[ 2\text{Ti} + \text{O}_2 \rightarrow 2\text{TiO}_2 \]

Step 3: Writing the Decomposition of Silver(I) Oxide

Silver(I) oxide (Ag_2O) decomposes into silver (Ag) and oxygen gas (O_2). The unbalanced equation is:\[ \text{Ag}_2\text{O} \rightarrow \text{Ag} + \text{O}_2 \]

Step 4: Balance the Decomposition of Silver(I) Oxide

To balance the equation, place a coefficient of 4 in front of Ag and 2 in front of Ag_2O:\[ 2\text{Ag}_2\text{O} \rightarrow 4\text{Ag} + \text{O}_2 \]

Step 5: Writing the Combustion of Propanol

Propanol (C_3H_7OH) burns in air producing carbon dioxide (CO_2) and water (H_2O):\[ \text{C}_3\text{H}_7\text{OH} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2O \]

Step 6: Balance the Combustion of Propanol

Balance carbon by placing a 3 in front of CO_2, then balance hydrogen with a 4 in front of H_2O. Finally, balance oxygen by placing a 9/2 or 4.5 in front of O_2. To avoid fractions, double all coefficients:\[ 2\text{C}_3\text{H}_7\text{OH} + 9\text{O}_2 \rightarrow 6\text{CO}_2 + 8\text{H}_2O \]

Step 7: Writing the Combustion of Methyl tert-butyl ether

Methyl tert-butyl ether (C_5H_{12}O) burns to form carbon dioxide (CO_2) and water (H_2O):\[ \text{C}_5\text{H}_{12}\text{O} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2O \]

Step 8: Balance the Combustion of Methyl tert-butyl ether

Balance carbon by adding a 5 in front of CO_2 and hydrogen with a 6 in front of H_2O. Then, balance the oxygen by placing an 8 in front of O_2:\[ \text{C}_5\text{H}_{12}\text{O} + 8\text{O}_2 \rightarrow 5\text{CO}_2 + 6\text{H}_2O \]

Key Concepts

Balancing Equations

Balancing equations is a fundamental skill in chemistry that ensures the conservation of mass and energy during chemical reactions. Each chemical equation must have an equal number of each type of atom on both sides of the equation. To balance an equation, you may need to place coefficients (whole numbers) in front of compounds to adjust the number of atoms.

Here's a simple process for balancing equations:

• Write the unbalanced equation with correct chemical formulas.
• Identify the number of each type of atom on both sides.
• Use coefficients to balance the atoms, starting with the most complex molecule.
• Ensure the smallest whole number coefficients are used.

Remember, balancing does not change the molecular identities; it only changes the coefficients to ensure every atom is accounted for in the reaction.

Combustion Reactions

Combustion reactions are a type of chemical reaction where a substance combines with oxygen gas, releasing energy in the form of heat and light. This is an important reaction in our daily lives as it's commonly seen when engines run or when wood burns in a fireplace.

Typical attributes of combustion reactions include:

• Reactants include a hydrocarbon and oxygen.
• Products are usually carbon dioxide (CO_2) and water (H_2O).
• These reactions are exothermic, meaning they release energy.

To balance combustion reactions, start by balancing the carbon atoms, followed by the hydrogen atoms, and finally the oxygen atoms. If you encounter fractional coefficients, multiply all coefficients by the smallest number possible to turn them into whole numbers.

Decomposition Reactions

Decomposition reactions involve a single compound breaking down into two or more simpler substances. These reactions are the opposite of synthesis reactions and often require energy input, such as heat, light, or electricity, to proceed.

This type of reaction can be recognized by:

• The presence of a single reactant.
• The breaking down of the compound into simpler products.
• Often resulting in the release of gases or the change of states.

One classic example of a decomposition reaction is the breakdown of silver(I) oxide (Ag_2O) into silver metal (Ag) and oxygen gas (O_2). Balancing these reactions involves making sure the total number of each type of atom is the same on both sides of the equation.

Synthesis Reactions

Synthesis reactions are fundamental in chemistry, involving the combination of two or more reactants to produce a single product. These reactions are also known as combination reactions and are essential in forming new compounds from simpler ones.

Key characteristics of synthesis reactions include:

• Multiple reactants form one product.
• It usually involves elements or simple compounds reacting together.
• The reaction is often exothermic, releasing energy as the new bonds form.

For example, when titanium (Ti) reacts with oxygen (O_2) to form titanium dioxide (TiO_2), it is a synthesis reaction. Balancing synthesis reactions requires ensuring that the number of each type of atom in the reactants equals the number of those atoms in the products.