Question

Write a balanced chemical equation for the reaction that occurs when (a) titanium metal undergoes a combination reaction with ${\mathrm{O}}_2(g);$ (b) silver(I) oxide decomposes into silver metal and oxygen gas when heated; (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.

Short answer

a) $2Ti+O_2\to 2Ti{O}_2$ b) $2A{g}_{2}O\to 4Ag+O_2$ c) $C_3{H}_{7}OH+\frac{9}{2}{O}_2\to 3C{O}_2+4H_{2}O$ d) $C_5{H}_{12}O+\frac{11}{2}{O}_2\to 5C{O}_2+6H_{2}O$

Step-by-step solution

Write the unbalanced equation

Write the reactants and products in the form of an unbalanced equation. $Ti+O_2\to Ti{O}_2$

Balance the equation

Add stoichiometric coefficients to balance the number of atoms of each element on both sides of the equation. $2Ti+O_2\to 2Ti{O}_2$ b) Decomposition of silver(I) oxide into silver metal and oxygen gas

Write the unbalanced equation

Write the reactants and products in the form of an unbalanced equation. $A{g}_{2}O\to Ag+O_2$

Balance the equation

Add stoichiometric coefficients to balance the number of atoms of each element on both sides of the equation. $2A{g}_{2}O\to 4Ag+O_2$ c) Combustion of Propanol (C3H7OH) in the air

Write the unbalanced equation

Write the reactants and products in the form of an unbalanced equation. $C_3{H}_{7}OH+O_2\to C{O}_2+H_{2}O$

Balance the equation

Add stoichiometric coefficients to balance the number of atoms of each element on both sides of the equation. $C_3{H}_{7}OH+\frac{9}{2}{O}_2\to 3C{O}_2+4H_{2}O$ d) Combustion of Methyl tert-butyl ether (C5H12O) in the air

Write the unbalanced equation

Write the reactants and products in the form of an unbalanced equation. $C_5{H}_{12}O+O_2\to C{O}_2+H_{2}O$

Balance the equation

Add stoichiometric coefficients to balance the number of atoms of each element on both sides of the equation. $C_5{H}_{12}O+\frac{11}{2}{O}_2\to 5C{O}_2+6H_{2}O$

Key concepts

Combination Reaction

In a combination reaction, two or more substances combine to form a single more complex compound. An everyday example of a combination reaction is the rusting of iron, where iron combines with oxygen to form iron oxide. In the provided exercise, titanium undergoes a combination reaction with oxygen to form titanium dioxide (TiO₂).

The key to understanding this type of reaction lies in remembering that all the reactants are combining, meaning you typically start with more substances that are simpler in nature and end with fewer that are more complex. To balance this type of reaction, you ensure that the number of atoms for each element is the same on both sides of the equation. Often, one may need to adjust the stoichiometric coefficients, which are the numbers placed in front of compounds to balance the equation.

Decomposition Reaction

Conversely, a decomposition reaction involves a single compound breaking down into two or more simpler substances. This is the opposite of the combination reaction. These reactions often require an input of energy, such as heat, light, or electricity, to occur. A classic example is the decomposition of silver oxide into silver and oxygen when heated, as demonstrated in the exercise.

When balancing decomposition reactions, you'll take the opposite approach compared to combination reactions. Here, you have a single reactant breaking into multiple products, and the challenge is to balance these products' atoms by adjusting their coefficients accurately. Understanding the initial compound's chemical composition is crucial to predict the resulting elements or simpler compounds accurately.

Combustion Reaction

A combustion reaction is an exothermic reaction in which a substance combines with oxygen, releasing energy in the form of light and heat. Combustion reactions are a type of combination reaction that typically involves hydrocarbons reacting with oxygen to produce carbon dioxide and water, as seen in the burning of propanol and methyl tert-butyl ether in the provided exercise.

Correctly balancing combustion reactions can be tricky since they often involve dealing with diatomic oxygen, which is O₂, and requires careful distribution of oxygen atoms between carbon dioxide and water in the products. The key is to first balance the carbon and hydrogen atoms before dealing with the oxygen atoms, often resulting in fractional coefficients when dealing with liquid fuels burning in the air as seen in the steps provided.

Stoichiometric Coefficients

Finally, stoichiometric coefficients are the numbers used in a chemical equation to balance the number of atoms of each element on both sides of the reaction. They represent the ratio at which reactants combine and products form, adhering to the law of conservation of mass. For students to grasp the concept, it's essential to understand that stoichiometry is more than balancing equations; it's a quantitative relationship between the reactants and products in a chemical reaction.

Using the coefficients, scientists can predict the amount of product formed from given quantities of reactants or vice versa. This is key to understanding chemical reactions in a lab as well as industrial processes. Students often struggle with fractions as coefficients, but in reality, they signify that reactions can occur in portions of molecules (as in the equation for propanol combustion) and they can usually be converted to whole numbers by multiplying through by an appropriate factor.