Question

Write a balanced chemical equation for the reaction that occurs when (a) $\mathrm{Mg}(s)$ reacts with ${\mathrm{Cl}}_2(g);$ (b) barium carbonate decomposes into barium axide and carbon dioxide gas when heated; (c) the hydrocarbon styrene, ${\mathrm{C}}_8{\mathrm{H}}_8(l)$, is combusted in air; (d) dimethylether, ${\mathrm{CH}}_3{\mathrm{OCH}}_3(g)$, is combusted in air.

Short answer

a) $Mg(s)+C{l}_2(g)\to 2MgC{l}_2(s)$ b) $BaC{O}_3(s)\to BaO(s)+C{O}_2(g)$ c) $C_8{H}_8(l)+11O_2(g)\to 8C{O}_2(g)+4H_{2}O(l)$ d) $2C{H}_{3}OC{H}_3(g)+5O_2(g)\to 2C{O}_2(g)+6H_{2}O(l)$

Step-by-step solution

Write the Unbalanced Reaction

Let's first write down the chemical reaction of magnesium (Mg) with chlorine gas (Cl2). Mg(s) + Cl2(g) → MgCl2(s)

Balance the Chemical Reaction

Now, let's check if the reaction is balanced or not. The number of magnesium atoms is already equal on both sides, but there are 2 chlorine atoms in the reactant side, while there is only 1 in the product side. We will add a coefficient "2" to the MgCl2 to balance the equation: Mg(s) + Cl2(g) → 2MgCl2(s) Now, the reaction is balanced. b) Decomposition of Barium Carbonate:

Write the Unbalanced Reaction

First, let's write down the decomposition reaction of barium carbonate (BaCO3) into barium oxide (BaO) and carbon dioxide gas (CO2). BaCO3(s) → BaO(s) + CO2(g)

Balance the Chemical Reaction

The reaction is already balanced, as there are equal numbers of atoms on both sides of the equation. c) Combustion of Styrene:

Write the Unbalanced Reaction

We have the hydrocarbon styrene (C8H8) which combusts in the air (meaning it reacts with oxygen (O2)) to form carbon dioxide (CO2) and water (H2O). C8H8(l) + O2(g) → CO2(g) + H2O(l)

Balance the Chemical Reaction

To balance the reaction, we can start by balancing the carbon atoms, then hydrogen atoms, and finally oxygen atoms. C8H8(l) + O2(g) → 8CO2(g) + 4H2O(l) Now we can balance the oxygen atoms: C8H8(l) + 11O2(g) → 8CO2(g) + 4H2O(l) Now, the reaction is balanced. d) Combustion of Dimethylether:

Write the Unbalanced Reaction

Let's start with the unbalanced reaction of dimethylether (CH3OCH3) combustion with oxygen (O2) along with carbon dioxide (CO2) and water (H2O) as products. CH3OCH3(g) + O2(g) → CO2(g) + H2O(l)

Balance the Chemical Reaction

We'll start by balancing the carbon atoms, then hydrogen atoms, and finally oxygen atoms. 2CH3OCH3(g) + O2(g) → 2CO2(g) + H2O(l) Now let's balance the hydrogen atoms: 2CH3OCH3(g) + O2(g) → 2CO2(g) + 6H2O(l) Finally, we will balance the oxygen atoms: 2CH3OCH3(g) + 5O2(g) → 2CO2(g) + 6H2O(l) Now, the reaction is balanced.

Key concepts

Chemical Reactions

Chemical reactions are processes in which one or more substances, the reactants, are converted to one or more different substances, the products. During these transformations, the bonds between atoms break and new ones form, which requires energy changes. For example, when magnesium reacts with chlorine, a transfer of electrons occurs, forming magnesium chloride. This type of reaction, where elements combine to form a compound, is known as a synthesis reaction.

To fully comprehend a chemical reaction, you must first write down the unbalanced equation and then proceed to balance it, which is a crucial step to ensure the conservation of mass. The ability to write and balance chemical equations is fundamental in the study of chemistry. It is as though you are writing a sentence that describes what happens in the reaction, but using symbols and formulas instead of words.

Stoichiometry

Stoichiometry is the area of chemistry that pertains to the quantitative relationships among reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced in a given reaction. The term comes from the Greek words 'stoicheion' (element) and 'metron' (measure).

How Does Stoichiometry Apply?

In the provided exercises, stoichiometry is evident in the careful balancing of atoms on both sides of the equation. When magnesium combines with chlorine gas, or styrene combusts, the principle of stoichiometry requires that the number of atoms of each element in the reactants equals the number in the products. This principle is based on the Law of Conservation of Mass, which states that matter is neither created nor destroyed in a chemical reaction.

Combustion Reactions

Combustion reactions are a type of chemical reaction where a compound, usually containing carbon and hydrogen, reacts with an oxidizing agent, such as oxygen, to produce heat and light. For example, the combustion of hydrocarbons like styrene or dimethylether in air releases energy and produces carbon dioxide and water as products.

These reactions are exothermic, meaning they release energy. In the context of our example, when styrene combusts in air, it's necessary to balance the equation to ensure it accurately represents the stoichiometry of the process. The balanced equation shows the exact proportions of reactants and products, allowing us to calculate the amount of energy released and reactants consumed.

Decomposition Reactions

Decomposition reactions are the reverse of synthesis reactions; they involve a single compound breaking down into two or more simpler substances. These reactions often require an input of energy, such as heat, light, or electricity, to occur. A common example from our exercise is the decomposition of barium carbonate into barium oxide and carbon dioxide gas when heated.

This type of reaction demonstrates the concept of stoichiometry as well, even though the provided example (barium carbonate decomposition) is balanced as written. It's important to check whether all types of atoms are balanced, as sometimes the smallest coefficients are the key to balancing the entire equation. Decomposition reactions are very useful in industrial processes and in understanding the breakdown of materials over time.