Problem 70 - Chemistry The Central Science

Question

Write a balanced equation for each of the following reactions: (a) Burning magnesium metal in a carbon dioxide atmosphere reduces the \(\mathrm{CO}_{2}\) to carbon. (b) In photosynthesis, solar energy is used to produce glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) and \(\mathrm{O}_{2}\) from carbon dioxide and water. (c) When carbonate salts dissolve in water, they produce basic solutions.

Step-by-Step Solution

Answer

The short answer to the question is as follows: (a) \(2\textnormal{Mg} + \textnormal{CO}_2 \to 2\textnormal{MgO} + \textnormal{C}\) (b) \(6\textnormal{CO}_2 + 6\textnormal{H}_2\textnormal{O} \to \textnormal{C}_6\textnormal{H}_{12}\textnormal{O}_6 + 6\textnormal{O}_2\) (c) \(\textnormal{Na}_2\textnormal{CO}_3 + \textnormal{H}_2\textnormal{O} \to 2\textnormal{NaOH} + \textnormal{H}_2\textnormal{CO}_3\)

Step 1: Identify the reactants and products

In this reaction, magnesium (Mg) reacts with carbon dioxide (CO2) to produce magnesium oxide (MgO) and carbon (C).

Step 2: Write the unbalanced equation

The unbalanced equation for this reaction is: Mg + CO2 -> MgO + C

Step 3: Balance the equation

To balance the equation, we need to make sure the number of atoms for each element is equal on both sides of the equation. Mg + CO2 -> MgO + C 2Mg + CO2 -> 2MgO + C The balanced equation is: \(2\textnormal{Mg} + \textnormal{CO}_2 \to 2\textnormal{MgO} + \textnormal{C}\) #b) Photosynthesis (producing glucose and O2 from CO2 and H2O)#

Step 4: Identify the reactants and products

In this reaction, carbon dioxide (CO2) and water (H2O) react under sunlight to produce glucose (C6H12O6) and oxygen (O2) gas.

Step 5: Write the unbalanced equation

The unbalanced equation for this reaction is: CO2 + H2O -> C6H12O6 + O2

Step 6: Balance the equation

To balance the equation, we need to make sure the number of atoms for each element is equal on both sides of the equation. 6CO2 + 6H2O -> C6H12O6 + 6O2 The balanced equation is: \(6\textnormal{CO}_2 + 6\textnormal{H}_2\textnormal{O} \to \textnormal{C}_6\textnormal{H}_{12}\textnormal{O}_6 + 6\textnormal{O}_2\) #c) Dissolution of carbonate salts in water to produce basic solutions#

Step 7: Identify the reactants and products

In this reaction, we can use sodium carbonate (Na2CO3) as an example of a carbonate salt. It reacts with water (H2O) to produce sodium hydroxide (NaOH) and carbonic acid (H2CO3).

Step 8: Write the unbalanced equation

The unbalanced equation for this reaction is: Na2CO3 + H2O -> NaOH + H2CO3

Step 9: Balance the equation

To balance the equation, we need to make sure the number of atoms for each element is equal on both sides of the equation. Na2CO3 + H2O -> 2NaOH + H2CO3 The balanced equation is: \(\textnormal{Na}_2\textnormal{CO}_3 + \textnormal{H}_2\textnormal{O} \to 2\textnormal{NaOH} + \textnormal{H}_2\textnormal{CO}_3\)

Key Concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry that ensures the same number of atoms exist on both sides of a chemical reaction. When a reaction occurs, you must account for the conservation of mass, meaning that atoms are neither created nor destroyed. For example, consider the reaction of magnesium and carbon dioxide. Initially, you have the unbalanced equation: \(\text{Mg} + \text{CO}_2 \to \text{MgO} + \text{C}\).
To balance, observe the magnesium, which appears once on both sides. However, oxygen atoms need adjustment. By doubling the magnesium to two atoms, two oxygen atoms balance naturally on each side, leading to the balanced reaction: \(2\text{Mg} + \text{CO}_2 \to 2\text{MgO} + \text{C}\).
The most straightforward method to balance equations involves identifying each element's atoms, making adjustments systematically and often beginning with elements appearing in complex molecules, like oxygen in this case.

Photosynthesis

Photosynthesis is a fantastic natural process that converts light energy into chemical energy by forming glucose and oxygen from carbon dioxide and water. This process happens in plants, algae, and certain bacteria, contributing oxygen to the atmosphere and fueling life.
The chemical equation for photosynthesis initially unbalanced can be written as: \(\text{CO}_2 + \text{H}_2\text{O} \to \text{C}_6\text{H}_{12}\text{O}_6 + \text{O}_2\).
To reach a balanced reaction, you need 6 carbon atoms on both sides, 12 hydrogen atoms, and 18 oxygen atoms, balancing to: \(6\text{CO}_2 + 6\text{H}_2\text{O} \to \text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2\).
Balancing this equation highlights the intricate balance of elements and energy needed to sustain plant life and by extension, all life on Earth, as plants serve as primary producers in many ecosystems.

Carbonate Salts Dissolution

The dissolution of carbonate salts is a chemical process where carbonate compounds like sodium carbonate interact with water. This reaction typically results in the formation of a basic solution by producing hydroxide ions, alongside additional compounds.
Take sodium carbonate \((\text{Na}_2\text{CO}_3)\) mixed with water. The unbalanced equation would be: \(\text{Na}_2\text{CO}_3 + \text{H}_2\text{O} \to \text{NaOH} + \text{H}_2\text{CO}_3\).
Balancing it leads to producing two moles of sodium hydroxide: \(\text{Na}_2\text{CO}_3 + \text{H}_2\text{O} \to 2\text{NaOH} + \text{H}_2\text{CO}_3\).
This reaction highlights how carbonate salts, widespread as minerals or in industrial applications, can introduce bases into a solution, influencing pH balance essential in chemical processes, environmental science, and industry.