Problem 89 - Chemistry An Atoms First Approach

Question

Balance each of the following oxidation-reduction reactions by using the oxidation states method. a. \(\mathrm{C}_{2} \mathrm{H}_{6}(g)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) b. \(\mathrm{Mg}(s)+\mathrm{HCl}(a q) \rightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cl}^{-}(a q)+\mathrm{H}_{2}(g)\) c. \(\mathrm{Co}^{3+}(a q)+\mathrm{Ni}(s) \rightarrow \mathrm{Co}^{2+}(a q)+\mathrm{Ni}^{2+}(a q)\) d. \(\mathrm{Zn}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{ZnSO}_{4}(a q)+\mathrm{H}_{2}(g)\)

Step-by-Step Solution

Answer

The balanced reactions are: a. \[\mathrm{C}_{2}\mathrm{H}_{6}(g) + \frac{7}{2}\mathrm{O}_{2}(g) \rightarrow 2\mathrm{CO}_{2}(g) + 3\mathrm{H}_{2}\mathrm{O}(g)\] b. \[\mathrm{Mg}(s) + 2\mathrm{HCl}(a q) \rightarrow \mathrm{Mg}^{2+}(a q) + 2\mathrm{Cl}^{-}(a q) + \mathrm{H}_{2}(g)\] c. \[2\mathrm{Co}^{3+}(a q) + 2\mathrm{Ni}(s) \rightarrow 2\mathrm{Co}^{2+}(a q) + 2\mathrm{Ni}^{2+}(a q)\] d. \[\mathrm{Zn}(s) + \mathrm{H}_{2}\mathrm{SO}_{4}(a q) \rightarrow \mathrm{ZnSO}_{4}(a q) + \mathrm{H}_{2}(g)\]

Step 1: 1. Identify oxidation and reduction processes

In this reaction, carbon in \(\mathrm{C}_{2}\mathrm{H}_{6}\) gets oxidized to carbon dioxide \(\mathrm{CO}_{2}\), and oxygen in \(\mathrm{O}_{2}\) gets reduced to water \(\mathrm{H}_{2}\mathrm{O}\).

Step 2: 2. Determine the oxidation states of elements

The oxidation state of hydrogen is +1, carbon in ethane is -3, carbon in carbon dioxide is +4, and oxygen in oxygen gas and water is -2.

Step 3: 3. Balance the electrons gained and lost

Carbon goes from -3 to +4, losing 7 electrons in the process. Oxygen goes from 0 to -2, gaining 2 electrons. To balance the electrons, we need 2 carbon atoms and 7 oxygen atoms.

Step 4: 4. Balance the elements and overall reaction

The balanced reaction is: \[\mathrm{C}_{2}\mathrm{H}_{6}(g) + \frac{7}{2}\mathrm{O}_{2}(g) \rightarrow 2\mathrm{CO}_{2}(g) + 3\mathrm{H}_{2}\mathrm{O}(g)\] #b. Balancing \(\mathrm{Mg}(s)+\mathrm{HCl}(a q) \rightarrow \mathrm{Mg}^{2+}(a q)+\mathrm{Cl}^{-}(a q)+\mathrm{H}_{2}(g)\)#

Step 5: 1. Identify oxidation and reduction processes

In this reaction, magnesium is oxidized to \(\mathrm{Mg}^{2+}\) and hydrogen in \(\mathrm{HCl}\) is reduced to \(\mathrm{H}_{2}\).

Step 6: 2. Determine the oxidation states of elements

The oxidation state of magnesium is 0, magnesium in \(\mathrm{Mg}^{2+}\) is +2, hydrogen in \(\mathrm{HCl}\) is +1, and hydrogen in \(\mathrm{H}_{2}\) is 0.

Step 7: 3. Balance the electrons gained and lost

Magnesium goes from 0 to +2, losing 2 electrons. Hydrogen goes from +1 to 0, gaining 1 electron. To balance the electrons, we need 2 hydrogen atoms.

Step 8: 4. Balance the elements and overall reaction

The balanced reaction is: \[\mathrm{Mg}(s) + 2\mathrm{HCl}(a q) \rightarrow \mathrm{Mg}^{2+}(a q) + 2\mathrm{Cl}^{-}(a q) + \mathrm{H}_{2}(g)\] #c. Balancing \(\mathrm{Co}^{3+}(a q)+\mathrm{Ni}(s) \rightarrow \mathrm{Co}^{2+}(a q)+\mathrm{Ni}^{2+}(a q)\)#

Step 9: 1. Identify oxidation and reduction processes

In this reaction, nickel gets oxidized to \(\mathrm{Ni}^{2+}\), and cobalt in \(\mathrm{Co}^{3+}\) gets reduced to \(\mathrm{Co}^{2+}\).

Step 10: 2. Determine the oxidation states of elements

The oxidation state of nickel is 0, nickel in \(\mathrm{Ni}^{2+}\) is +2, cobalt in \(\mathrm{Co}^{3+}\) is +3, and cobalt in \(\mathrm{Co}^{2+}\) is +2.

Step 11: 3. Balance the electrons gained and lost

Nickel goes from 0 to +2, losing 2 electrons. Cobalt goes from +3 to +2, gaining 1 electron. To balance the electrons, we need 2 cobalt atoms.

Step 12: 4. Balance the elements and overall reaction

The balanced reaction is: \[2\mathrm{Co}^{3+}(a q) + 2\mathrm{Ni}(s) \rightarrow 2\mathrm{Co}^{2+}(a q) + 2\mathrm{Ni}^{2+}(a q)\] #d. Balancing \(\mathrm{Zn}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{ZnSO}_{4}(a q)+\mathrm{H}_{2}(g)\)#

Step 13: 1. Identify oxidation and reduction processes

In this reaction, zinc gets oxidized to \(\mathrm{ZnSO}_{4}\) and hydrogen in \(\mathrm{H}_{2}\mathrm{SO}_{4}\) gets reduced to \(\mathrm{H}_{2}\).

Step 14: 2. Determine the oxidation states of elements

The oxidation state of zinc is 0, zinc in \(\mathrm{ZnSO}_{4}\) is +2, hydrogen in \(\mathrm{H}_{2}\mathrm{SO}_{4}\) is +1, and hydrogen in \(\mathrm{H}_{2}\) is 0.

Step 15: 3. Balance the electrons gained and lost

Zinc goes from 0 to +2, losing 2 electrons. Hydrogen goes from +1 to 0, gaining 1 electron. To balance the electrons, we need 2 hydrogen atoms.

Step 16: 4. Balance the elements and overall reaction

The balanced reaction is: \[\mathrm{Zn}(s) + \mathrm{H}_{2}\mathrm{SO}_{4}(a q) \rightarrow \mathrm{ZnSO}_{4}(a q) + \mathrm{H}_{2}(g)\]

Key Concepts

Oxidation States Method

Understanding the oxidation states method is essential for balancing redox reactions. This technique helps identify which elements undergo oxidation and reduction during a chemical reaction. Let's break it down:- **Oxidation** refers to the loss of electrons, resulting in an increase in oxidation state.- **Reduction** is the gain of electrons, leading to a decrease in oxidation state.Oxidation states provide a way to keep track of electron transfer. For instance, in the scenario involving ethane (\(\mathrm{C}_{2}\mathrm{H}_{6}\)), the carbon undergoes oxidation, moving from an oxidation state of -3 to +4. Meanwhile, oxygen goes from an oxidation state of 0 to -2 during its reduction, when forming \(\mathrm{H}_{2}\mathrm{O}\). By analyzing these changes, we can identify how many electrons are lost by one element and gained by another, paving the way to balance the reaction effectively.

Balancing Chemical Equations

Balancing chemical equations is crucial to maintain the law of conservation of mass, ensuring that atoms are neither created nor destroyed. In the case of redox reactions, this balance is not just about atoms, but also electrons. The steps include:1. **Identify each element's oxidation states** to understand which are oxidized and reduced.2. **Ensure that the number of electrons lost equals the number of electrons gained.** This means that if X electrons are transferred in oxidation, Y electrons must be transferred in reduction, and X must equal Y for the equation to balance.For example, in the reaction of magnesium (\(\mathrm{Mg}(s)\)) with hydrochloric acid (\(\mathrm{HCl}(aq)\)), one magnesium atom loses two electrons, while each hydrogen ion requires one electron to be reduced. Therefore, we need two \(\mathrm{HCl}\) molecules to accept the two electrons from magnesium, resulting in the balanced equation.

Electron Transfer in Reactions

Electron transfer is an integral part of redox reactions and is essentially the heart of these processes. When electrons are transferred from one substance to another, the substance that loses electrons is oxidized and the one that gains electrons is reduced. Here's how it manifests:- **Oxidizing agent**: The substance that gains electrons (and is reduced).- **Reducing agent**: The substance that loses electrons (and is oxidized).In the case with nickel (\(\mathrm{Ni}(s)\)) and cobalt ions (\(\mathrm{Co}^{3+}(aq)\)), nickel acts as the reducing agent by losing electrons to become \(\mathrm{Ni}^{2+}(aq)\), while cobalt serves as the oxidizing agent by gaining those electrons to change from \(\mathrm{Co}^{3+}(aq)\) to \(\mathrm{Co}^{2+}(aq)\). Recognizing these roles helps in understanding the electron flow and balancing reactions at a molecular level.

Reduction Processes

Reduction processes are vital for balancing redox reactions, focusing on the gain of electrons by a particular substance. This is the counterpart to oxidation, and they occur simultaneously in reactions.A reduction process can be identified by:- A decrease in the oxidation state of an element.- The addition of electrons to an atom or molecule.Take, for example, the reduction of hydrogen in sulfuric acid during the reaction with zinc (\(\mathrm{Zn}(s)\)). Here, hydrogen goes from an oxidation state of +1 in \(\mathrm{H}_{2}\mathrm{SO}_{4}(aq)\) to 0 in \(\mathrm{H}_{2}(g)\), indicating a gain of electrons. These electrons are provided by zinc, which is simultaneously oxidized. In every redox reaction, recognizing the reduction process helps balance both the charge and the atoms involved, ensuring the entire reaction equation is balanced correctly.