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Chapter 17: Problem 39

Determine the oxidation number of each atom in \(\mathrm{CO}_{2}\) .

Short Answer

Expert verified
The oxidation state of carbon in CO2 is +4 and that of oxygen is -2.

Step by step solution

01

Determine the Oxidation Number of Oxygen

Knowing that oxygen usually has an oxidation state of -2, you can apply it directly here. For each atom of oxygen in the CO2 molecule, the oxidation state is -2.
02

Determine the Oxidation Number of Carbon

Knowing that the total oxidation state of a neutral molecule is zero, you can set up the equation to find the oxidation state of carbon. Let's denote carbon's oxidation state as x, so: x + 2*(-2) = 0. Solve this equation to find the oxidation state of carbon.
03

Solve the Equation

Solving the equation x - 4 = 0 will give you x = 4. So, the oxidation state of carbon in the CO2 molecule is +4.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the CO2 Molecule
Carbon dioxide, commonly represented as \( \text{CO}_2 \), is a simple yet essential chemical compound. It consists of one carbon atom covalently double bonded to two oxygen atoms. This linear arrangement is crucial as it influences both the chemical behavior and physical properties of the molecule.
It's a widely occurring molecule used by plants in photosynthesis and found as a major component of the Earth's atmosphere. Recognizing its structure helps us understand the context in which we determine the oxidation numbers of its atoms.
Oxidation State Calculation in CO2
Calculating oxidation states is a fundamental skill in chemistry, helping to understand the electron distribution in molecules. In the case of the \( \text{CO}_2 \) molecule, this process becomes straightforward.
Let's break it down further:
  • Oxygen: Oxygen generally has an oxidation state of -2. In carbon dioxide, each oxygen atom maintains this state due to its high electronegativity.
  • Carbon: To determine carbon's oxidation state, we apply the rule that the sum of oxidation states in a molecule must equal its net charge, which for \( \text{CO}_2 \) is 0. Hence, we set up the equation:
    \( x + 2(-2) = 0 \)
    Solving this equation for \( x \), the oxidation state of carbon is revealed to be +4.
Understanding these calculations helps in analyzing chemical reactions where electron transfer plays a crucial role.
The Concept of a Neutral Molecule
A neutral molecule is one with no net electrical charge. In other words, the total positive charges equal the total negative charges. This is significant when calculating oxidation states as it provides guidance on how the states should sum up.

For instance, in \( \text{CO}_2 \):
  • The sum of oxidation states is zero because the molecule is neutral, simplifying the calculation process by establishing a mathematical balance for assigning states to individual elements.
  • Both carbon and oxygen states add up to zero, with carbon at +4 and two oxygens each at -2, reflecting their natural tendencies and bonding characteristics.
Recognizing the neutrality of a molecule supports a structured approach in solving for chemical properties and behavior.

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Most popular questions from this chapter

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Calculate the Equilibrium Constant, using the Standard Cell Voltage The graphing calculator can run a program that calculates the equilibrium constant for an electrochemical cell using an equation called the Nernst equation, given the standard potential and the number of electrons transferred. Given that the standard potential is 2.041 V and that two electrons are transferred, you will calculate the equilibrium constant. The program will be used to make the calculations. Go to Appendix c. If you are using a TI-83 Plus, you can download the program NERNST and data and run the application as directed. If you are using another calculator, your teacher will provide you with key- strokes and data sets to use. After you have run the program, answer the following questions. \begin{equation} \begin{array}{l}{\text { a. What is the equilibrium constant when }} \\\ {\text { the standard potential is } 0.099 ?} \\ {\text { b. What is the equilibrium constant when }} \\ {\text { the standard potential is } 1.125 ?} \\\ {\text { c. What is the equilibrium constant when }} \\ {\text { the standard potential is } 2.500 ?}\end{array} \end{equation}
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