Problem 23 - General Chemistry

Question

Give chemical equations for the conversion of carbon in coal to methane, \(\mathrm{CH}_{4}\).

Step-by-Step Solution

Answer

The balanced chemical equation is \(C + 2H_2 \rightarrow CH_4\).

Step 1: Understanding the Conversion

In this process, carbon (essentially from coal, represented as graphite) is converted into methane (\(CH_4\)). Methane formation typically involves a reaction of carbon sources with hydrogen.

Step 2: Balancing the Equation

To convert carbon (\(C\)) into methane (\(CH_4\)), we need to balance the following chemical reaction: \(C + 2H_2 \rightarrow CH_4\). This indicates that each carbon atom needs two molecules of hydrogen gas.

Step 3: Identifying Reactants and Products

In the balanced reaction \(C + 2H_2 \rightarrow CH_4\), the reactants are carbon (\(C\)) and hydrogen gas (\(H_2\)), while methane (\(CH_4\)) is the product.

Key Concepts

Carbon Conversion

Carbon conversion is the process of transforming carbon atoms from one form into another, often in a chemical reaction. In the context of coal to methane conversion, this involves taking carbon from coal, typically represented as graphite, and reacting it to form methane. Coal is primarily carbon, and when we talk about conversion, we're referring to the use of carbon atoms to create new compounds through chemical reactions. The conversion to methane implies a significant transformation, requiring an adequate energy source and precise conditions. This kind of transformation is essential in various industrial processes, particularly in the energy sector, where methane is valued as a cleaner alternative to other fossil fuels. Understanding carbon conversion helps in optimizing such reactions for better energy efficiency and reduced emissions.

Methane Formation

Methane formation is a chemical reaction where carbon and hydrogen atoms combine to create methane (CH_4). Methane is a simple hydrocarbon and is one of the most common components of natural gas. This formation process typically involves:

• Carbon as a reactant, which often originates from coal or other hydrocarbons.
• Hydrogen gas (H_2) as a crucial reactant, providing the necessary hydrogen atoms to bond with carbon.

The reaction can be represented as: \[C + 2H_2 \rightarrow CH_4\]This equation demonstrates the stoichiometry of the reaction—showing that two molecules of hydrogen gas are required to fully react with one carbon atom to yield one methane molecule. This balance is crucial for efficient methane synthesis and is applied in both laboratory settings and large-scale industrial processes.

Balanced Chemical Reaction

A balanced chemical reaction is one where the number of atoms for each element involved is equal on both the reactant and product sides of the equation. This balance ensures the law of conservation of mass is upheld, meaning no atoms are lost or gained; they are simply rearranged.In the conversion of carbon to methane, the balanced equation is:\[C + 2H_2 \rightarrow CH_4\]Here, we see:

• One carbon atom on both sides.
• Four hydrogen atoms on both sides, coming from two molecules of hydrogen.

Balancing equations is essential for predicting reaction yields and ensuring that all reactants are used efficiently. It's a fundamental step in chemical reaction design, crucial for industrial synthesis and environmental considerations.