Understanding the Enthalpy Change in the Formation of Methane (CH4)

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Introduction

In the realm of chemistry, understanding the change in enthalpy for chemical reactions is crucial for predicting the energy transfer during reactions. One common reaction involves the formation of methane (CH4) from solid carbon in its graphite form and hydrogen gas. This article will guide you through the process of calculating this enthalpy change using Hess's Law, which is particularly useful when direct measurement is impractical due to slow reaction rates.

What is Enthalpy Change?

Enthalpy change, denoted as ( \Delta H ), is the total change in energy during a chemical reaction. It can be exothermic (where energy is released) or endothermic (where energy is absorbed). In the case of methane formation, we are interested in determining how much energy is either released or absorbed when solid carbon (graphite) reacts with hydrogen gas (H2).

The Challenge of Measuring Directly

The enthalpy change for methane formation cannot be measured directly in a lab environment. The main reason for this is the reaction's slow rate, making it difficult to observe temperature changes in the surrounding medium. However, by using data from combustion reactions of methane, carbon, and hydrogen, we can utilize Hess's Law to find this value indirectly.

Understanding Hess's Law

Hess's Law states that if a chemical reaction can be expressed as the sum of two or more reactions, the total enthalpy change for the reaction is equal to the sum of the enthalpy changes of the individual reactions. This principle allows chemists to calculate enthalpy changes for complex reactions easily.

Step-by-Step Calculation Using Hess's Law

Step 1: Identify the Desired Reaction

We want to determine the enthalpy change for the following reaction:
Equation:
[ \text{C (s, graphite)} + 2 \text{H}_2(g) \rightarrow \text{CH}_4(g) ]

Step 2: Reverse Reactions to Express Final Products

To leverage Hess's Law, we review the combustion reactions for the relevant substances. The combustion of methane can be expressed as:
Combustion of Methane:
[ \text{CH}_4(g) + 2 \text{O}_2(g) \rightarrow \text{CO}_2(g) + 2 \text{H}_2O(l) \quad (\Delta H = -890.3 , \text{kJ/mol}) ]

Reversing this equation gives us:
[ \text{CO}_2(g) + 2 \text{H}_2O(l) \rightarrow \text{CH}_4(g) + 2 \text{O}_2(g) \quad (\Delta H = +890.3 , \text{kJ/mol}) ]

Step 3: Incorporate Combustion Reactions of Carbon and Hydrogen

Next, we use the combustion of carbon and hydrogen to yield CO2 and H2O, respectively:
Combustion of Carbon:
[ ext{C (s, graphite)} + \text{O}_2 (g) \rightarrow \text{CO}_2(g) \quad (\Delta H = -393.5 , \text{kJ/mol}) ]

Combustion of Hydrogen:
[ 2 \text{H}_2(g) + \text{O}_2(g) \rightarrow 2 \text{H}_2O(l) \quad (\Delta H = -571.6 , \text{kJ/mol}, 1 \text{ mole of water}) ]

To match the number of water molecules needed in our target reaction, we multiply the hydrogen combustion equation by 2: [ 2 \text{H}_2(g) + \text{O}_2(g) \rightarrow 2 \text{H}_2O(l) \quad (\Delta H = -285.8 , \text{kJ/mol} \times 2) ]

Summary of Enthalpies

  1. Combustion of Carbon (reversed):
    • ( \Delta H = +393.5 ) kJ/mol
  2. Combustion of Hydrogen (doubled):
    • ( \Delta H = -571.6 ) kJ/mol
  3. Reversed Combustion of Methane:
    • ( \Delta H = +890.3 ) kJ/mol

Step 4: Combine All Enthalpy Changes

Following Hess's Law, we sum these enthalpy changes: [ \Delta H_{total} = (-393.5) + (-571.6) + (+890.3) ]

  • Calculate this:
    [ \Delta H_{total} = -74.8 , \text{kJ/mol} ]

Final Conclusion

The enthalpy change for the formation of methane from its elements, solid carbon (graphite) and hydrogen gas, is approximately -74.8 kJ/mol. This indicates that forming methane is an exothermic reaction, which releases some energy to the surroundings. Thus, using Hess's Law allows us to effectively deduce the enthalpy changes of complex reactions based on simpler, measurable ones.

This process not only illustrates the utility of Hess's Law in thermodynamics but also enhances our understanding of the energetic relationship between chemical reactants and products within the field of chemistry.


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