Problem 73 - General Chemistry: Principles and Modern Applications

Question

Substitute natural gas (SNG) is a gaseous mixture containing \(\mathrm{CH}_{4}(\mathrm{g})\) that can be used as a fuel. One reaction for the production of SNG is $$\begin{aligned} 4 \mathrm{CO}(\mathrm{g})+8 \mathrm{H}_{2}(\mathrm{g}) & \longrightarrow \\ 3 \mathrm{CH}_{4}(\mathrm{g})+\mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) & \Delta H^{\circ}=? \end{aligned}$$ Use appropriate data from the following list to determine \(\Delta H^{\circ}\) for this SNG reaction. $$\begin{array}{l} \text { C(graphite) }+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}(\mathrm{g}) \\ \quad\quad\quad\quad\quad\quad\quad\quad\qquad \Delta H^{\circ}=-110.5 \mathrm{k} \mathrm{J} \end{array}$$$$\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g}) \quad \Delta H^{\circ}=-283.0 \mathrm{kJ}$$ $$\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \quad \Delta H^{\circ}=-285.8 \mathrm{kJ}$$ $$\begin{array}{l} \text { C(graphite) }+2 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{CH}_{4}(\mathrm{g}) \\ \qquad \Delta H^{\circ}=-74.81 \mathrm{kJ} \end{array}$$ $$\begin{aligned} \mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+& 2 \mathrm{H}_{2} \mathrm{O}(1) \\ & \Delta H^{\circ}=-890.3 \mathrm{kJ} \end{aligned}$$

Step-by-Step Solution

Answer

The enthalpy change \(\Delta H^∘\) for the production of SNG is \(-2699.93 kJ\)

Step 1: Identify the reactions that make up the SNG production reaction

The production of SNG is given by the reaction:\[4 CO(g) + 8 H2(g) → 3 CH4(g) + CO2(g) + 2 H2O(l)\]This can be broken down into the following reactions from the given list: \[4 [C(graphite) + 0.5 O2(g) → CO(g)]\]\[4 [2 H2(g) + O2(g) → 2 H2O(l) ]\]\[3 [C(graphite) + 2 H2(g) → CH4(g)]\]and\[1 [CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l)]\]

Step 2: Calculate the enthalpy changes of the individual reactions

\[ΔH°_1 = 4 × (-110.5 kJ) = -442 kJ\] for the first reaction.\[ΔH°_2 = 4 × (-285.8 kJ) = -1143.2 kJ\] for the second reaction.\[ΔH°_3 = 3 × (-74.81 kJ) = -224.43 kJ\] for the third reaction.\[ΔH°_4 = 1 × (-890.3 kJ) = -890.3 kJ\] for the final reaction.

Step 3: Calculate the total enthalpy change of the reaction

The total enthalpy change for the reaction will be the sum of the enthalpy changes of the individual steps. This can be calculated as \[ ΔH^∘ = ΔH°_1 + ΔH°_2 + ΔH°_3 + ΔH°_4 = -442 kJ + -1143.2 kJ + -224.43 kJ + -890.3 kJ = -2699.93 kJ \]

Key Concepts

Substitute Natural Gas (SNG)

Substitute natural gas, or SNG, is an alternative fuel that replicates the properties and uses of conventional natural gas. SNG primarily consists of methane (CH4), making it a valuable energy source for heating, electricity generation, and as a fuel for vehicles. One of the reasons SNG is advantageous is that it can be transported and stored using the existing natural gas infrastructure.

Due to its high energy content, SNG is considered an efficient energy carrier. The production of SNG involves chemical processes that convert raw materials such as coal, biomass, or industrial waste into a gaseous form. This conversion process aims to reduce dependency on traditional natural gas sources and contribute to energy security and sustainability.

Emphasizing the significance of SNG, it is crucial for energy systems that are transitioning towards more renewable energy sources. By using SNG, countries can reduce their fossil fuel consumption in a gradual yet effective manner while maintaining energy efficiency.

Methane (CH4) Production

Methane is a critical component of substitute natural gas. It is produced through complex chemical reactions as part of the SNG production process. The main chemical equation for methane production in the context of SNG involves the reaction of carbon monoxide (CO) and hydrogen gas ( H_2 ):
- 4CO(g) + 8H_2(g) → 3CH_4(g) + CO_2(g) + 2H_2O(l)

This reaction synthesizes methane by converting CO and H_2 through the interaction with catalysts, resulting in a transformation that generates water and carbon dioxide as byproducts. These byproducts, specifically CO_2, require management to ensure the environmental impacts are minimized.

Methane is prized for its clean-burning properties compared to other hydrocarbons. Efficient production of methane means creating more environmentally friendly fuel solutions, reducing reliance on crude oil, and supporting efforts towards sustainability and the reduction of carbon footprints.

Chemical Reaction Enthalpy

Chemical reaction enthalpy refers to the change in heat content or energy during a chemical reaction, often denoted as ΔH^ ∘. For the production of SNG, calculating the enthalpy change is essential to understand the energy requirements or output associated with the reaction.

In the provided SNG production reaction, we determine the ΔH^ ∘ by adding the enthalpy changes of smaller, individual reactions. These smaller reactions are the combustion and formation reactions of the reagents and products:

• 4 x (C(graphite) + 0.5O_2(g) → CO(g)) with ΔH^ ∘ = -442 kJ
• 4 x (2H_2(g) + O_2(g) → 2H_2O(l)) with ΔH^ ∘ = -1143.2 kJ
• 3 x (C(graphite) + 2H_2(g) → CH_4(g)) with ΔH^ ∘ = -224.43 kJ
• 1 x (CH_4(g) + 2O_2(g) → CO_2(g) + 2H_2O(l)) with ΔH^ ∘ = -890.3 kJ

By summing these values, we find the total enthalpy change of the entire SNG reaction as ΔH^ ∘ = -2699.93 kJ.

Understanding the enthalpy is vital for designing energy-efficient processes, optimizing industrial applications, and developing more sustainable energy production methods. It serves as a foundation for assessing the feasibility and environmental impact of chemical reactions.