Problem 53 - Chemistry: An Atoms-Focused Approach

Question

Using data in Appendix \(4,\) calculate \(\Delta H_{\mathrm{rxn}}\) for the production of acetylene from the controlled combustion of methane: $$6 \mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{C}_{2} \mathrm{H}_{2}(g)+2 \mathrm{CO}(g)+10 \mathrm{H}_{2}(g)$$ Is this an endothermic or an exothermic reaction?

Step-by-Step Solution

Answer

Question: Calculate the change in enthalpy (ΔH) for the controlled combustion of methane to produce acetylene using the data from Appendix 4, and determine whether the reaction is endothermic or exothermic.

Step 1: Identify the enthalpies for each reactant and product

Using the data provided in Appendix 4, we can find the enthalpies (ΔH) for each reactant and product within the balanced chemical equation. Let's organize them into a table: | Compound | Formula | ΔH (kJ/mol) | |----------|---------|------------| | Methane | CH₄ | ΔH₁ | | Oxygen | O₂ | ΔH₂ | | Acetylene | C₂H₂ | ΔH₃ | | Carbon Monoxide | CO | ΔH₄ | | Molecular Hydrogen | H₂ | ΔH₅ | In this scenario, the given enthalpies from Appendix 4 are theoretical numbers. Replace ΔH₁ through ΔH₅ with the values given in Appendix 4.

Step 2: Calculate the sum of ΔH for reactants and products

Now, we need to calculate the sum of the enthalpies for the reactants side and the products side, respectively. For this, we multiply the enthalpies of each compound by the coefficients in the balanced chemical equation and then add them up. Reactants: (6 × ΔH₁) + (ΔH₂) Products: (2 × ΔH₃) + (2 × ΔH₄) + (10 × ΔH₅)

Step 3: Calculate the ΔH for the reaction

To find the change in enthalpy for the reaction (ΔHₙ), we use the following formula: ΔHₙ = (sum of ΔH of products) - (sum of ΔH of reactants) Plug in the values we found in Step 2: ΔHₙ = [(2 × ΔH₃) + (2 × ΔH₄) + (10 × ΔH₅)] - [(6 × ΔH₁) + (ΔH₂)]

Step 4: Determine if the reaction is endothermic or exothermic

If the calculated ΔHₙ is positive, it means we have an endothermic reaction, as the reaction absorbs heat. If the ΔHₙ is negative, it means we have an exothermic reaction, as the reaction releases heat. Find the sign of ΔHₙ and classify the reaction as endothermic or exothermic. In conclusion, by following the steps above and using the Appendix 4 data, we'll calculate ΔHₙ for the controlled combustion of methane to produce acetylene, and determine if the reaction is endothermic or exothermic.

Key Concepts

Combustion Reaction

A combustion reaction is a chemical process by which a substance combines with oxygen, releasing energy in the form of light or heat. In the example given, we have methane (\(\text{CH}_4\)). Methane is commonly used as a fuel source because it combusts and releases substantial amounts of energy.Typically, in a combustion reaction, you will observe the reactants combining with oxygen (\(\text{O}_2\)). This results in the formation of products such as carbon dioxide (\(\text{CO}_2\)) and water (\(\text{H}_2\text{O}\)). However, the reaction given in your exercise is controlled, producing different products: acetylene (\(\text{C}_2\text{H}_2\)), carbon monoxide (\(\text{CO}\)), and hydrogen gas (\(\text{H}_2\)).Key points about combustion reactions:

• Combustion reactions require oxygen as a reactant.
• They typically produce energy, observable as heat or light.
• The products of combustion can vary based on the conditions and elements involved.

In the context of chemical engineering or controlled laboratory settings, combustion reactions can be manipulated to yield specific products, such as in this scenario.

Endothermic vs Exothermic Reactions

Chemical reactions are often classified based on their energy change as either endothermic or exothermic. Understanding this aspect is crucial when discussing enthalpy changes.**Exothermic Reactions**:

• These reactions release energy to the surroundings.
• The enthalpy change (\(\Delta H\)) is negative.
• Commonly noted by an increase in temperature or release of heat.

A typical example of an exothermic reaction is the combustion process where large amounts of energy are emitted.**Endothermic Reactions**:

• These reactions absorb energy from their surroundings.
• The enthalpy change (\(\Delta H\)) is positive.
• Often noticed by a decrease in temperature of the surrounding environment.

The fact that a reaction can be endothermic or exothermic helps in understanding how energy changes during the chemical process. By calculating enthalpy change, you can determine the kind of reaction by assessing the sign (+/-) of the calculated \(\Delta H\).

Enthalpy Calculation

To calculate the enthalpy change (\(\Delta H_{ ext{rxn}}\)) of a reaction, you sum up the enthalpy values of the products and subtract the enthalpy sum of the reactants. This process helps in quantifying the energy change during the reaction.Here’s the generalized approach:1. **Identify**: List all the reactants and products and determine their enthalpy (\(\Delta H\)) values from a data source such as Appendix 4.2. **Reactants and Products**: Use the balanced chemical equation to ensure that the coefficients of substances are used correctly when calculating the enthalpy sum.3. **Calculation**: - For reactants: Multiply the enthalpy values by their respective coefficients and sum them. - For products: Do the same as above for the products.The formula:\[\Delta H_{ ext{rxn}} = \text{(sum of } \Delta H \text{ of products)} - \text{(sum of } \Delta H \text{ of reactants)}\]By substituting the enthalpy values into this formula, you acquire the energy change associated with the reaction. Depending on whether \(\Delta H_{ ext{rxn}}\) is negative or positive, you determine if the reaction is exothermic or endothermic. This calculation is essential for predicting reaction feasibilities and for practical applications in energy management.