Question

Acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}(g)\), is used in welding. (a) Write a balanced equation for the combustion of acetylene gas to \(\mathrm{CO}_{2}(\mathrm{~g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{I})\). (b) How much heat is produced in burning \(1 \mathrm{~mol}\) of \(\mathrm{C}_{2} \mathrm{H}_{2}\) under standard conditions if both reactants and products are brought to \(298 \mathrm{~K} ?(\mathrm{c})\) What is the maximum amount of useful work that can be accomplished under standard conditions by this reaction?

Short answer

(a) The balanced combustion equation for acetylene is: \( 2\mathrm{C}_{2} \mathrm{H}_{2}(g) + 5\mathrm{O}_{2}(g) \rightarrow 4\mathrm{CO}_{2}(g) + 2\mathrm{H}_{2} \mathrm{O}(l) \) (b) The heat produced in burning 1 mole of \(\mathrm{C}_{2}\mathrm{H}_{2}\) under standard conditions is 2145.6 kJ. (c) The maximum amount of useful work that can be accomplished under standard conditions is 2016.62 kJ/mol.

Step-by-step solution

(a) Write a balanced combustion equation for acetylene

The combustion of acetylene involves reacting the gas with oxygen to form carbon dioxide and water. To achieve a balanced equation, we must ensure that there are equal numbers of each type of element/atom on both sides of the equation: \[ \mathrm{C}_{2} \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g) + \mathrm{H}_{2} \mathrm{O}(l) \] Balancing the equation: \[ 2\mathrm{C}_{2} \mathrm{H}_{2}(g) + 5\mathrm{O}_{2}(g) \rightarrow 4\mathrm{CO}_{2}(g) + 2\mathrm{H}_{2} \mathrm{O}(l) \]

(b) Calculate the heat produced in burning 1 mole of C2H2

To find the heat produced, we need to find the change in enthalpy (∆H) for the combustion of 1 mole of C2H2. We will use standard enthalpies of formation (∆Hf) for data: For C2H2(g): +227 kJ/mol, For CO2(g): -393.5 kJ/mol, For H2O(l): -285.8 kJ/mol. Using the balanced equation and the standard enthalpies of formation: \[ \Delta H = [4(-393.5) + 2(-285.8)] - 2(227) \] Converting the values: \[ \Delta H = [-1574 + (-571.6)] - (454) \] \[ \Delta H = -2145.6 \, \mathrm{kJ/mol} \] The heat produced in burning 1 mole of C2H2 under standard conditions is 2145.6 kJ.

(c) Calculate the maximum useful work under standard conditions

For constant temperature and pressure, the maximum useful work can be calculated: \[ \Delta G_{\mathrm{max}} = \Delta H - T\Delta S \] We are given standard conditions (temperature T = 298 K). To find the change in entropy (∆S), using standard molar entropies S: For C2H2(g): 200.94 J/mol∙K, For O2(g): 205.14 J/mol∙K, For CO2(g): 213.7 J/mol∙K, For H2O(l): 70.0 J/mol∙K. Using the balanced equation and standard molar entropies: \[ \Delta S = [(4 \times 213.7) + (2 \times 70) - [(2 \times 200.94) + (5 \times 205.14)]] \] \[ \Delta S = [854.8 + 140] - [401.88 + 1025.7] \] \[ \Delta S = -432.8 \frac{\mathrm{J}}{\mathrm{mol} \cdot \mathrm{K}} \] Using ∆Gmax = ∆H - T∆S, and converting ∆S in J to kJ: \[ \Delta G_{\mathrm{max}} = -2145.6 - (298)(-0.4328) \] \[ \Delta G_{\mathrm{max}} = -2145.6 + 128.98 \] \[ \Delta G_{\mathrm{max}} = -2016.62 \, \mathrm{kJ/mol} \] The maximum amount of useful work that can be accomplished under standard conditions is 2016.62 kJ/mol.

Key concepts

Enthalpy Change

In a chemical reaction, the enthalpy change (abla H) represents the heat exchanged under constant pressure. For combustion reactions, this is crucial since they release heat, making them exothermic. In our acetylene combustion example, calculating abla H helps determine how much energy is given off when acetylene burns.
When burning acetylene, the enthalpy change is obtained using the standard enthalpies of formation for the reactants and products involved.
We compute it as follows:\[ abla H = [4(-393.5) + 2(-285.8)] - [2(227)] = -2145.6 \] kJ/mol.
This indicates that 2145.6 kJ of heat is released for each mole of acetylene combusted. This negative value confirms an exothermic reaction, a characteristic feature of combustion processes.

Entropy Change

Entropy change (abla S) measures the disorder or randomness in a system during a reaction. Reactions often cause changes in the arrangement and movement of molecules, affecting entropy.
In combustion, this is marked by a transition from gases and liquids, impacting the disorder of the system. The combustion of acetylene involves calculating the difference in entropy from reactants to products:
\[ abla S = [4 imes 213.7 + 2 imes 70] - [2 imes 200.94 + 5 imes 205.14] = -432.8 \] J/mol∙K.
A negative abla S here signifies that the reaction leads to a more ordered, less random set of products, which is typical in such exothermic processes.

Gibbs Free Energy

Gibbs free energy (abla G) gives insight into the spontaneity and maximum useful work obtainable from a chemical reaction. It combines enthalpy and entropy changes using the formula:
\[ abla G = abla H - Tabla S \]
For acetylene combustion, at 298 K, it allows us to calculate the potential work from this reaction:
\[ abla G = -2145.6 - 298(-0.4328) = -2016.62 \] kJ/mol.
This negative value illustrates spontaneity, indicating that acetylene readily combusts under standard conditions, releasing energy to do work efficiently.

Acetylene Combustion

Acetylene combustion involves burning \( C_2H_2 \) to produce carbon dioxide and water. This reaction is vital in processes demanding intense heat, such as welding.
The balanced chemical equation demonstrates the stoichiometry of this combustion reaction:
\[ 2C_2H_2 + 5O_2 \rightarrow 4CO_2 + 2H_2O \]
This equation shows two moles of acetylene reacting with five moles of oxygen, forming four moles of carbon dioxide and two moles of water. Such reactions are known for their high heat output, which is harnessed in industrial applications.

Thermodynamics

Thermodynamics studies energy transformations, providing insights into reaction behaviors like acetylene's combustion. It involves concepts like enthalpy, entropy, and Gibbs free energy, offering a framework to predict reaction spontaneity and efficiency.
When acetylene combusts, it aligns with thermodynamics principles showing energy transfer and work potential as part of chemical processes.

• Heat Exchange: The reaction releases significant heat, and understanding abla H helps quantify this transfer.
• Disorder and Efficiency: Analyzing abla S and abla G helps determine system randomness changes and useful work potential.

By understanding these thermodynamic properties, one can predict the feasibility and energetic demands of chemical reactions, crucial for applications like welding that rely on acetylene combustion.