Question

Use bond energies to estimate \(\Delta H\) for the combustion of one mole of acetylene: $$\mathrm{C}_{2} \mathrm{H}_{2}(g)+\frac{5}{2} \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$

Short answer

To estimate the change in enthalpy (∆H) for the combustion of one mole of acetylene, we first identify the types and quantities of bonds in the reactants and products: 1 C≡C triple bond, 2 C-H single bonds, and 5 O=O double bonds in reactants; 4 C=O double bonds and 2 O-H single bonds in the products. Using the given bond energies, we calculate the energy used to break bonds in reactants (4151 kJ/mol) and the energy released from the formation of bonds in products (4124 kJ/mol). Subtracting these values, we find ∆H to be -27 kJ/mol.

Step-by-step solution

Identify the bonds in the reactants and products and their quantities

The balanced equation for the combustion reaction of acetylene is given below: \[\mathrm{C}_{2} \mathrm{H}_{2}(g)+\frac{5}{2} \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\] In the reactants, we have: - \(1\) C≡C triple bond in acetylene molecule - \(2\) C-H single bonds in acetylene molecule - \(5\) O=O double bonds in oxygen molecule In the products, we have: - \(4\) C=O double bonds in carbon dioxide molecules - \(2\) O-H single bonds in water molecule

Obtain bond energy values

Use the provided bond energy values or look them up if needed. For this example, we will use the following bond energy values: C≡C: 835 kJ/mol C-H: 413 kJ/mol O=O: 498 kJ/mol C=O: 799 kJ/mol O-H: 464 kJ/mol Note: Bond energies may vary slightly between sources.

Calculate the energy required to break bonds in reactants

Multiply the bond energy value of each bond by the number of that bond type in the reactants and then sum up all the values: Energy used to break bonds = (1 × C≡C bond energy) + (2 × C-H bond energy) + (5 × O=O bond energy) = (1 × 835 kJ/mol) + (2 × 413 kJ/mol) + (5 × 498 kJ/mol) = 835 kJ/mol + 826 kJ/mol + 2490 kJ/mol = 4151 kJ/mol

Calculate the energy released from the formation of bonds in products

Multiply the bond energy value of each bond by the number of that bond type in the products and then sum up all the values: Energy released from the formation of bonds = (4 × C=O bond energy) + (2 × O-H bond energy) = (4 × 799 kJ/mol) + (2 × 464 kJ/mol) = 3196 kJ/mol + 928 kJ/mol = 4124 kJ/mol

Estimate the change in enthalpy (∆H)

Subtract the energy released from the formation of bonds in products from the energy used to break bonds in reactants: ∆H = Energy released - Energy used = 4124 kJ/mol - 4151 kJ/mol = -27 kJ/mol The estimated change in enthalpy for the combustion of one mole of acetylene is -27 kJ/mol.

Key concepts

Understanding Combustion Reactions

A combustion reaction is a chemical process where a substance combines with oxygen to produce energy in the form of heat and light. It's essentially burning. In our example, acetylene (a hydrocarbon) reacts with oxygen to produce carbon dioxide and water. During this process, bonds in the reactants are broken, and new bonds in the products are formed. This type of reaction is exothermic, meaning it releases energy.

Key points to remember:

• Involves oxygen as a reactant.
• Produces energy, typically as heat and light.
• Commonly forms carbon dioxide and water.

Understanding how bonds are broken and formed is crucial to predict the energy changes during combustion.

Enthalpy Change in Reactions

Enthalpy change (\(\Delta H\) is the measure of energy absorbed or released during a chemical reaction at constant pressure. For combustion reactions, the enthalpy change indicates whether the process is exothermic or endothermic. In the case of acetylene combustion, the enthalpy change is negative (\(\Delta H = -27\, \text{kJ/mol}\)), which means the reaction releases energy. This makes it exothermic.

Why it matters:

• Helps quantify the energy change.
• Indicates the reaction type (exothermic or endothermic).
• Plays a role in understanding reaction feasibility.

When analyzing \(\Delta H\), consider both bond breaking in reactants and bond forming in products.

The Role of Chemical Bonds

Chemical bonds are the connections holding atoms together in molecules. Different types of bonds have different strengths, which affect the energy needed to break them. In our acetylene combustion example:

• A C≡C triple bond is stronger, requiring more energy to break.
• C-H and O=O bonds in the reactants also influence the energy calculations.

Bond energies are crucial to estimate the total energy changes in reactions. By summing the energies required to break bonds and formed in new bonds, we can determine the overall reaction enthalpy. This calculation helps predict the reaction's thermodynamic properties.

Acetylene Combustion Explained

Acetylene (C\(_2\)H\(_2\)) is a simple hydrocarbon with a distinct C≡C triple bond, making it highly reactive. When it combusts, it reacts with oxygen to form carbon dioxide and water, releasing energy in the process. This specific reaction demonstrates how acetylene's chemical structure influences its combustion behavior.

Key moments in acetylene combustion:

• The breaking of C≡C and C-H bonds.
• The combination with oxygen (O\(_2\)) to form new bonds.
• Release of large amounts of energy due to efficient bond formation in CO\(_2\) and H\(_2\)O.

Understanding acetylene combustion provides insights into its uses in industries like welding, where its energy release is a vital component.