Problem 54 - Chemistry: An Atoms-Focused Approach

Question

Using data in Appendix \(4,\) calculate \(\Delta H_{\mathrm{rxn}}\) for the production of acetylene from the reaction between calcium carbide and water, given that the \(\Delta H_{f}^{\circ}\) of \(\mathrm{CaC}_{2}\) is \(-59.8 \mathrm{kJ} / / \mathrm{mol}\) $$\mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{C}_{2} \mathrm{H}_{2}(g)+\mathrm{Ca}(\mathrm{OH})_{2}(s)$$. Is this an endothermic or an exothermic reaction?

Step-by-Step Solution

Answer

Is the reaction endothermic or exothermic? The enthalpy change of reaction (ΔH_rxn) is -126.9 kJ/mol, and the reaction is exothermic.

Step 1: Identify the given data

We are given the following information: - ΔHf° (CaC2) = -59.8 kJ/mol - The reaction: CaC2(s) + 2H2O(l) → C2H2(g) + Ca(OH)2(s)

Step 2: Find the ΔHf° values for reactants and products

In order to calculate the ΔH_rxn, we need to find the ΔHf° values for all reactants and products. We can find these values in Appendix 4. - ΔHf°(H2O) = -285.8 kJ/mol - ΔHf°(C2H2) = 226.7 kJ/mol - ΔHf°(Ca(OH)2) = -985.0 kJ/mol

Step 3: Calculate the enthalpy change of reaction (ΔH_rxn)

Now we will use the following equation to calculate ΔH_rxn: ΔH_rxn = Σ [ΔHf°(products)] - Σ [ΔHf°(reactants)] ΔH_rxn = [ΔHf°(C2H2) + ΔHf°(Ca(OH)2)] - [ΔHf°(CaC2) + 2 * ΔHf°(H2O)] Plugging in the values: ΔH_rxn = [(226.7 kJ/mol) + (-985.0 kJ/mol)] - [(-59.8 kJ/mol) + 2 * (-285.8 kJ/mol)] ΔH_rxn = (-758.3 kJ/mol) - (-631.4 kJ/mol) ΔH_rxn = -126.9 kJ/mol

Step 4: Determine if the reaction is endothermic or exothermic

Since ΔH_rxn = -126.9 kJ/mol is a negative value, this implies that the reaction is exothermic. It means that the reaction releases energy in the form of heat.

Step 5: Answer

The enthalpy change of reaction (ΔH_rxn) for the production of acetylene from the reaction between calcium carbide and water is -126.9 kJ/mol. This is an exothermic reaction.

Key Concepts

Exothermic Reaction

An exothermic reaction is a chemical process that releases energy, primarily in the form of heat. It occurs when the energy needed to break the bonds in the reactants is less than the energy released when new bonds are formed in the products. This leads to a net release of energy into the surroundings, making them warmer. Exothermic reactions are characterized by a negative enthalpy change (\(\Delta H\)).

Common examples of exothermic reactions include combustion, respiration, and certain oxidation processes. In the context of the reaction between calcium carbide and water, the negative value calculated for \(\Delta H_{rxn}\), specifically -126.9 kJ/mol, indicates that this is an exothermic process. The negative sign of \(\Delta H_{rxn}\) serves as a clear indicator that heat is being released during the reaction.

Reaction Enthalpy Calculation

Calculating the enthalpy change (\(\Delta H_{rxn}\)) for a reaction involves using the enthalpy of formation (\(\Delta H_f^\circ\)) for each of the reactants and products involved in the reaction. The enthalpy of formation is the heat change associated with the formation of one mole of a compound from its elements in their standard states.

To calculate the \(\Delta H_{rxn}\), follow these steps:

• Identify the \(\Delta H_f^\circ\) values for each reactant and product, typically found in reference materials like a chemistry appendix.
• Apply the formula: \(\Delta H_{rxn} = \Sigma [\Delta H_f^\circ(products)] - \Sigma [\Delta H_f^\circ(reactants)]\)
• Sum up the enthalpy of formation for the products and subtract the sum of the enthalpies for the reactants.

Using the given reaction of calcium carbide and water to form acetylene and calcium hydroxide, we calculate:\[\Delta H_{rxn} = [(226.7 + (-985.0)) - ((-59.8) + 2 \times (-285.8))] = -126.9 \text{kJ/mol}\]

Calcium Carbide and Water Reaction

The reaction between calcium carbide (\(\text{CaC}_2\)) and water (\(\text{H}_2\text{O}\)) is a classic example studied in chemistry, producing acetylene gas (\(\text{C}_2\text{H}_2\)) and calcium hydroxide (\(\text{Ca(OH)}_2\)).

This reaction can be represented as:\[\text{CaC}_2(s) + 2 \text{H}_2\text{O}(l) \rightarrow \text{C}_2\text{H}_2(g) + \text{Ca(OH)}_2(s)\]In this process, calcium carbide reacts vigorously with water, releasing energy and forming acetylene gas, a valuable compound widely used as a fuel and in organic synthesis. Calcium hydroxide, a by-product, is a solid that can be handled easily.

Acetylene, being the key product, has applications in welding and as a precursor to various chemical compounds. This reaction is an economically significant method of obtaining acetylene from readily available materials, demonstrating the practical aspect of such exothermic reactions in industrial chemistry. Understanding the energy changes in this reaction is critical for ensuring safe handling and optimizing industrial processes.