Question

Calcium carbide \(\left(\mathrm{CaC}_{2}\right)\) reacts with water to form acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) and \(\mathrm{Ca}(\mathrm{OH})_{2}\). From the following enthalpy of reaction data and data in Appendix \(C\), calculate \(\Delta H_{f}^{\circ}\) for \(\mathrm{CaC}_{2}(s):\) \(\mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{C}_{2} \mathrm{H}_{2}(g)\) \(\Delta H^{\circ}=-127.2 \mathrm{~kJ}\)

Short answer

The enthalpy of formation for calcium carbide (CaC2) is approximately 1204.7 kJ/mol.

Step-by-step solution

Write down the equation for enthalpy of reaction

We will use the following equation for enthalpy of reaction: ∆H° = ∑n * ∆Hf°(products) - ∑n * ∆Hf°(reactants)

Identify the enthalpy of formation values

From Appendix C, we have the following enthalpy of formation values: ∆Hf°(H2O(l)) = -285.8 kJ/mol ∆Hf°(Ca(OH)2(s)) = -987.0 kJ/mol ∆Hf°(C2H2(g)) = 226.7 kJ/mol

Plug the values into the equation

Recall the balanced chemical equation and the provided enthalpy of reaction: CaC2(s) + 2 H2O(l) → Ca(OH)2(s) + C2H2(g) ∆H° = -127.2 kJ Plugging the enthalpy of formation values into the equation, we get: -127.2 kJ = [(1 * ∆Hf°(Ca(OH)2(s)) + 1 * ∆Hf°(C2H2(g))) - (1 * ∆Hf°(CaC2(s)) + 2 * ∆Hf°(H2O(l)))] Replace the known values: -127.2 kJ = [(1 * (-987.0 kJ/mol) + 1 * (226.7 kJ/mol)) - (1 * ∆Hf°(CaC2(s)) + 2 * (-285.8 kJ/mol))]

Solve for ∆Hf°(CaC2(s))

Simplify the equation for ∆Hf°(CaC2(s)): -127.2 kJ = (-760.3 kJ/mol) - ∆Hf°(CaC2(s)) + 571.6 kJ/mol Next, isolate the term ∆Hf°(CaC2(s)): ∆Hf°(CaC2(s)) = 571.6 kJ/mol - 127.2 kJ + 760.3 kJ/mol Finally, calculate the value for ∆Hf°(CaC2(s)): ∆Hf°(CaC2(s)) = 1204.7 kJ/mol The enthalpy of formation for calcium carbide (CaC2) is approximately 1204.7 kJ/mol.

Key concepts

Understanding Calcium Carbide

Calcium carbide ( CaC_2 ) is a unique and versatile compound. When you look at calcium carbide, you're really looking at a substance that's famous for its ability to produce acetylene gas when combined with water.
The compound is ionic, consisting of calcium and tiny molecules of carbide.
Carbide ions are composed of two carbon atoms bonded together, and this is what makes calcium carbide react with water in such an interesting way.
When water ( H_2O ) reacts with calcium carbide, it forms acetylene ( C_2H_2 ) gas, along with calcium hydroxide as a byproduct.
This process is not only curious from a chemistry standpoint but also practically useful in industries where acetylene is a valued gas for cutting and welding purposes.
It essentially showcases the conversion of solid substances into gaseous forms through chemical reactions.

The Role of Acetylene

Acetylene ( C_2H_2 ) is a fascinating molecule with a straightforward yet highly combustible structure. Frequently, acetylene is cherished for its use in the industrial sectors, particularly in welding and cutting metals.
The formation of acetylene through the reaction of calcium carbide with water is an example of how compounds can be transformed into different states of matter, showing the versatility of chemical reactions.
Acetylene is a gas that burns very hot and is used in the oxyacetylene torch, a tool for cutting and welding metals.
The simple act of CaC_2 irreacting with water to form acetylene is a wonderful example of chemistry in everyday action.

Exploring the Enthalpy of Reaction

The enthalpy of reaction ( ΔH ) is a concept that quantifies the heat change during a chemical reaction.
When CaC_2 reacts with water to produce Ca(OH)_2 and C_2H_2 , the enthalpy of the reaction ( ΔH^ ) is not just a number but a measure of energy transformation.
In simple terms, this value tells us how much energy is absorbed or released when the reaction occurs.
This helps in understanding whether a reaction is endothermic (absorbing energy) or exothermic (releasing energy).
The reaction between calcium carbide and water has a reported ΔH^ of -127.2 kJ, which means the reaction releases energy, making it exothermic.
This release helps in predicting and controlling the reaction conditions in practical situations.

Delving into Enthalpy Calculations

Enthalpy calculations are an essential part of understanding chemical reactions. These calculations help us determine how energy flows and changes within a system.
Using the equation: ΔH° = ∑n * ΔHf°(products) - ∑n * ΔHf°(reactants), we can calculate the enthalpy change of a reaction.
For the reaction of calcium carbide and water, inserting the known enthalpy of formation values allows us to calculate the unknown enthalpy of formation for CaC_2 .
By rearranging and solving the equation, we find that ΔHf°(CaC_2 ) is approximately 1204.7 kJ/mol.
The calculated value helps to understand the energy involved and confirms the exothermic nature of the reaction.
These calculations are crucial as they also help predict reaction feasibility and stability.