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 $\mathrm{C},$ calculate $\mathrm{\Delta }{H}_f^{\circ }$ for ${\mathrm{CaC}}_2(s):$ $$\begin{array}{rl}{\mathrm{CaC}}_2(s)+2{\mathrm{H}}_2\mathrm{O}(l)& ⟶\mathrm{Ca}(\mathrm{OH}{)}_2(s)+{\mathrm{C}}_2{\mathrm{H}}_2(g)\\ & \mathrm{\Delta }{H}^{\circ }=-127.2\mathrm{kJ}\end{array}$$

Short answer

The standard enthalpy of formation for calcium carbide (CaC2) is approximately -1203 kJ/mol.

Step-by-step solution

Write down the enthalpy change for the reaction

We are given the enthalpy change of the reaction as: $$\mathrm{\Delta }{H}^{\circ }=-127.2\mathrm{kJ}$$

Recall the formula for enthalpy change of a reaction

The enthalpy change of a reaction can be calculated using the following equation: $$\mathrm{\Delta }{H}^{\circ }=\sum \mathrm{\Delta }{H}_f^{\circ }(\text{products})-\sum \mathrm{\Delta }{H}_f^{\circ }(\text{reactants})$$

Write down the enthalpies of formation for the other substances

From Appendix C, we find the following standard enthalpies of formation: $$\begin{array}{rl}\mathrm{\Delta }{H}_f^{\circ }({\mathrm{H}}_2\mathrm{O}(l))& =-285.8\mathrm{kJ}/\mathrm{mol}\\ \mathrm{\Delta }{H}_f^{\circ }({\mathrm{C}}_2{\mathrm{H}}_2(g))& =226.7\mathrm{kJ}/\mathrm{mol}\\ \mathrm{\Delta }{H}_f^{\circ }(\mathrm{Ca}(\mathrm{OH}{)}_2(s))& =-986.1\mathrm{kJ}/\mathrm{mol}\end{array}$$ We are looking for the standard enthalpy of formation for CaC2(s), which we will denote as ΔHf°(CaC2(s)).

Substitute the values into the formula

Now, we can substitute the given values into the formula for enthalpy change of the reaction: $$\begin{array}{rl}-127.2\text{kJ}& =[\mathrm{\Delta }{H}_f^{\circ }(\mathrm{Ca}(\mathrm{OH}{)}_2(s))+\mathrm{\Delta }{H}_f^{\circ }({\mathrm{C}}_2{\mathrm{H}}_2(g))]-[\mathrm{\Delta }{H}_f^{\circ }({\mathrm{CaC}}_2(s))+2\mathrm{\Delta }{H}_f^{\circ }({\mathrm{H}}_2\mathrm{O}(l))]\\ -127.2\text{kJ}& =[-986.1+226.7-2(285.8)\mathrm{kJ}/\mathrm{mol}-\mathrm{\Delta }{H}_f^{\circ }({\mathrm{CaC}}_2(s))]\end{array}$$

Solve for ΔHf°(CaC2(s))

Now, we will solve for the standard enthalpy of formation for CaC2(s): $$\begin{array}{rl}\mathrm{\Delta }{H}_f^{\circ }({\mathrm{CaC}}_2(s))& =-986.1+226.7-2(285.8)+127.2\\ \mathrm{\Delta }{H}_f^{\circ }({\mathrm{CaC}}_2(s))& =-1203\mathrm{kJ}/\mathrm{mol}\end{array}$$ The standard enthalpy of formation for calcium carbide (CaC2) is approximately -1203 kJ/mol.

Key concepts

Calcium Carbide

Calcium carbide, chemically represented as ${\text{CaC}}_2$, is an important compound used in various industrial applications. It is a grayish-black solid and known for its ability to react with water to produce acetylene ${\text{C}}_2{\text{H}}_2$ which is a valuable gas in welding and chemical synthesis. This compound is prominent in industries such as metal cutting, lighting, and chemical manufacturing due to its efficient and explosive nature when reacting with water.

• Calcium carbide was first discovered in the late 19th century and quickly became essential.
• It is produced industrially by reacting lime and coke at high temperatures.
• The reaction with water involves the formation of byproducts such as calcium hydroxide ${\text{Ca(OH)}}_2$.

Understanding the properties and reactions of calcium carbide is crucial in the context of energy production and chemical manufacturing processes.

Enthalpy Change

Enthalpy change is a key concept in thermochemistry, which describes the amount of heat absorbed or released during a chemical reaction at constant pressure. It is typically expressed in kilojoules per mole (kJ/mol) and is denoted as $\mathrm{\Delta }H$. In many chemical reactions, knowing the enthalpy change helps in assessing the energy efficiency and feasibility of the process.

• Enthalpy change can be exothermic (heat releasing) or endothermic (heat absorbing). An example is the -127.2 kJ given for the reaction involving calcium carbide, indicating an exothermic reaction.
• It is crucial for calculating other thermodynamic properties like Gibbs free energy.
• Understanding enthalpy change aids in energy balance calculations in industrial processes.

Therefore, mastering enthalpy change calculations helps in predicting whether a reaction will occur spontaneously.

Chemical Reactions

Chemical reactions are processes where reactants are transformed into products. These reactions entail bonds breaking and forming, leading to a transformation in the chemical structure. The reaction of calcium carbide with water is an excellent example. When calcium carbide $({\text{CaC}}_2)$ reacts with water, it produces acetylene $({\text{C}}_2{\text{H}}_2)$ and calcium hydroxide $({\text{Ca(OH)}}_2)$.

• This particular reaction is widely used in the commercial production of acetylene gas, which is useful in welding.
• Chemical reactions can be classified based on how the substances interact, such as synthesis, decomposition, single-replacement, and double-replacement reactions.
• The energy changes associated with reactions, like enthalpy change, are fundamental to comprehending these processes on an energetic level.

By observing chemical reactions, scientists can learn about various substances' properties and how they change under different conditions.

Thermochemistry

Thermochemistry focuses on the study of the energy changes accompanying chemical reactions and physical transformations. It integrates principles of both chemistry and thermodynamics, offering insights into reaction energetics.

• Thermochemistry principles help in calculating important thermodynamic quantities such as enthalpy ($\mathrm{\Delta }H$), entropy ($\mathrm{\Delta }S$), and Gibbs free energy ($\mathrm{\Delta }G$).
• The study can predict the direction of chemical reactions and their energy needs.
• It is essential for designing energy-efficient chemical processes in varied industries, including petrochemicals, food, and pharmaceuticals.

Thermochemistry provides the tools to calculate the energy output of reactions like the reaction between calcium carbide and water, helping engineers and scientists create more sustainable and efficient industrial processes.