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 \(\mathrm{CaC}_{2}(s)\) : $$ \begin{array}{r} \mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(s)+\mathrm{C}_{2} \mathrm{H}_{2}(g) \\ \Delta H^{\circ}=-127.2 \mathrm{~kJ} \end{array} $$

Short answer

Using the given reaction and enthalpy change, and applying Hess's Law and the enthalpy of formation data from Appendix C, we can calculate the enthalpy of formation for Calcium carbide as follows: $$ -127.2 \text{ kJ} = [ \Delta H_{f}^{\circ} (\mathrm{Ca}(\mathrm{OH})_2(s)) + \Delta H_{f}^{\circ} (\mathrm{C}_2 \mathrm{H}_2(g))] - [\Delta H_{f}^{\circ} (\mathrm{CaC}_2(s)) + 2 \cdot \Delta H_{f}^{\circ} (\mathrm{H}_2 \mathrm{O}(l))] $$ Rearrange the equation to solve for \(\Delta H_{f}^{\circ} (\mathrm{CaC}_2(s)\)) and perform the necessary calculations to obtain the value.

Step-by-step solution

(Write down the reaction and enthalpy change)

To solve this problem, we need to consider the given reaction: $$ \mathrm{CaC}_2(s) + 2 \mathrm{H}_2 \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_2(s) + \mathrm{C}_2 \mathrm{H}_2(g) $$ And its enthalpy change (\(\Delta H^{\circ}\)): $$ \Delta H^{\circ} = -127.2 \text{ kJ} $$ #Step 2: Locate Enthalpy of Formation Data for the Other Species#

(Locate enthalpy of formation data)

Look up the standard enthalpy of formation data in Appendix C for each species involved in the reaction. We need values for the following species: H\(_2\)O(l), Ca(OH)\(_2\)(s), and C\(_2\)H\(_2\)(g). #Step 3: Apply Hess's Law#

(Use Hess's Law)

Hess's Law states that the enthalpy change for a chemical reaction is equal to the sum of the standard enthalpy of formation of the products minus the sum of the standard enthalpy of formation of the reactants. In mathematical terms, $$ \Delta H^{\circ} = \sum \Delta H_{f}^{\circ} \text{(products)} - \sum \Delta H_{f}^{\circ} \text{(reactants)} $$ #Step 4: Substitute the Known Values into the Equation#

(Substitute values into the equation)

Substitute the given enthalpy change (\(\Delta H^{\circ} = -127.2\text{ kJ}\)) and the enthalpy of formation values for the other species from Appendix C into the equation from Step 3, $$ -127.2 \text{ kJ} = [ \Delta H_{f}^{\circ} (\mathrm{Ca}(\mathrm{OH})_2(s)) + \Delta H_{f}^{\circ} (\mathrm{C}_2 \mathrm{H}_2(g))] - [\Delta H_{f}^{\circ} (\mathrm{CaC}_2(s)) + 2 \cdot \Delta H_{f}^{\circ} (\mathrm{H}_2 \mathrm{O}(l))] $$ #Step 5: Solve for the Unknown Enthalpy of Formation#

(Solve for the unknown enthalpy of formation)

Rearrange the equation from Step 4 to solve for the unknown enthalpy of formation (\(\Delta H_{f}^{\circ} (\mathrm{CaC}_2(s)\)), and perform the necessary calculations. This will give you the \(\Delta H_{f}^{\circ}\) for \(\mathrm{CaC}_2(s)\).

Key concepts

Hess's Law

Understanding Hess's Law is pivotal in thermochemistry, as it offers a practical way to calculate the enthalpy change of a reaction when direct measurement is challenging. The law is based on the principle that the total enthalpy change during a chemical reaction is the same regardless of the number of steps in the reaction. In essence, if a process can be written as the sum of several steps, the enthalpy change for the overall process is the sum of the enthalpy changes for each individual step.

When solving thermochemistry problems such as calculating the enthalpy of formation, Hess's Law allows us to use known enthalpies of formation for some substances to deduce unknown ones. It is a pathway-independent function, meaning that only the initial and final states are considered. To apply Hess's Law proficiently, one must remember to correctly balance chemical equations and ensure units are consistent throughout the calculation.

For instructional purposes, it is crucial to stress the importance of the stoichiometry involved in the equations. Using Hess's Law is not merely an act of calculation but also an exercise in understanding how reactions can be interconnected. By systematically applying Hess's Law, students can gain insight into reaction mechanisms and the related energetic changes.

Thermochemistry Calculations

Thermochemistry calculations involve quantifying the heat and energy changes that occur during chemical reactions. These calculations are indispensable in predicting the direction and extent of chemical processes. The standard enthalpy change, \( \Delta H^\circ \), is one of the key components in these calculations, representing the heat change at standard conditions (1 atm pressure and the specified temperature, usually 25°C or 298 K).

Standard enthalpies of formation, \( \Delta H_{f}^\circ \), are central to thermochemistry calculations. They represent the enthalpy change when one mole of a compound is formed from its elements in their standard states. By convention, the standard enthalpy of formation for a pure element in its stable form is zero. When solving for an unknown \( \Delta H_{f}^\circ \), thermochemistry calculations involve algebraically combining these standard enthalpies to match the process being studied.

Mathematics aside, conceptual understanding is key. It might help students to think of thermochemistry like solving a puzzle: each piece of data fits together to build the bigger picture of what's happening energetically in a reaction. Emphasizing this analogy can help demystify the process and encourage deeper understanding rather than rote memorization of steps and numbers.

Standard Enthalpy Change

The concept of standard enthalpy change, denoted as \( \Delta H^\circ \), is essential in studying chemical reactions and their energy dynamics. At its core, it is the heat change associated with a chemical reaction under standard conditions. Standard enthalpy changes can be either endothermic, absorbing heat from the surroundings (\( \Delta H^\circ > 0 \)), or exothermic, releasing heat to the surroundings (\( \Delta H^\circ < 0 \)).

When discussing standard enthalpy change, it is crucial to understand that it is directly tied to the quantity of a substance. Typically, \( \Delta H^\circ \) is expressed per mole, providing a standardized way of comparing the energetics of different reactions. A key takeaway for students is that standard enthalpy change is not an absolute value; instead, it is relative to the defined standard states of the reactants and products.

In educational contexts, using clear and relatable examples can facilitate students' grasp of the concept. An effective approach might be to contrast everyday energy exchanges, like the warmth from a burning candle (exothermic) or the absorption of heat by melting ice (endothermic), with chemical reactions to illustrate endo- and exothermic processes in terms students can easily visualize.