Question

Given the following data $$\mathrm{Ca}(s)+2 \mathrm{C}(\text { graphite }) \longrightarrow \mathrm{CaC}_{2}(s)$$ \(\Delta H=-62.8 \mathrm{kJ}\) $$ \mathrm{Ca}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CaO}(s) $$ \(\Delta H=-635.5 \mathrm{kJ}\) $$ \mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q) $$ \(\Delta H=-653.1 \mathrm{kJ}\) $$ \mathrm{C}_{2} \mathrm{H}_{2}(g)+\frac{5}{2} \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) $$ \(\Delta H=-1300 . \mathrm{kJ}\) $$ \mathrm{C}(\text {graphite})+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(\mathrm{g}) $$ \(\Delta H=-393.5 \mathrm{kJ}\) calculate \(\Delta H\) for the reaction $$ \mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{C}_{2} \mathrm{H}_{2}(g) $$

Short answer

The enthalpy change, ∆H, for the target reaction \(\mathrm{CaC}_{2}(s) + 2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{C}_{2} \mathrm{H}_{2}(g)\) is \(-1799.9\,\mathrm{kJ}\).

Step-by-step solution

Identify the target reaction

The target reaction is $$ \mathrm{CaC}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{C}_{2} \mathrm{H}_{2}(g) $$ Our goal is to find its enthalpy change, ∆H.

Manipulate the given reactions using Hess's Law

We need to manipulate the given reactions in such a way that they will sum up to the target reaction. The most straightforward way we can do that is to find a way for the given reactions to cancel out as many compounds as possible while resulting in the target reaction. Here's how we can manipulate them: 1. Reverse the first reaction and double the second and fifth reaction to obtain the correct coefficients for the target reaction: $$\mathrm{CaC}_{2(s)} \longrightarrow \mathrm{Ca(s)} + 2 \mathrm{C(graphite)}$$ \(\Delta H = 62.8\,\mathrm{kJ}\) (reversed) $$2(\mathrm{Ca}(s)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CaO}(s))$$ \(2 \Delta H = 2(-635.5)\,\mathrm{kJ}\) (multiplied by 2) $$2(\mathrm{C}(\text {graphite})+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(\mathrm(g)))$$ \(2 \Delta H = 2(-393.5)\,\mathrm{kJ}\) (multiplied by 2) 2. Add the third and fourth reaction as they are: $$\mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)$$ \(\Delta H = -653.1\,\mathrm{kJ}\) $$\mathrm{C}_{2} \mathrm{H}_{2}(g)+\frac{5}{2} \mathrm{O}_{2}(g) \longrightarrow 2\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)$$ \(\Delta H = -1300\,\mathrm{kJ}\)

Combine the manipulated reactions

Now, sum up the manipulated reactions. The intermediate compounds will cancel out, resulting in the target reaction: $$ \mathrm{CaC}_{2}(s) + 2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{C}_{2} \mathrm{H}_{2}(g) $$

Calculate the enthalpy change of the target reaction

Add the enthalpies change (∆H) of the manipulated reactions to find the ∆H of the target reaction: $$\Delta H_\text{target} = 62.8\,\mathrm{kJ} + 2(-635.5)\,\mathrm{kJ} + 2(-393.5)\,\mathrm{kJ} - 653.1\,\mathrm{kJ} - 1300\,\mathrm{kJ}$$ $$\Delta H_\text{target} = -1799.9\,\mathrm{kJ}$$ So the enthalpy change, ∆H, for the target reaction is -1799.9 kJ.

Key concepts

Enthalpy Change

Enthalpy change (\( \Delta H \)) is a fundamental concept in thermodynamics, especially when analyzing chemical reactions. It represents the heat absorbed or released during a chemical reaction at constant pressure. Whether a reaction absorbs or releases heat determines if it is endothermic or exothermic:

• Endothermic Reaction: Absorbs heat from the surroundings, resulting in a positive enthalpy change.
• Exothermic Reaction: Releases heat to the surroundings, resulting in a negative enthalpy change.

For the given problem, we are interested in finding the enthalpy change for a specific reaction. Using Hess's Law, we can determine the overall enthalpy change by manipulating and summing the enthalpy changes of a series of reactions. This allows us to indirectly calculate the energy change of a reaction that may be difficult to measure directly.

Always remember that the conservation of energy principle applies, meaning total energy remains constant. Therefore, even if individual reactions vary in their heat exchanges, their combined action results in the precise energy change needed for the target reaction.

Chemical Reactions

Chemical reactions involve the transformation of one or more substances into different substances. This transformation involves the breaking and forming of chemical bonds, and it is always accompanied by a flow of energy. When analyzing a chemical reaction:

• The reactants are the starting materials.
• The products are the substances formed as a result of the reaction.

The given exercise involves several reactions, each with its specific reactants and products. The target reaction formation requires a meticulous adjustment of individual reactions to achieve the desired end result using Hess's Law. Part of the skill in chemistry is recognizing how these reactions can be manipulated through reversing, multiplying, or adding to align with your goal.

Understanding these reactions in terms of their physical states and heat exchanges is pivotal in determining how energy flows and how the reactions interact with each other. In essence, mastering how to piece together given reactions to form a target reaction using Hess's Law is a critical skill for problem-solving in chemistry.

Calorimetry

Calorimetry is the science of measuring the amount of heat exchanged in chemical reactions or physical changes. It is a vital tool for understanding energy changes and determining the enthalpy change of reactions. During a calorimetric process:

• A sample undergoing the change is enclosed in a calorimeter.
• The heat absorbed or released by the reaction causes a temperature change in the surrounding medium.

The exercise here is essentially a theoretical application of the principles used in calorimetry to find the enthalpy change of a reaction. Although a calorimeter isn't physically involved, the mathematical manipulation of reactions functionally serves the same purpose.

Effective application of calorimetry requires consideration of several factors, including the specific heat of substances involved and the careful balancing of equation elements to ensure accuracy in calculated energy changes. Thus, even theoretical calorimetry exercises emphasize the importance of precision in calculating and interpreting energy changes in chemical processes.