Calculate Reaction Enthalpy For 2 NaOH(s) + CaCl2(s) Reaction

Introduction

In chemistry, understanding the heat changes associated with chemical reactions is crucial. Reaction enthalpy, a fundamental concept in thermochemistry, quantifies the heat absorbed or released during a chemical reaction at constant pressure. Determining the reaction enthalpy is essential for predicting reaction spontaneity, optimizing reaction conditions, and designing efficient chemical processes. One powerful method for calculating reaction enthalpy involves utilizing standard formation enthalpies, readily available in thermochemical tables. This article delves into the process of calculating reaction enthalpy using standard formation enthalpies, specifically focusing on the reaction between solid sodium hydroxide ($NaOH$) and solid calcium chloride ($CaCl_2$) to form solid calcium hydroxide ($Ca(OH)_2$) and solid sodium chloride ($NaCl$). We will explore the underlying principles, the step-by-step calculation, and the significance of the result in understanding the reaction's energy profile.

Understanding Standard Formation Enthalpies

To effectively calculate reaction enthalpy, it's vital to grasp the concept of standard formation enthalpy. Standard formation enthalpy, denoted as ΔHf°, is the change in enthalpy when one mole of a compound is formed from its constituent elements in their standard states under standard conditions (298 K and 1 atm pressure). The standard state of an element is its most stable form under standard conditions (e.g., oxygen as O2(g), carbon as graphite). Standard formation enthalpies are typically tabulated for a wide range of compounds, providing a valuable resource for thermochemical calculations. These values are always given in kJ/mol, indicating the enthalpy change per mole of the compound formed.

Using these standard formation enthalpies, we can calculate the enthalpy change for any reaction using Hess's Law. Hess's Law states that the enthalpy change for a reaction is independent of the pathway taken, meaning the overall enthalpy change is the sum of the enthalpy changes for each step in the reaction. This allows us to calculate the reaction enthalpy (ΔHrxn°) using the following equation:

ΔHrxn° = ΣnΔHf°(products) - ΣnΔHf°(reactants)

Where:

• ΔHrxn° is the standard reaction enthalpy.
• Σ represents the summation.
• n is the stoichiometric coefficient of each species in the balanced chemical equation.
• ΔHf°(products) is the standard formation enthalpy of each product.
• ΔHf°(reactants) is the standard formation enthalpy of each reactant.

This equation is a cornerstone in thermochemistry, enabling the calculation of enthalpy changes for complex reactions using readily available standard formation enthalpy data. The key is to have a balanced chemical equation and the standard formation enthalpies for all reactants and products involved. This method simplifies the process of determining whether a reaction is exothermic (releases heat, ΔHrxn° < 0) or endothermic (absorbs heat, ΔHrxn° > 0), which is crucial for understanding and predicting chemical behavior.

The Reaction: 2 NaOH(s) + CaCl₂(s) → Ca(OH)₂(s) + 2 NaCl(s)

The reaction we will analyze is the reaction between solid sodium hydroxide ($NaOH$) and solid calcium chloride ($CaCl_2$) to form solid calcium hydroxide ($Ca(OH)_2$) and solid sodium chloride ($NaCl$). The balanced chemical equation for this reaction is:

$2 NaOH(s) + CaCl_2(s) ightarrow Ca(OH)_2(s) + 2 NaCl(s)$

This equation tells us that two moles of solid sodium hydroxide react with one mole of solid calcium chloride to produce one mole of solid calcium hydroxide and two moles of solid sodium chloride. Each of these compounds has a specific standard formation enthalpy, which we will use to calculate the overall reaction enthalpy. The physical states of the reactants and products (in this case, all solids) are crucial for accurate calculations, as the enthalpy of formation can vary depending on the state.

Before proceeding with the calculation, we need to obtain the standard formation enthalpy values (ΔHf°) for each compound involved. These values are typically found in thermochemical tables within chemistry textbooks, online databases, or resources like the ALEKS Data tab mentioned in the original prompt. It's important to use reliable sources for these values, as discrepancies can lead to inaccurate results. Let's assume we have consulted a reliable source and obtained the following standard formation enthalpies (in kJ/mol):

• ΔHf° [NaOH(s)] = -425.6 kJ/mol
• ΔHf° [CaCl₂(s)] = -795.8 kJ/mol
• ΔHf° [Ca(OH)₂(s)] = -986.1 kJ/mol
• ΔHf° [NaCl(s)] = -411.1 kJ/mol

These values represent the enthalpy change when one mole of each compound is formed from its elements in their standard states. For example, the standard formation enthalpy of NaOH(s) (-425.6 kJ/mol) signifies the heat released when one mole of solid sodium hydroxide is formed from solid sodium, gaseous hydrogen, and gaseous oxygen under standard conditions. With these values in hand, we can now proceed to calculate the reaction enthalpy using Hess's Law.

Calculating the Reaction Enthalpy (ΔHrxn°)

Now that we have the balanced chemical equation and the standard formation enthalpies for each reactant and product, we can apply Hess's Law to calculate the standard reaction enthalpy (ΔHrxn°). The equation we will use is:

ΔHrxn° = ΣnΔHf°(products) - ΣnΔHf°(reactants)

Where 'n' represents the stoichiometric coefficient for each species in the balanced equation.

Let's break down the calculation step-by-step:

1. Identify the products and their stoichiometric coefficients:
   • Ca(OH)₂(s): coefficient = 1
   • NaCl(s): coefficient = 2
2. Identify the reactants and their stoichiometric coefficients:
   • NaOH(s): coefficient = 2
   • CaCl₂(s): coefficient = 1
3. Multiply the standard formation enthalpy of each species by its stoichiometric coefficient:
   • For Ca(OH)₂(s): 1 mol * (-986.1 kJ/mol) = -986.1 kJ
   • For NaCl(s): 2 mol * (-411.1 kJ/mol) = -822.2 kJ
   • For NaOH(s): 2 mol * (-425.6 kJ/mol) = -851.2 kJ
   • For CaCl₂(s): 1 mol * (-795.8 kJ/mol) = -795.8 kJ
4. Sum the enthalpies of formation for the products:
   • ΣnΔHf°(products) = (-986.1 kJ) + (-822.2 kJ) = -1808.3 kJ
5. Sum the enthalpies of formation for the reactants:
   • ΣnΔHf°(reactants) = (-851.2 kJ) + (-795.8 kJ) = -1647.0 kJ
6. Apply Hess's Law equation:
   • ΔHrxn° = ΣnΔHf°(products) - ΣnΔHf°(reactants)
   • ΔHrxn° = (-1808.3 kJ) - (-1647.0 kJ)
   • ΔHrxn° = -1808.3 kJ + 1647.0 kJ
   • ΔHrxn° = -161.3 kJ

Therefore, the standard reaction enthalpy (ΔHrxn°) for the reaction between solid sodium hydroxide and solid calcium chloride is -161.3 kJ. This result is crucial in determining the energy profile of the reaction and understanding its spontaneity.

Interpretation of the Result

The calculated standard reaction enthalpy (ΔHrxn°) for the reaction is -161.3 kJ. The negative sign indicates that the reaction is exothermic, meaning it releases heat into the surroundings. This release of heat signifies that the products (calcium hydroxide and sodium chloride) have a lower enthalpy (or energy content) than the reactants (sodium hydroxide and calcium chloride). In other words, the formation of products is energetically favorable, leading to the release of energy in the form of heat.

The magnitude of the reaction enthalpy (-161.3 kJ) provides further insight into the amount of heat released per mole of reaction. This value represents the heat released when two moles of solid sodium hydroxide react with one mole of solid calcium chloride under standard conditions. A larger negative value indicates a greater amount of heat released, implying a more exothermic reaction. In practical terms, this means that the reaction is likely to generate significant heat, which could be important to consider in a laboratory or industrial setting.

The exothermic nature of this reaction suggests that it is thermodynamically favorable, meaning it has a tendency to proceed spontaneously under standard conditions. However, it's important to note that enthalpy is only one factor determining spontaneity. Entropy (a measure of disorder) also plays a crucial role, as described by Gibbs Free Energy equation (ΔG = ΔH - TΔS). While the negative enthalpy change favors spontaneity, the overall spontaneity of the reaction depends on the balance between enthalpy and entropy changes at a given temperature.

In summary, the negative reaction enthalpy calculated for this reaction signifies an exothermic process with a tendency to release heat and proceed spontaneously. Understanding the magnitude and sign of the reaction enthalpy is vital for predicting and controlling chemical reactions, making it a fundamental concept in thermochemistry and chemical engineering.

Conclusion

In conclusion, we have successfully calculated the standard reaction enthalpy (ΔHrxn°) for the reaction between solid sodium hydroxide and solid calcium chloride using standard formation enthalpies and Hess's Law. By carefully applying the equation ΔHrxn° = ΣnΔHf°(products) - ΣnΔHf°(reactants), we determined that the reaction releases -161.3 kJ of heat under standard conditions. This negative value signifies an exothermic reaction, indicating that the formation of products is energetically favorable and the reaction has a tendency to proceed spontaneously.

This calculation exemplifies the power and utility of standard formation enthalpies in predicting and understanding the heat changes associated with chemical reactions. By knowing the standard formation enthalpies of reactants and products, chemists and engineers can readily calculate the reaction enthalpy for a wide range of reactions. This information is crucial for various applications, including:

• Predicting reaction spontaneity: A negative ΔHrxn° suggests a thermodynamically favorable reaction.
• Optimizing reaction conditions: Understanding heat changes helps in designing reactors and controlling reaction temperatures.
• Designing new chemical processes: Reaction enthalpy is a key factor in assessing the feasibility and efficiency of chemical processes.
• Safety considerations: Knowing the heat released or absorbed by a reaction is essential for safe handling of chemicals.

Furthermore, this exercise highlights the importance of fundamental thermochemical concepts in chemistry. Standard formation enthalpies and Hess's Law provide a robust framework for analyzing chemical reactions from an energy perspective. By mastering these concepts, students and professionals can gain a deeper understanding of chemical behavior and apply it to various fields.

In summary, the ability to calculate reaction enthalpies using standard formation enthalpies is a valuable skill in chemistry. This calculation not only provides insight into the energy profile of a reaction but also serves as a cornerstone for more advanced thermochemical analyses and applications. By understanding and utilizing these principles, we can better predict, control, and harness the power of chemical reactions for a variety of purposes.