Calculate Enthalpy Change (ΔH) For 2 NOCl(g) → N2(g) + O2(g) + Cl2(g)

Introduction

In the realm of chemical thermodynamics, understanding the enthalpy change (ΔH) of a reaction is crucial for determining whether a reaction is exothermic (releases heat) or endothermic (absorbs heat). The enthalpy change, also known as the heat of reaction, is the difference between the enthalpy of the products and the enthalpy of the reactants. This article delves into the calculation of ΔH for the given reaction:

$$2 NOCl(g) \rightarrow N_2(g) + O_2(g) + Cl_2(g)$$

using Hess's Law and provided thermochemical data. We will explore the underlying principles, step-by-step calculations, and the significance of ΔH in chemical reactions. By the end of this discussion, you will have a solid understanding of how to calculate enthalpy changes and interpret their implications.

Understanding Enthalpy Change (ΔH)

Enthalpy change (ΔH) is a thermodynamic property that measures the heat absorbed or released in a chemical reaction at constant pressure. It's a crucial concept in understanding the energy dynamics of chemical processes. A negative ΔH indicates an exothermic reaction, where heat is released into the surroundings, while a positive ΔH signifies an endothermic reaction, where heat is absorbed from the surroundings. Understanding enthalpy changes allows chemists to predict the feasibility and energy requirements of various chemical reactions.

The enthalpy change of a reaction depends on several factors, including the nature of the reactants and products, the physical states of the substances involved, and the temperature and pressure at which the reaction occurs. Standard enthalpy change (ΔH°) refers to the enthalpy change when a reaction is carried out under standard conditions, typically 298 K (25 °C) and 1 atm pressure. These standard values are essential for comparing the energy changes of different reactions and are often tabulated for various chemical processes.

Hess's Law: A Cornerstone for ΔH Calculations

At the heart of calculating enthalpy changes lies Hess's Law, a fundamental principle in thermochemistry. Hess's Law states that the enthalpy change for a reaction is independent of the pathway taken, meaning that the overall ΔH for a reaction is the sum of the enthalpy changes for the individual steps involved. This law is particularly useful when the enthalpy change for a reaction cannot be directly measured, but can be determined by breaking the reaction down into a series of steps with known ΔH values. Hess's Law is a direct consequence of enthalpy being a state function, meaning it depends only on the initial and final states, not the path taken.

Using Hess's Law, we can manipulate given thermochemical equations (reversing them, multiplying them by coefficients) and their corresponding ΔH values to construct the target reaction. When reversing a reaction, the sign of ΔH is changed, and when multiplying a reaction by a coefficient, the ΔH is multiplied by the same coefficient. By carefully arranging these equations, we can cancel out intermediate species and arrive at the overall reaction, with the total ΔH being the sum of the adjusted ΔH values of the individual steps.

Given Thermochemical Equations

To calculate the enthalpy change for the reaction, we are provided with the following thermochemical equations:

Equation 1:

$$\frac{1}{2} N_2(g) + \frac{1}{2} O_2(g) \rightarrow NO(g) \quad \Delta H_{1} = +90.3 \text{ kJ}$$

Equation 2:

$$NO(g) + \frac{1}{2} Cl_2(g) \rightarrow NOCl(g) \quad \Delta H_{2} = +38 \text{ kJ}$$

These equations provide the enthalpy changes for the formation of nitrogen monoxide (NO) and nitrosyl chloride (NOCl) from their respective elements. Our goal is to manipulate these equations, using Hess's Law, to derive the target reaction and calculate its enthalpy change.

Target Reaction

The target reaction for which we want to calculate the enthalpy change is:

$$2 NOCl(g) \rightarrow N_2(g) + O_2(g) + Cl_2(g)$$

This reaction represents the decomposition of two moles of nitrosyl chloride (NOCl) into one mole each of nitrogen gas (N2), oxygen gas (O2), and chlorine gas (Cl2). By strategically using the given thermochemical equations, we can determine the enthalpy change for this reaction.

Step-by-Step Calculation of ΔHrxn

To calculate the enthalpy change for the target reaction, we need to manipulate the given equations to match the reactants and products in the desired stoichiometry. This involves reversing equations and multiplying them by appropriate coefficients.

Step 1: Reverse Equation 2

The target reaction involves the decomposition of NOCl, so we need to reverse Equation 2 to have NOCl as a reactant:

$$-1 \times [NO(g) + \frac{1}{2} Cl_2(g) \rightarrow NOCl(g)] \quad \Delta H_{2} = +38 \text{ kJ}$$

Reversed Equation 2:

$$NOCl(g) \rightarrow NO(g) + \frac{1}{2} Cl_2(g) \quad \Delta H'_{2} = -38 \text{ kJ}$$

When we reverse the reaction, we also change the sign of the enthalpy change. So, the new enthalpy change (ΔH'2) is -38 kJ.

Step 2: Multiply Reversed Equation 2 by 2

Since the target reaction involves 2 moles of NOCl, we need to multiply the reversed Equation 2 by 2:

$$2 \times [NOCl(g) \rightarrow NO(g) + \frac{1}{2} Cl_2(g)] \quad \Delta H'_{2} = -38 \text{ kJ}$$

Multiplied Equation:

$$2 NOCl(g) \rightarrow 2 NO(g) + Cl_2(g) \quad \Delta H''_{2} = 2 \times (-38 \text{ kJ}) = -76 \text{ kJ}$$

Multiplying the equation by 2 also multiplies the enthalpy change by 2, giving us ΔH''2 = -76 kJ.

Step 3: Reverse and Multiply Equation 1 by 2

The target reaction requires N2 and O2 as products, so we need to reverse Equation 1 and multiply it by 2:

$$-2 \times [\frac{1}{2} N_2(g) + \frac{1}{2} O_2(g) \rightarrow NO(g)] \quad \Delta H_{1} = +90.3 \text{ kJ}$$

Modified Equation 1:

$$2 NO(g) \rightarrow N_2(g) + O_2(g) \quad \Delta H'_{1} = -2 \times (90.3 \text{ kJ}) = -180.6 \text{ kJ}$$

Reversing the equation changes the sign of ΔH1, and multiplying by 2 multiplies the enthalpy change by 2, resulting in ΔH'1 = -180.6 kJ.

Step 4: Add the Modified Equations

Now, we add the modified equations to obtain the target reaction:

$$2 NOCl(g) \rightarrow 2 NO(g) + Cl_2(g) \quad \Delta H''_{2} = -76 \text{ kJ}$$

$$2 NO(g) \rightarrow N_2(g) + O_2(g) \quad \Delta H'_{1} = -180.6 \text{ kJ}$$

Adding these equations gives us:

$$2 NOCl(g) \rightarrow N_2(g) + O_2(g) + Cl_2(g)$$

Step 5: Calculate the Overall ΔHrxn

Using Hess's Law, we sum the enthalpy changes of the modified equations:

$$\Delta H_{rxn} = \Delta H'_{1} + \Delta H''_{2} = -180.6 \text{ kJ} + (-76 \text{ kJ})$$

$$\Delta H_{rxn} = -256.6 \text{ kJ}$$

Therefore, the enthalpy change for the reaction is -256.6 kJ.

Final Answer

The enthalpy change (ΔHrxn) for the reaction

$$2 NOCl(g) \rightarrow N_2(g) + O_2(g) + Cl_2(g)$$

is -256.6 kJ. This negative value indicates that the reaction is exothermic, meaning it releases heat into the surroundings.

Significance of ΔHrxn

The enthalpy change (ΔHrxn) provides valuable insights into the energy characteristics of a chemical reaction. In this case, the negative ΔHrxn of -256.6 kJ signifies that the decomposition of nitrosyl chloride (NOCl) into nitrogen, oxygen, and chlorine gases is an exothermic process. This means that the reaction releases heat, making it energetically favorable. Exothermic reactions tend to occur spontaneously, especially at lower temperatures, because the system moves to a lower energy state.

Implications for Reaction Stability and Kinetics

Understanding the enthalpy change is crucial for predicting the stability of chemical compounds and the kinetics of reactions. For instance, if a reaction is highly exothermic, the products are more stable than the reactants, and the reaction is likely to proceed at a faster rate. Conversely, endothermic reactions, which require energy input, may not occur spontaneously unless sufficient energy is supplied. The magnitude of ΔHrxn also provides information about the amount of heat released or absorbed, which is vital in industrial processes for optimizing reaction conditions and ensuring safety.

Applications in Chemical Engineering

In chemical engineering, the enthalpy change is a key parameter in designing reactors and optimizing reaction processes. For exothermic reactions, heat management is critical to prevent overheating and potential hazards, while for endothermic reactions, an external heat source may be necessary to drive the reaction forward. The ΔHrxn is used in calculations for heat transfer, energy balance, and process control, ensuring efficient and safe operation of chemical plants. Furthermore, it helps in the selection of appropriate materials and equipment that can withstand the thermal conditions of the reaction.

Environmental Considerations

The enthalpy change also has environmental implications. Exothermic reactions can release significant amounts of heat, contributing to thermal pollution if not properly managed. Additionally, the products of a reaction may have environmental impacts, and understanding the energy involved helps in assessing the overall environmental footprint. For example, reactions that produce greenhouse gases and release heat can exacerbate global warming, highlighting the need for sustainable and energy-efficient chemical processes.

Conclusion

Calculating the enthalpy change (ΔHrxn) using Hess's Law is a fundamental skill in chemistry. By understanding the principles of thermochemistry and manipulating thermochemical equations, we can determine the heat absorbed or released in a chemical reaction. In the case of the reaction $2 NOCl(g) \rightarrow N_2(g) + O_2(g) + Cl_2(g)$, the enthalpy change is calculated to be -256.6 kJ, indicating an exothermic reaction. This knowledge is essential for predicting reaction feasibility, optimizing chemical processes, and understanding the broader implications of chemical reactions in various fields.

By mastering these concepts, students and professionals alike can gain a deeper appreciation for the energy dynamics of chemical reactions and their applications in real-world scenarios. Understanding enthalpy changes allows for better predictions, safer processes, and more sustainable chemical practices.