Calculating Heat Of Reaction Using Hess's Law For 2 N2(g) + 5 O2(g) → 2 N2 O5(g)
In the realm of chemical thermodynamics, understanding the heat exchange in chemical reactions is paramount. This article delves into the application of Hess's Law to determine the enthalpy change (ΔH°) for a specific reaction using a set of given reactions and their respective enthalpy changes. We will walk through the process step-by-step, demonstrating how to manipulate and combine chemical equations to arrive at the desired reaction and its corresponding ΔH° value. This method is crucial for predicting the energy requirements or releases in chemical processes, making it a cornerstone of chemical engineering and research. Let's embark on this journey of unraveling the intricacies of thermochemistry and master the art of calculating reaction enthalpies.
Introduction to Hess's Law
Hess's Law is a fundamental principle in thermochemistry, stating that the enthalpy change (ΔH°) of a reaction is independent of the pathway taken from the initial reactants to the final products. In simpler terms, it means that whether a reaction occurs in one step or multiple steps, the total enthalpy change remains the same. This law is a direct consequence of the fact that enthalpy is a state function, meaning it only depends on the initial and final states of the system, not on the path taken to get there.
Understanding Hess's Law is crucial for calculating enthalpy changes for reactions that are difficult or impossible to measure directly. By using a series of known reactions, we can manipulate and combine their enthalpy changes to determine the ΔH° for the target reaction. This technique is particularly valuable in industrial chemistry, where predicting the energy requirements of a reaction can significantly impact process design and efficiency. For instance, calculating the heat released or absorbed in a reaction helps in designing reactors that can effectively manage the heat, ensuring safety and optimal yield. Moreover, Hess's Law is instrumental in determining the stability of chemical compounds and predicting the feasibility of reactions under different conditions. The application of Hess's Law extends beyond simple calculations; it provides a deeper understanding of the energetic landscape of chemical reactions, paving the way for innovation in chemical synthesis and material science.
Problem Statement
Our primary goal is to calculate the standard enthalpy change (ΔH°) at 298 K for the following reaction:
To achieve this, we are provided with a set of reactions and their corresponding ΔH° values. These reactions serve as building blocks, which we will manipulate and combine using Hess's Law to arrive at the target reaction. The given reactions are:
ightarrow 2 H_2O(g) ext{ } ΔH°_1 = -483.6 ext{ kJ}$ 2. $N_2 O_5(g) + H_2O(g) ightarrow 2 HNO_3(l) ext{ } ΔH°_2 = -76.6 ext{ kJ}$ 3. $1/2 N_2(g) + 3/2 O_2(g) + 1/2 H_2(g) ightarrow HNO_3(l) ext{ } ΔH°_3 = -174.1 ext{ kJ}$
These equations, along with their enthalpy changes, form the foundation of our calculation. By strategically reversing reactions, multiplying them by coefficients, and summing them, we can construct the target reaction. The key is to ensure that all intermediate species cancel out, leaving only the reactants and products of the desired reaction. Each manipulation of a reaction must be accompanied by a corresponding manipulation of its ΔH° value. For example, reversing a reaction changes the sign of ΔH°, and multiplying a reaction by a coefficient multiplies its ΔH° by the same coefficient. The careful application of these rules, guided by the principles of Hess's Law, will lead us to the final answer. This process not only demonstrates the power of Hess's Law but also highlights the importance of meticulous attention to detail in thermochemical calculations.
Step-by-Step Solution Using Hess's Law
Now, let's proceed with the step-by-step solution to determine the heat of reaction for the target equation using Hess's Law. We will manipulate the given equations to match the target equation and then sum their ΔH° values.
1. Manipulating Equation 3
The target reaction requires 2 moles of $N_2O_5(g)$ as a product. Equation 3 has $HNO_3(l)$ as a product. To obtain $N_2O_5(g)$, we need to reverse Equation 2 and multiply Equation 3 by 2. First, let's multiply Equation 3 by 2:
This gives us:
2. Reversing and Manipulating Equation 2
Next, we reverse Equation 2 to get $N_2O_5(g)$ as a product:
3. Multiplying the Reversed Equation 2 by 2
Since we need 2 moles of $N_2O_5(g)$, we multiply the reversed equation by 2:
Which leads to:
4. Manipulating Equation 1
Now, let's look at Equation 1. We need to eliminate $H_2O(g)$. Since Equation 1 has $H_2O(g)$ as a product, we keep it as is.
5. Combining the Equations
Now, let's sum the modified equations:
ightarrow 2 HNO_3(l)] ext{ } ΔH°{3a} = 2 imes (-174.1 ext{ kJ}) = -348.2 ext{ kJ}$ 2. $2 imes [2 HNO_3(l) ightarrow N_2 O_5(g) + H_2O(g)] ext{ } ΔH°{2a} = 2 imes (76.6 ext{ kJ}) = 153.2 ext{ kJ}$ 3. $2 H_2(g) + O_2(g) ightarrow 2 H_2O(g) ext{ } ΔH°_1 = -483.6 ext{ kJ}$
Adding these equations:
Simplifying, we get:
6. Calculating the Total ΔH°
Now, we sum the ΔH° values:
ΔH° = 2 × **ΔH°**3 + 2 × **ΔH°**2 + **ΔH°**1
ΔH° = 2 × (-174.1 kJ) + 2 × (76.6 kJ) + (-483.6 kJ) = -348.2 kJ + 153.2 kJ - 483.6 kJ = -678.6 kJ
Therefore, the heat of reaction at 298 K for the reaction is -678.6 kJ.
Final Answer
The heat of reaction (ΔH°) at 298 K for the reaction:
is -678.6 kJ. This negative value indicates that the reaction is exothermic, meaning it releases heat into the surroundings. The calculation demonstrates the power and utility of Hess's Law in determining enthalpy changes for reactions that may be difficult or impossible to measure directly. By carefully manipulating and combining known reactions, we can predict the energy changes associated with complex chemical processes. This understanding is vital in various fields, including industrial chemistry, environmental science, and materials science, where energy management and reaction feasibility are critical considerations.
Conclusion
In conclusion, we have successfully calculated the enthalpy change (ΔH°) for the reaction $2 N_2(g) + 5 O_2(g) ightarrow 2 N_2 O_5(g)$ using Hess's Law. By strategically manipulating the given reactions and their corresponding ΔH° values, we determined that the reaction is exothermic, with a ΔH° of -678.6 kJ. This process underscores the importance of Hess's Law as a fundamental tool in thermochemistry, allowing us to predict the heat released or absorbed in chemical reactions without direct experimentation.
The significance of understanding and applying Hess's Law extends far beyond textbook exercises. It is a practical skill that enables chemists and engineers to design and optimize chemical processes, ensuring energy efficiency and safety. For instance, in the development of new industrial processes, Hess's Law can be used to estimate the overall energy requirements, helping to select the most cost-effective and environmentally friendly reaction pathways. Similarly, in environmental chemistry, it can be applied to assess the energy changes associated with pollution formation and degradation, informing strategies for pollution control and remediation. The principles of Hess's Law also play a crucial role in materials science, where the stability and reactivity of materials are often determined by their enthalpy changes. The ability to predict these changes accurately can guide the design of new materials with desired properties, such as high thermal stability or specific reactivity. Furthermore, the application of Hess's Law contributes to a deeper understanding of chemical thermodynamics, fostering innovation and advancements in various scientific and technological fields. By mastering this law, scientists and engineers can unlock new possibilities in chemical synthesis, energy production, and materials design, ultimately leading to a more sustainable and efficient future.
