Question

Formation of ammonia is shown by the reaction, \(\mathrm{N}_{2(g)}+3 \mathrm{H}_{2(g)} \rightarrow 2 \mathrm{NH}_{3(g)} ; \Delta_{r} H^{\circ}=-91.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) What will be the enthalpy of reaction for the decomposition of \(\mathrm{NH}_{3}\) according to the reaction? \(2 \mathrm{NH}_{3(g)} \rightarrow \mathrm{N}_{2(g)}+3 \mathrm{H}_{2(g)} ; \Delta_{r} H^{\circ}=?\) (a) \(-91.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (b) \(+91.8 \mathrm{k} J \mathrm{~mol}^{-1}\) (c) \(-45.9 \mathrm{~kJ} \mathrm{~mol}^{-1}\) (d) \(+45.9 \mathrm{~kJ} \mathrm{~mol}^{-1}\)

Short answer

+91.8 kJ mol^{-1}

Step-by-step solution

Identify the Original Reaction and Its Enthalpy of Formation

The original reaction for the formation of ammonia is given as \[\mathrm{N}_{2(g)}+3\mathrm{H}_{2(g)} \rightarrow 2\mathrm{NH}_{3(g)} ; \Delta_{r}H^{\circ}=-91.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\].This reaction is the reverse of the decomposition reaction we need to find the enthalpy for, and it has an enthalpy change of -91.8 kJ/mol.

Understand the Relationship Between Forward and Reverse Reactions

The enthalpy change for a reverse reaction is equal in magnitude but opposite in sign to the enthalpy change of the forward reaction. Knowing this, we can determine the enthalpy change for the decomposition of ammonia.

Calculate the Enthalpy of the Decomposition Reaction

Using the relationship between the forward and reverse reaction enthalpies, the enthalpy of reaction for the decomposition of ammonia is the negative of the enthalpy of formation:\[\Delta_{r}H^{\circ} = -(-91.8 \mathrm{~kJ} \mathrm{~mol}^{-1}) = +91.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\].

Key concepts

Chemical Thermodynamics

At its core, chemical thermodynamics addresses the link between energy and chemical reactions. It allows us to quantify the energy changes that accompany chemical processes, which is essential for understanding how substances interact with their environment, whether it's within a laboratory flask or the vast ecosystem of our planet.

One of the main principles of this field is the concept of enthalpy, denoted by the symbol 'H'. Enthalpy is the measure of total energy of a thermodynamic system, including both internal energy and the energy required to displace its environment. When we talk about the 'enthalpy of reaction', we're referring to the change in enthalpy that occurs as reactants are converted to products during a chemical reaction. This is symbolized by ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline

Forward and Reverse Reactions

To grasp how reactions unfold, it's helpful to understand the dynamics between forward and reverse reactions. A forward reaction is the process where reactants form products, as outlined by the chemical equation. The reverse reaction, on the other hand, takes the products back into reactants.

In any reversible reaction, the forward and reverse processes can reach a state of dynamic equilibrium, where the rates of both reactions are equal, resulting in no net change in concentration of reactants and products.

Now, every reaction has an associated enthalpy change. If the reaction is exothermic in the forward direction, releasing heat into the surroundings (indicated by a negative ewline ewline value), the reverse reaction will be endothermic, absorbing the same amount of heat (positive ewline ewline value). Therefore, the enthalpy of reaction for the reverse process will always have an equal magnitude but opposite sign to that of the forward process.

Enthalpy Change

The enthalpy change, denoted by the symbol ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline (ΔH), is a vital concept in energy and its transfer during chemical reactions. It is defined as the heat released or absorbed at constant pressure because most chemical reactions occur at atmospheric pressure.

Understanding the direction of enthalpy change is crucial. An exothermic reaction, such as the formation of ammonia from nitrogen and hydrogen, releases heat, thereby exhibiting a negative ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline (ΔH value). Conversely, an endothermic reaction requires heat from its surroundings, resulting in a positive ewline ewline ewline ewline ewline ewline ewline ewline ewline ewline (ΔH value).

Each reaction is associated with a standard enthalpy change ewline ewline , given circumstances such as standard state conditions, which include a pressure of 1 bar. This standardized value lets us predict and understand thermal behavior across a range of reactions. The key takeaway from the ammonia decomposition exercise is that enthalpy is a transferable quantity across reverse reactions and can be used to predict the energy change of a reaction proceeding in the opposite direction. For example, if the enthalpy change for the formation of ammonia is ewline ewline , the decomposition of ammonia will have an enthalpy of reaction of ewline ewline , simply flipping the sign to indicate an absorption of energy.