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Enthalpy change is a key concept in chemistry, particularly in the study of reactions. It refers to the heat absorbed or released during a chemical reaction at constant pressure. This parameter is crucial when predicting the energy flow in a reaction. In the exercise, the reaction between nitrogen (\( \mathrm{N}_{2}(g) \)) and oxygen (\( \mathrm{O}_{2}(g) \)) to form nitrogen dioxide (\( \mathrm{NO}_{2}(g) \)) requires an input of energy because it is endothermic. The enthalpy change (\( \Delta H \)) is given as 67.7 kJ per mole of \( \mathrm{N}_{2} \).When calculating the heat input for the reaction, understanding that \( \Delta H \) is the energy required to convert reactants into products is essential. In endothermic reactions like this one, energy is absorbed, meaning the system gains energy from its surroundings. Calculating the total energy involves determining the moles of product formed from the limiting reactant in the reaction and multiplying by the \( \Delta H \).This gives a complete picture of the energy dynamics in the reaction, helping in predicting how much heat is required to achieve the desired product yield. Remember, knowing whether a reaction is endothermic or exothermic is crucial for understanding how it will interact with its environment.

The concept of a limiting reactant is vital for determining the maximum possible yield of a chemical reaction. Essentially, the limiting reactant is the substance that is completely used up first, stopping the reaction from continuing and thus determining how much product can be formed.In our scenario, nitrogen gas (\( \mathrm{N}_{2}\)) and oxygen gas (\( \mathrm{O}_{2}\)) are mixed together. To find the limiting reactant, you measure the initial amounts of each reactant, in moles. Then, based on the balanced reaction equation, you compare the mole ratios required. For this equation, the ratio is 1 mole of \( \mathrm{N}_{2}\)) to 2 moles of \( \mathrm{O}_{2}\)).

• If the quantity of \( \mathrm{N}_{2}\)) is less than half of \( \mathrm{O}_{2}\)), then \( \mathrm{N}_{2}\)) is the limiting reactant.
• Conversely, if the available amount of \( \mathrm{O}_{2}\)) is less than twice that of \( \mathrm{N}_{2}\)), \( \mathrm{O}_{2}\)) becomes limiting.

Determining the limiting reactant allows us to identify which reactant will dictate the total amount of product formed, in this case, \( \mathrm{NO}_{2}\)). Recognizing this helps in calculating the maximum potential yield and the necessary energy involved in the reaction.

Balancing chemical reactions is an essential skill in chemistry. It ensures that the law of conservation of mass is observed, where no atoms are lost or gained in a chemical reaction. In the given exercise, we begin with an unbalanced equation: \[ \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}_{2}(g) \]To balance it, each type of atom must have the same number on both sides of the equation. For example, nitrogen atoms should be balanced by adjusting the coefficients in the equation. Oxygen, which is present in two molecules on each side, should also be accounted for.The balanced equation becomes:\[ \mathrm{N}_{2}(g) + 2\mathrm{O}_{2}(g) \longrightarrow 2\mathrm{NO}_{2}(g) \]Here, one molecule of \( \mathrm{N}_{2} \) reacts with two molecules of \( \mathrm{O}_{2} \) to form two molecules of \( \mathrm{NO}_{2} \).Balancing involves a simple trial and error method or the use of algebraic techniques, and it’s crucial for understanding reaction stoichiometry. This process ensures that calculations about the reaction, including the amount of reactants used and the product formed, are accurate and reliable.