Problem 59 - General Chemistry: Principles and Modern Applications

Question

The reaction \(\mathrm{N}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}), \quad \Delta H^{\circ}=\) \(+181 \mathrm{kJ},\) occurs in high-temperature combustion processes carried out in air. Oxides of nitrogen produced from the nitrogen and oxygen in air are intimately involved in the production of photochemical smog. What effect does increasing the temperature have on (a) the equilibrium production of \(\mathrm{NO}(\mathrm{g})\) (b) the rate of this reaction?

Step-by-Step Solution

Answer

(a) The equilibrium production of \(\mathrm{NO}(\mathrm{g})\) will increase. (b) The rate of reaction will also increase.

Step 1: Understanding Le Chatelier's Principle

Le Chatelier's Principle states that when a system at chemical equilibrium is disturbed by a change in temperature, pressure, or concentration of components, the system adjusts so as to reduce or counteract the effect of the change. This principle helps to predict how the position of equilibrium will shift.

Step 2: Effect of temperature on equilibrium position

The reaction given is an endothermic reaction because its heat (delta H) is positive. This means heat is absorbed in the formation of products, causing the reaction to be favored in the direction where heat is consumed, that is, towards the products side. When the temperature increases in a reaction vessel, it means more 'heat' has been added to the system. In order to counter this change, the reaction shifts in the direction where that 'heat' will be absorbed, which in an endothermic reaction is towards the right or the product's side. Thus, increasing the temperature increases the equilibrium production of \(\mathrm{NO}(\mathrm{g})\).

Step 3: Effect of temperature on reaction rate

The reaction rate generally increases with increase in temperature. In most cases, increasing the temperature increases the kinetic energy of the molecules, causing them to collide more frequently and with more energy which increases the probability of a successful reaction.

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is a key concept in understanding chemical equilibrium. When a system at equilibrium is exposed to a change, such as temperature, pressure, or concentration, it will adjust itself to counteract that change. Imagine balancing a seesaw – if you add weight to one side, the seesaw adjusts to maintain balance. Similarly, in chemical reactions, when you change conditions, the system shifts the position of equilibrium to reduce the effect of those changes.

In the context of the reaction \[\mathrm{N}_2(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g}),\] we can apply this principle. When temperature increases, the equilibrium will shift to absorb that added heat, as the system attempts to restore balance. This principle not only helps us understand the shift in equilibrium but is also crucial for predicting the behavior of reactions under different conditions.

Endothermic Reactions

Endothermic reactions absorb energy, specifically heat, from their surroundings during the reaction. In the given exercise, the reaction \[\Delta H^{\circ} = +181 \mathrm{kJ}\] is positive, which signifies it's endothermic. Unlike exothermic reactions, where energy is released, endothermic reactions need energy input to proceed.

When there's a rise in temperature in an endothermic reaction, the system receives additional energy. According to Le Chatelier's Principle, the system addresses this change by shifting equilibrium towards the side that consumes more heat – the products side. Thus, in our reaction, increasing temperature favors the formation of \(\mathrm{NO}(\mathrm{g})\), meaning more nitrogen monoxide is produced. Understanding whether a reaction is endothermic is crucial as it dictates how equilibrium shifts with temperature changes.

Reaction Rate

Reaction rate refers to how quickly reactants turn into products in a chemical reaction. Several factors affect this rate, one major being temperature. When the temperature is increased, the molecules involved in the reaction gain kinetic energy. This increase in energy causes molecules to move faster, leading to more collisions.

However, for a collision to lead to a reaction, it must occur with sufficient energy – known as the activation energy. As the temperature increases, not only do collisions become more frequent, but they are also more energetic. This results in a higher reaction rate because more collisions meet the necessary energy threshold.

• More collisions per unit time.
• Higher energy collisions, increasing the chance of overcoming activation energy.

For the \(\mathrm{N}_2(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})\) reaction, an increase in temperature not only shifts equilibrium but also accelerates the rate at which \(\mathrm{NO}\) is formed, speeding up the whole process.