Question

Explain, using Le Châtelier's principle, why the equilibrium constant for the formation of NO from \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) increases with increasing temperature, whereas the equilibrium constant for the formation of \(\mathrm{NO}_{2}\) from NO and \(\mathrm{O}_{2}\) decreases with increasing temperature.

Short answer

In conclusion, based on Le Châtelier's principle, the equilibrium constant for the formation of NO from \( N_{2} \) and \( O_{2} \) increases with increasing temperature because the reaction is endothermic, so the system favors the products when the temperature increases. On the other hand, the equilibrium constant for the formation of \( NO_{2} \) from NO and \( O_{2} \) decreases with increasing temperature because the reaction is exothermic, so the system favors the reactants when the temperature increases.

Step-by-step solution

Le Châtelier's principle and temperature

Le Châtelier's principle states that if a system at equilibrium is subjected to a change in temperature, pressure, or concentration of a component, the system will adjust its position to counteract the change. In the case of temperature, if a reaction is exothermic (releases heat), an increase in temperature will shift the equilibrium to favor the reactants, thus decreasing the equilibrium constant K. If a reaction is endothermic (absorbs heat), an increase in temperature will shift the equilibrium to favor the products, thus increasing the equilibrium constant K.

Reaction 1: Formation of NO from N2 and O2

The reaction for the formation of NO can be written as: \( N_{2}(g) + O_{2}(g) \rightleftharpoons 2NO(g) \) This reaction is endothermic, meaning it absorbs heat. Therefore, when the temperature is increased, the equilibrium will shift to favor the products (NO).

Effect of temperature on Reaction 1

As the reaction is endothermic, an increase in temperature will favor the formation of more NO molecules. This means that the equilibrium constant K for this reaction will increase as the temperature increases.

Reaction 2: Formation of NO2 from NO and O2

The reaction for the formation of NO2 can be written as: \( 2NO(g) + O_{2}(g) \rightleftharpoons 2NO_{2}(g) \) This reaction is exothermic, meaning it releases heat. Therefore, when the temperature is increased, the equilibrium will shift to favor the reactants (NO and O2).

Effect of temperature on Reaction 2

As the reaction is exothermic, an increase in temperature will favor the consumption of NO2 molecules and increase the formation of NO and O2. This means that the equilibrium constant K for this reaction will decrease as the temperature increases. In conclusion, using Le Châtelier's principle, we can explain that the equilibrium constant for the formation of NO from N2 and O2 increases with increasing temperature since it is an endothermic reaction, whereas the equilibrium constant for the formation of NO2 from NO and O2 decreases with increasing temperature since it is an exothermic reaction.

Key concepts

Equilibrium Constant

The equilibrium constant, known as \( K \), quantifies the ratio of the concentrations of products to reactants at equilibrium for a particular reaction. It reflects the state of balance between the forward and reverse reactions. When discussing chemical reactions, knowing the value of \( K \) is crucial because:

• A large \( K \) (>1) indicates a reaction that heavily favors the formation of products.
• A small \( K \) (<1) indicates a reaction that favors reactants.

Changes in temperature can affect the equilibrium constant, especially when considering endothermic or exothermic reactions, which we'll discuss next. Understanding \( K \) provides insights into how reactions shift under different conditions.

Endothermic Reactions

Endothermic reactions are those that absorb energy, usually in the form of heat, from their surroundings. A common way to identify these reactions is:

• They often feel cold to the touch as heat is absorbed from the environment.
• The products have higher energy than the reactants.

Increasing the temperature in an endothermic reaction can shift the equilibrium towards the formation of products. This happens because the system attempts to counteract the increase in temperature by absorbing more heat. Consequently, the equilibrium constant \( K \) typically increases for an endothermic reaction as the temperature rises.

Exothermic Reactions

Exothermic reactions release energy to their surroundings, usually as heat. They can be recognized by:

• Reactions feeling hot as heat is being released.
• The products having lower energy than the reactants.

In exothermic reactions, an increase in temperature tends to shift the equilibrium towards the reactants. This is because the system reduces the excess heat by favoring the reaction that releases less heat (the reverse reaction). As a result, the equilibrium constant \( K \) decreases with a rise in temperature for exothermic reactions.

Temperature Effect on Equilibrium

The effect of temperature on equilibrium is well explained by Le Châtelier's Principle. It states that a system at equilibrium will adjust to counteract the effects of changes imposed on it, such as temperature changes.
In an **endothermic reaction**, increasing the temperature leads to more products being formed since the reaction absorbs heat. Therefore, \( K \) increases.
In contrast, in an **exothermic reaction**, increasing the temperature causes the formation of more reactants, as the system tries to absorb the extra heat by favoring the formation of less-energetic reactants. This results in a decreased \( K \).
Understanding how temperature influences the equilibrium allows chemists to manipulate conditions to favor the production of desired substances, making it a crucial aspect of chemical reaction engineering.