Question

How do the following changes affect the value of the equilibrium constant for a gas-phase exothermic reaction: (a) removal of a reactant or product, (b) decrease in the volume, (c) decrease in the temperature, (d) addition of a catalyst?

Short answer

In summary, for a gas-phase exothermic reaction: (a) removal of a reactant or product does not affect the value of the equilibrium constant, as it only depends on the reaction and temperature; (b) a decrease in volume does not directly impact the value of the equilibrium constant, as it is not affected by pressure changes; (c) a decrease in temperature causes the equilibrium constant to increase, as it directly affects the reaction rate; and (d) the addition of a catalyst does not affect the value of the equilibrium constant, but allows the reaction to reach equilibrium faster.

Step-by-step solution

(a) Removal of a reactant or product

The concept of Le Chatelier's principle states that if a system at equilibrium is subjected to a change in concentration, pressure (or volume), or temperature, the system will adjust itself to counteract the effect of the change and a new equilibrium will be established. If a reactant is removed, the equilibrium will shift to the left (toward the reactants) to compensate for the loss of the reactant. If a product is removed, the equilibrium will shift to the right (toward the products) to compensate for the loss of the product. It's important to note that these changes do not change the value of the equilibrium constant. The equilibrium constant only depends on the reaction and temperature, not the concentrations of the reactants and products. Therefore, removing a reactant or product does not affect the value of the equilibrium constant.

(b) Decrease in volume

A decrease in volume corresponds to an increase in pressure. According to Le Chatelier's principle, when pressure increases, the equilibrium will shift in the direction that results in a decrease in pressure. This means that the reaction will shift towards the side with fewer moles of gas. For an exothermic reaction, the volume change might cause a shift in equilibrium, but it does not impact the value of the equilibrium constant directly since it is not affected by pressure changes.

(c) Decrease in temperature

For a gas-phase exothermic reaction, a decrease in temperature will cause the equilibrium to shift to the side that produces heat (the exothermic direction). This will favor the forward reaction, and thus, the equilibrium constant will increase. Since the change in temperature affects the rate of the reaction, it directly impacts the value of the equilibrium constant.

(d) Addition of a catalyst

Catalysts have the ability to decrease the activation energy of a reaction, which consequently increases the rate of both forward and reverse reactions equally. However, catalysts do not change the relative concentrations of reactants and products at equilibrium. As a result, the addition of a catalyst does not affect the value of the equilibrium constant, but helps the reaction reach equilibrium faster.

Key concepts

Le Chatelier's Principle

When you are dealing with chemical reactions that have reached a state of balance, one of the most powerful tools to predict how the system will respond to changes is Le Chatelier's principle. Basically, it says that if an equilibrium system is disturbed, it will adjust in a way that counteracts the disturbance and a new equilibrium is established. It's like the system is trying to maintain its composure when external conditions shift.

Picture a seesaw perfectly balanced with kids on each end. If you suddenly add more weight to one side, the seesaw will tip, right? Similarly, if you increase the concentration of a reactant in our chemical system, the equilibrium shifts to make more product to balance things out. The same thing happens with changes in volume or pressure – the system just wants to stay balanced. But remember, Le Chatelier's principle is like the rulebook for the game, it doesn't change the seesaw itself—in chemical terms, the equilibrium constant stays the same unless you change the temperature.

Exothermic Reaction

An exothermic reaction is one where heat feels like a side product; it's released into the surroundings like a warm hug. Think of it like burning wood in a fireplace. The wood transforms into ash and smoke, but it also gives off heat that warms the room. In chemical language, these reactions release energy when bonds form in the products, and they can be spotted in equations by a negative heat sign.

Now, if you chill this kind of reaction by decreasing the temperature, Le Chatelier's principle tells us the equilibrium wants to bring the heat back up. So, it favors the direction that produces more heat, which is forward here, creating more products and reflecting an increase in the equilibrium constant. It's all interconnected – temperature shifts can modify the equilibrium constant in exothermic reactions, but messing with concentrations or pressure doesn't fiddle with this constant value.

Gas-phase Reaction

Picture a gas-phase reaction as a dance between particles that fly freely in a container, bumping and jiving with each other. These particles are the reactants and products in a state of gas. Now, if we cramp their style by decreasing their dance floor, which is effectively decreasing the volume of their container, we're basically increasing the pressure.

The dancers react! According to our trusty Le Chatelier's principle, they want to alleviate this newfound crowding by shifting to the side of the reaction with fewer participants—in this case, fewer gas molecules. However, while this shift may change the distribution of dancers (reactants and products), it's not changing the overall music they dance to (the equilibrium constant remains the same). That's a constant provided by the nature of the reaction itself and remains untouched unless we turn up or down the temperature.

Catalysts in Equilibrium

Now, let's talk about the life of the party: catalysts. They're like that one person who gets everyone dancing faster but doesn't change the number of folks on the dance floor – they just make it easier for people to start dancing with each other. In chemical terms, catalysts speed up both the forward and reverse reactions equally without favoring either side. Therefore, they get us to the equilibrium state quicker but don't change the actual position of equilibrium.

The equilibrium constant, which tells us the ratio of product to reactant concentrations when everything is balanced, remains unchanged with a catalyst. What's fascinating is that catalysts can totally transform how fast a chemical manufacturer can produce products, but they never alter the recipe – the final balance of ingredients in our chemical reaction remains constant.