Question

There is only one value of the equilibrium constant for a particular system at a particular temperature, but there are an infinite number of equilibrium positions. Explain.

Short answer

In a chemical system, the equilibrium constant (K) defines the relationship between the concentrations of reactants and products for a specific reaction at a given temperature and remains constant for that particular system at that temperature. On the other hand, the equilibrium position refers to the specific concentration levels of reactants and products in an equilibrium mixture, which can vary for the same reaction depending on the initial concentrations. There is only one equilibrium constant for a particular system at a specific temperature because it reflects the balance between the forward and reverse reactions at that temperature. However, there are infinite equilibrium positions because various sets of reactant and product concentrations can satisfy the equilibrium constant for a particular system, representing different combinations of reactant and product concentrations.

Step-by-step solution

Define equilibrium constant and equilibrium position

The equilibrium constant (K) defines the relationship between the concentrations of reactants and products for a specific reaction at a given temperature. It is a characteristic of the reaction and remains constant for a particular system at a particular temperature. On the other hand, the equilibrium position refers to the specific concentration levels of reactants and products in an equilibrium mixture. It can vary for the same reaction depending on the initial concentrations of the reactants and products. #Step 2: Relation between equilibrium constant and equilibrium position#

Explain the relation between equilibrium constant and equilibrium position

The equilibrium constant (K) is the ratio of the concentrations of products to reactants in a reaction, raised to the power of their stoichiometric coefficients. For a reversible reaction of the form: \(a\)A + \(b\)B ↔ \(c\)C + \(d\)D The equilibrium constant (K) can be defined as: K = \(\frac{[C]^c \cdot [D]^d}{[A]^a \cdot [B]^b}\) In this equation, the brackets refer to the molar concentrations of the components at equilibrium, and 'a', 'b', 'c', and 'd' are their respective stoichiometric coefficients. When the system reaches equilibrium, this ratio remains constant. #Step 3: Explain why there is only one equilibrium constant for a particular system at a specific temperature#

One equilibrium constant per system at a given temperature

The equilibrium constant (K) depends on the temperature because it reflects the balance between the forward and reverse reactions. A particular system at a specific temperature has a certain characteristic balance between the forward and reverse reactions, this allows the system to maintain equilibrium. As the temperature changes, the balance between the rates of the forward and reverse reactions may shift, which in turn causes the equilibrium constant to change. However, at a particular temperature, there is only one equilibrium constant value for a particular system. #Step 4: Explain why there are infinite equilibrium positions#

Infinite equilibrium positions

For a given system and temperature, various sets of reactant and product concentrations might satisfy the equilibrium constant. This is because the equilibrium constant only defines the ratio of product concentrations raised to the powers of their stoichiometric coefficients, and reactant concentrations raised to the powers of their stoichiometric coefficients. Therefore, there are an infinite number of combinations of reactant and product concentrations that can satisfy the equilibrium constant for a particular system. These different combinations of reactant and product concentrations represent different equilibrium positions for the same system.

Key concepts

Equilibrium Position

In the context of chemical reactions, the term 'equilibrium position' refers to the specific concentrations of reactants and products that the system achieves when it reaches equilibrium. Importantly, while the equilibrium constant (K) is fixed for a given reaction at a particular temperature, the equilibrium position can vary. The equilibrium position is influenced by factors such as the initial concentrations of reactants and products.

• Different starting concentrations can lead to different equilibrium positions.
• Even though the allowed concentration ratios can vary, the equilibrium constant remains unchanged.

The flexibility of the equilibrium position allows a system to adapt to changes while maintaining the correct ratio of concentrations as defined by the equilibrium constant. Thus, for a single reaction, there could be countless equilibrium positions corresponding to different initial setups.

Chemical Equilibrium

Chemical equilibrium is the state of a reversible reaction where the rate of the forward reaction equals the rate of the reverse reaction. At this point, although the concentrations of reactants and products remain constant, they are not necessarily equal. The system reaches a balance where the ratio of product to reactant concentrations is consistent.

• Equilibrium does not imply that reactants and products are present in equal amounts.
• The dynamics continue at the molecular level, even though macroscopic changes cease to be observable.

It is important to understand that achieving equilibrium does not mean that the reaction has stopped, but rather that a dynamic balance has been established where reactants are continuously converted into products and vice versa without any net change.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. Each molecule participating in a reaction is part of this relationship, as defined by its stoichiometric coefficient in the balanced chemical equation. Stoichiometric coefficients are integral in determining the equilibrium constant expression.

• For example, in the reaction \(aA + bB \rightleftharpoons cC + dD\), the coefficients \(a\), \(b\), \(c\), and \(d\) tell us the ratio in which the molecules react.
• These coefficients dictate the exponents used in the equilibrium constant expression \(K = \frac{[C]^c [D]^d}{[A]^a [B]^b}\).

The precise understanding of stoichiometry is essential for predicting the quantities of products formed or reactants consumed, which is crucial for both lab calculations and industrial chemical processes.

Concentration Ratios

Concentration ratios in equilibrium scenarios are crucial for understanding how the equilibrium constant maintains its consistency. These ratios are calculated using the concentrations of reactants and products at equilibrium to fit the model set by the equilibrium constant equation. The equilibrium constant expression makes use of these ratios to ensure the balance of the reaction.

• Concentration ratios take into account the different powers to which the concentrations are raised, reflecting the stoichiometry of the reaction.
• A correct concentration ratio will satisfy the equilibrium condition \(K = \frac{[C]^c [D]^d}{[A]^a [B]^b}\).

By manipulating initial concentrations and observing the resulting equilibrium position, scientists can derive deeper insights into the properties of the reaction and devise ways to optimize conditions for desired outcomes.