Question

For a given reaction at a given temperature, the special ratio of products to reactants defined by the equilibrium constant is always equal to the same number. Explain why this is true, no matter what initial concentrations of reactants (or products) may have been taken in setting up an experiment.

Short answer

In summary, the equilibrium constant (K) remains constant for a given reaction at a given temperature, regardless of the initial concentrations of reactants or products, because it represents the inherent property of the reaction at that temperature. Changing initial concentrations causes the system to adjust by altering the rates of forward or reverse reactions until the ratio defined by K is reached, and equilibrium is restored. K solely depends on temperature, making it a uniquely defined characteristic of a reaction at a particular temperature.

Step-by-step solution

Understand the Equilibrium Constant

The equilibrium constant (K) is a ratio of the concentration of the products, raised to their respective stoichiometric coefficients, to the concentration of the reactants, raised to their respective stoichiometric coefficients, at a particular temperature. Mathematically, for a reaction: \(aA + bB \rightleftharpoons cC + dD\) The equilibrium constant is expressed as: \[K = \frac{[C]^c[D]^d}{[A]^a[B]^b}\] At equilibrium, the concentrations of reactants/products will not change over time because the forward and reverse rates are equal.

Understand the Dependence on Temperature

The equilibrium constant K is temperature-dependent. As the temperature changes, the value of K will change, affecting the concentrations of products and reactants at equilibrium. However, at a constant temperature, the value of K remains constant for the same reaction. It does not depend on the initial concentrations of reactants or products.

Explaining the Consistency of K at a Given Temperature

When we change the initial concentrations of reactants or products in a reaction, the system will adjust itself to reach the new equilibrium state that corresponds to the same value of K at the given temperature. As the system deviates from the equilibrium state, it will respond either by increasing the rate of the forward or reverse reactions, ensuring that the value of K is maintained. For example, when initial concentrations are increased or decreased, the system will react by consuming or producing more reactants or products accordingly, until the ratio of the concentrations defined by K is reached and equilibrium is reached once again.

Conclusion

In summary, the equilibrium constant (K) is always equal to the same number for a given reaction at a given temperature, no matter what initial concentrations of reactants or products are chosen, because it represents the inherent property of the reaction and determines the equilibrium concentrations of reactants and products. When initial concentrations are changed, a new equilibrium state is established that corresponds to the same value of K, which is only temperature-dependent. This consistency explains why the equilibrium constant is a uniquely defined characteristic of a reaction at a particular temperature.

Key concepts

Chemical Equilibrium

In the realm of chemistry, understanding the state of chemical equilibrium is pivotal. It occurs when a chemical reaction and its reverse reaction proceed at the same rate, leading to a constant concentration of reactants and products over time.

Consider a simplistic reaction, such as the production of water from hydrogen and oxygen gases. If we place hydrogen and oxygen in a sealed container and ignite them, they will react to form water. Eventually, a point is reached where, despite continuing reactions, the amount of water, hydrogen, and oxygen remain unchanged. This point marks the chemical equilibrium.

At equilibrium, the rate at which reactants A and B convert into products C and D becomes equal to the rate at which C and D reform into A and B. Symbolically, if we denote the concentration with square brackets, this balance can be represented as follows:
At equilibrium: Rate(forward) = Rate(reverse)Where: - Rate(forward) = Rate at which A and B form C and D- Rate(reverse) = Rate at which C and D form A and B

Reaction Rates

When discussing chemical reactions, the term 'reaction rates' refers to the speed at which reactants turn into products. It is an intuitive concept—some reactions, like the explosive combustion of gasoline, happen almost instantly, while others, such as the rusting of iron, may take years to become noticeable.

The rate of a chemical reaction can be altered by various factors like concentration of reactants, surface area, temperature, and the presence of catalysts. For instance, increasing the concentration of reactants typically increases the reaction rate, as there are more particles available to interact and collide, forming products.

A higher temperature usually increases reaction rates as well because it provides particles with more energy, making collisions more frequent and forceful. This heightened activity can lead to a higher probability of overcoming the activation energy of the reaction, which is the minimum energy required for the reactants to convert into products.

Stoichiometry

The central principle of stoichiometry lies in the conservation of mass: matter is neither created nor destroyed in chemical reactions. Stoichiometry quantifies this by providing a precise measure of the relative amounts of reactants and products that participate in a chemical reaction.

Returning to the water-forming reaction, stoichiometry tells us that exactly two hydrogen molecules (H2) react with one oxygen molecule (O2) to produce two water molecules (H2O). Thus, the ratio is always 2:1:2. This allows chemists to predict the amounts of products formed from given amounts of reactants, and vice versa.

For any chemical reaction, the stoichiometric coefficients can be found by balancing the reaction. In the context of equilibrium, these coefficients play a crucial role because they also appear as exponents in the equilibrium constant expression, reflecting the balanced chemical equation.

Temperature Dependence

Temperature is a critical factor in chemistry, extensively influencing reaction rates and equilibrium states. This dependency is embodied in the behavior of the equilibrium constant (K) as well.

For most reactions, increasing the temperature shifts the equilibrium toward the products if the reaction is endothermic (absorbs heat) and toward reactants if exothermic (releases heat), based on Le Chatelier's principle. This occurs because the equilibrium constant itself changes with temperature.

An endothermic reaction's K value will increase with temperature, signifying a greater proportion of products at equilibrium. Conversely, an exothermic reaction's K decreases with increased temperature, favoring reactants.

Understanding this temperature dependence is crucial when predicting the direction of a reaction under varying conditions and for controlling industrial processes to optimize the yield of desired products.