Question

Suppose a reaction has the equilibrium constant \(K=1.7 \times 10^{-8}\) at a particular temperature. Will there be a large or small amount of unreacted starting material present when this reaction reaches equilibrium? Is this reaction likely to be a good source of products at this temperature?

Short answer

In conclusion, given the reaction at this temperature with the equilibrium constant \(K=1.7 \times 10^{-8}\), there will be a large amount of unreacted starting material when the reaction reaches equilibrium, and it is not likely to be a good source of desired products.

Step-by-step solution

Recap of equilibrium constant

The equilibrium constant (K) represents the ratio of the concentrations of products to reactants at equilibrium in a given chemical reaction at a particular temperature. If the K value is significantly greater than 1, it indicates that the forward reaction is favored, and the products are more abundant than the reactants. On the other hand, if the K value is significantly smaller than 1, it means that the reverse reaction is favored, and the reactants are more abundant than the products.

Analyzing the equilibrium constant

The given value of K is \(1.7 \times 10^{-8}\). Since this value is much less than 1, it indicates that the reaction favors the starting materials (reactants) rather than the products. This implies that a large amount of unreacted starting material will be present when the reaction reaches equilibrium.

Assessing the usefulness of the reaction for producing products

Since the equilibrium constant favors the reactants and not the products, this reaction would not be a good source of products at this particular temperature. The low value of the equilibrium constant indicates that only a small fraction of the reactants will convert into products, leading to a low yield. In conclusion, for the given reaction at this temperature, there will be a large amount of unreacted starting material, and it is not likely to be a good source of products. A different reaction or changing the reaction conditions may be necessary to obtain the desired products in higher amounts.

Key concepts

Understanding Chemical Equilibrium

Chemical equilibrium is a fundamental concept in chemistry, describing a state where the rates of the forward and reverse reactions in a chemical process are equal, resulting in no net change in the concentration of reactants and products over time. It's important to note that equilibrium does not mean the reactants and products are present in equal amounts, but rather that their quantities have stabilized in a particular ratio that is determined by the specific reaction conditions, such as temperature.
At equilibrium, the system is dynamic; molecules of reactants and products continuously interconvert, but their concentrations remain constant. The position of the equilibrium, which can lean towards the reactants or products, is quantitatively described by the equilibrium constant (K). A low K value, much smaller than 1 as in our EXERCISE, indicates that at equilibrium, the concentration of reactants will be high compared to the concentration of products. This suggests a large amount of unreacted starting material remains, and the reaction is not an efficient producer of products under the stated conditions.
When faced with calculations involving chemical equilibrium, it helps to remember that it's not about whether the reaction completely stops at some point, but rather that it reaches a state of balance. Understanding the concept of equilibrium allows you to predict the behavior of chemical systems, which is essential in fields such as chemical engineering, pharmacology, and environmental science.

The Role of the Reaction Quotient

The reaction quotient (Q) is another crucial concept closely related to the equilibrium constant. It serves as a mathematical tool that helps determine the direction in which a reaction mixture will shift to reach equilibrium. The formula for Q is identical to the formula for K, involving the concentrations of the reactants and products. However, Q can be calculated at any point in the reaction, not only at equilibrium.

Interpreting Q

If Q is less than K, the reaction will proceed forward to produce more products. Conversely, if Q is greater than K, the reaction will go in the reverse direction to produce more reactants. When Q equals K, the system is at equilibrium, and no further net change will occur. In the context of our EXERCISE, calculating Q can give us insight into the progress of the reaction and its proximity to equilibrium. This can be particularly useful in a laboratory setting or industrial process where adjustments may be made to drive the reaction to a more favorable position, such as increasing the yield of products if desired.

• Q < K: Reaction shifts right (toward products)
• Q > K: Reaction shifts left (toward reactants)
• Q = K: Reaction is at equilibrium

Le Chatelier's Principle and Shifts in Equilibrium

Understanding Le Chatelier's principle is crucial for predicting how a system at equilibrium responds to external changes. This principle states that if a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system will adjust itself to counteract the imposed change and a new equilibrium will be established.
For instance, if more reactants are added to the system, Le Chatelier's principle predicts that the equilibrium will shift to the right to produce more products, thus using up the added reactants. If the temperature is increased for an endothermic reaction, the equilibrium will also shift to the right, favoring the formation of products in order to absorb the extra heat.

Applications of Le Chatelier's Principle

Real-world applications include adjusting conditions in industrial synthesis to maximize product yields or understanding physiological responses to changes in the body's chemical balances. For the reaction in our EXERCISE, altering the temperature could change the value of the equilibrium constant, potentially making the reaction a better source of the desired products.
Le Chatelier's principle helps explain why the equilibrium constant in our EXERCISE is low. Due to the nature of the reaction and its existing conditions, the equilibrium lies far to the left (favoring reactants). Shifting such an equilibrium towards the products would require changing the reaction conditions, for example by removing products as they are formed or by changing the temperature for reactions where heat is absorbed or released.