Problem 12 - Chemistry Matter and Change

Question

Interpret Data The table below shows the value of the equilibrium constant for a reaction at three different temperatures. At which temperature is the concentration of the products the greatest? Explain your answer $$ \begin{array}{lll}{263 \mathrm{K}} & {273 \mathrm{K}} & {373 \mathrm{K}} \\\ {0.0250} & {0.500} & {4.500}\end{array} $$

Step-by-Step Solution

Answer

The concentration of products is the greatest at a temperature of 373 K. This is because the equilibrium constant (K) is the largest at this temperature (4.500), which indicates the greatest concentration of products relative to reactants at equilibrium.

Step 1: Understanding the equilibrium constant (K)

The equilibrium constant, K, helps us determine the concentration of products and reactants at equilibrium for a chemical reaction. The larger the value of K, the greater the concentration of products at equilibrium relative to the reactants.

Step 2: Comparing the values of K at each temperature

We have the values of K at 3 different temperatures: - K at 263 K: 0.0250 - K at 273 K: 0.500 - K at 373 K: 4.500

Step 3: Identifying the largest K value

We can see that the largest value of K is 4.500, which corresponds to a temperature of 373 K.

Step 4: Conclusion

Since the largest value of K represents the greatest concentration of products relative to reactants at equilibrium, we can conclude that the concentration of products is the greatest at a temperature of 373 K.

Key Concepts

Temperature Dependence of Equilibrium Constant

The equilibrium constant, often denoted as \( K \), is a crucial factor in understanding chemical reactions at equilibrium. It tells us how the concentrations of products compare to reactants under equilibrium conditions. One intriguing characteristic of \( K \) is that its value depends heavily on temperature. As temperature changes, the equilibrium position shifts, either favoring more products or more reactants. This is a reflection of Le Chatelier's principle, which states that a system at equilibrium will adjust to counteract the effects of any changes in temperature.
In endothermic reactions, where heat is absorbed, an increase in temperature generally results in an increased \( K \), suggesting a higher concentration of products. Conversely, in exothermic reactions, where heat is released, an increase in temperature usually leads to a decreased \( K \). Understanding the temperature dependence of the equilibrium constant aids in predicting how a reaction's equilibrium will shift as the temperature is changed.

Understanding Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction where the rates of the forward and reverse reactions are equal. At this stage, the concentrations of reactants and products remain constant over time, although they are not necessarily equal. It's important to note that equilibrium in a closed system does not mean the reactions stop, but rather that the concentrations stabilize because the speeds of both directions of the reaction are balanced.
Achieving chemical equilibrium depends on various factors: temperature, pressure, and the concentration of reactants and products. The equilibrium constant \( K \) is a numerical representation of this equilibrium state. When \( K \) is larger, it indicates that, at equilibrium, the reaction favors the formation of products over reactants. Therefore, examining the value of \( K \) at different temperatures tells us how the equilibrium position shifts in response to external changes, highlighting the dynamic nature of equilibrium in chemical processes.

The Role of Product Concentration in Chemical Equilibrium

Product concentration is a key factor in determining the position of equilibrium in a chemical reaction. At equilibrium, the concentrations of products and reactants have settled into a stable ratio, dictated by the equilibrium constant \( K \). For any chemical reaction at equilibrium, if \( K \) has a high value, this implies that the product concentration is quite high relative to the concentration of reactants.
When analyzing data from an equilibrium reaction, such as examining different temperatures, the value of \( K \) provides insights into the concentration of products. A higher value of \( K \) at a given temperature means that the equilibrium position is shifted towards the products. This is why, in the given exercise, at 373 K where \( K = 4.500 \), the concentration of products is the greatest. This understanding is vital for predicting and manipulating chemical reactions in practical applications, ranging from industrial processes to biological systems.