Question

Calculate \(K_{\mathrm{c}}\) for each reaction. \begin{equation}\begin{array}{l}{\text { a. } \mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) \quad K_{c}=5.9 \times 10^{-3}(\mathrm{at} 298 \mathrm{K})} \\ {\text { b. } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) \quad K_{\mathrm{c}}=3.7 \times 10^{8}(\mathrm{at} 298 \mathrm{K})} \\ {\text { c. } \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) \quad K_{\mathrm{c}}=4.10 \times 10^{-31}(\mathrm{at} 298 \mathrm{K})}\end{array}\end{equation}

Short answer

For reaction a, Kc is 5.9 x 10^-3; for reaction b, Kc is 3.7 x 10^8; for reaction c, Kc is 4.10 x 10^-31; all at 298 K.

Step-by-step solution

Calculate Kc for reaction a

For reaction a, the equilibrium constant, Kc, is given directly in the problem statement as the value of 5.9 x 10^-3 at 298 K. There is no calculation required for this part.

Calculate Kc for reaction b

Similarly, for reaction b, the equilibrium constant, Kc, is provided in the exercise as 3.7 x 10^8 at 298 K. Like reaction a, no calculation is needed here.

Calculate Kc for reaction c

As with the previous reactions, reaction c has its equilibrium constant, Kc, stated in the exercise. The given Kc value is 4.10 x 10^-31 at 298 K. No further calculations are necessary.

Key concepts

Understanding Chemical Equilibrium

Chemical equilibrium represents a state in a reversible chemical reaction where the rates of the forward and reverse reactions are equal, leading to no net change in the concentration of the reactants and products over time. It is a dynamic balance, not a static one, as molecules are continually reacting but in such a way that the overall concentrations remain constant.

To visualize this, imagine a busy intersection where an equal number of cars enter and leave from any direction. No side gets congested because the flow in equals the flow out. Similarly, in a chemical reaction at equilibrium, the rate at which the reactants turn into products equals the rate at which products revert back into reactants.

However, reaching chemical equilibrium doesn't necessarily mean that the reactants and products are present in equal amounts. The equilibrium position, which tells us the relative concentrations of reactants and products at equilibrium, varies depending on the reaction and the conditions under which it is carried out.

Calculating the Equilibrium Constant (\(K_c\))

The equilibrium constant, denoted as \(K_c\), is a number that provides a measure of the position of equilibrium for a reversible chemical reaction at a given temperature. It's calculated using the concentrations of the reactants and products at equilibrium.

For a general reaction: \(aA + bB \rightleftharpoons cC + dD\), the equilibrium constant \(K_c\) is expressed as: \[K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}\] where \([A]\), \([B]\), \([C]\), and \([D]\) represent the molar concentrations of the reactants and products at equilibrium, and raised to the power of their respective coefficients from the balanced equation.

Understanding how to calculate \(K_c\) is crucial for predicting the extent of a reaction, determining reaction yields, and making decisions about optimal reaction conditions. It's important to note that \(K_c\) is dimensionless, and its value is specific to a particular reaction at a particular temperature.

Applying Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept that helps us understand how a chemical reaction at equilibrium responds to changes in concentration, temperature, or pressure. Simply put, if an external change is applied to a system at equilibrium, the system adjusts in a way that counteracts the change and a new equilibrium is established.

For instance:

• If the concentration of a reactant is increased, the equilibrium will shift in the direction that consumes the added reactants, forming more products.
• If the system is subjected to a decrease in pressure, the equilibrium position moves in the direction that produces more gas molecules.
• If the system is heated, the equilibrium will favor the endothermic direction of the reaction to absorb the extra heat.

Le Chatelier's principle is an essential tool for chemists to predict the outcome of a reaction under different conditions and to design processes that optimize product yields.