Problem 6 - Chemistry and Chemical Reactivity

Question

The equilibrium constant, \(K_{c}\) for the reaction $$ 2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) $$ is \(3.9 \times 10^{-3}\) at \(300^{\circ} \mathrm{C} .\) A mixture contains the gases at the following concentrations: \(|\mathrm{NOCl}|=\) \(5.0 \times 10^{-3} \mathrm{mol} / \mathrm{L}_{\alpha}[\mathrm{NO}]=2.5 \times 10^{-3} \mathrm{mol} / \mathrm{L}_{u}\) and \(\left[\mathrm{Cl}_{2}\right]=2.0 \times 10^{-3} \mathrm{mol} / \mathrm{L} .\) Is the reaction at equilibrium at \(300^{\circ} \mathrm{C} ?\) If not, in which direction does the reaction proceed to come to equilibrium?

Step-by-Step Solution

Answer

The reaction is not at equilibrium; it will proceed forward.

Step 1: Write the Expression for the Reaction Quotient, Q

The reaction quotient \( Q \) is used to determine the direction a reaction will proceed to reach equilibrium. For the given reaction \( 2 \text{NOCl} \rightleftharpoons 2 \text{NO} + \text{Cl}_2 \), the expression for \( Q \) is similar to that of \( K_c \): \[ Q = \frac{[\text{NO}]^2[\text{Cl}_2]}{[\text{NOCl}]^2} \].

Step 2: Substitute Initial Concentrations into Q Expression

Substitute the given initial concentrations into the \( Q \) expression: \[ Q = \frac{(2.5 \times 10^{-3})^2(2.0 \times 10^{-3})}{(5.0 \times 10^{-3})^2} \].

Step 3: Calculate Q Value

Calculate \( Q \) using the substituted values: \[ Q = \frac{(6.25 \times 10^{-6})(2.0 \times 10^{-3})}{(25.0 \times 10^{-6})} \]. This simplifies to \[ Q = \frac{12.5 \times 10^{-9}}{25.0 \times 10^{-6}} = 5.0 \times 10^{-4} \].

Step 4: Compare Q with Kc

Compare the calculated value of \( Q \) to the given equilibrium constant \( K_c \) which is \( 3.9 \times 10^{-3} \). Since \( Q = 5.0 \times 10^{-4} \) is less than \( K_c \), the reaction is not at equilibrium.

Step 5: Determine the Direction of the Reaction

Since \( Q < K_c \), the reaction will proceed in the forward direction, producing more \( \text{NO} \) and \( \text{Cl}_2 \) until equilibrium is reached.

Key Concepts

Equilibrium Constant

The equilibrium constant, often represented as \( K_c \), is a critical concept in understanding chemical reactions. It provides insight into how concentrations of reactants and products relate at chemical equilibrium. For a general reaction \( aA + bB \leftrightharpoons cC + dD \), the equilibrium constant is expressed as:\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]Here, the concentrations are those present at equilibrium, and each concentration is raised to the power of its stoichiometric coefficient.
The value of \( K_c \) offers a window into the reaction’s dynamics:

• If \( K_c \) is large (>1), products dominate at equilibrium.
• If \( K_c \) is small (<1), reactants are more prevalent.

At equilibrium, the rates of the forward and reverse reactions are equal, meaning the concentration of reactants and products remains constant over time. Understanding \( K_c \) is crucial for predicting how a system might respond to certain changes, like temperature or pressure.

Chemical Equilibrium

Chemical equilibrium refers to the state in a reversible reaction where the forward and reverse reactions occur at the same rate. This results in a stable concentration of reactants and products. It’s important to note that equilibrium does not mean the reactants and products are equal, but rather that their rates of formation are balanced.
In this state, the reaction quotient \( Q \) equals the equilibrium constant \( K_c \). However, if \( Q \) does not equal \( K_c \), the system will shift:

• If \( Q < K_c \), the reaction will shift forward to produce more products.
• If \( Q > K_c \), the reaction will shift backwards, increasing reactants.

Chemical equilibrium is dynamic, not static. Molecules continually break and form, but because the forward and reverse rates are equal, the macroscopic properties remain unchanged. Adjustments to this balance occur naturally but can be influenced by changes in conditions like pressure or temperature.

Gaseous Reactions

Gaseous reactions are a specific type of chemical reaction where reactants and products exist in the gas phase. These reactions are often sensitive to changes in pressure and temperature, both of which can significantly impact reaction direction and equilibrium.
Understanding gaseous reactions involves considering several factors:

• **Pressure:** Changes can shift the equilibrium depending on the reaction’s stoichiometry. According to Le Chatelier's Principle, an increase in pressure shifts equilibrium towards the side with fewer gas molecules.
• **Temperature:** Raising temperature usually shifts the equilibrium towards the endothermic direction, absorbing heat, while lowering it favors the exothermic direction.
• **Volume:** Changing the container size also affects equilibrium. Reducing volume increases pressure, influencing the system towards fewer moles of gas.

Gaseous reactions play a crucial role in many industrial and natural processes, making their study valuable for understanding broader environmental and technological contexts. With gases, always consider the whole system's change, as all conditions are interconnected.