Problem 41 - Chemistry The Molecular Science

Question

Nitrosyl chloride, NOCl, decomposes to \(\mathrm{NO}\) and \(\mathrm{Cl}_{2}\) at high temperatures. $$ 2 \mathrm{NOCl}(\mathrm{g}) \rightleftharpoons 2 \mathrm{NO}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{~g}) $$ Suppose you place \(2.00 \mathrm{~mol} \mathrm{NOCl}\) in a \(1.00-\mathrm{L}\) flask, seal it, and raise the temperature to \(462^{\circ} \mathrm{C}\). When equilibrium has been established, \(0.66 \mathrm{~mol} \mathrm{NO}\) is present. Calculate the equilibrium constant \(K_{\mathrm{c}}\) for the decomposition reaction from these data.

Step-by-Step Solution

Answer

The equilibrium constant \( K_c \) is approximately 0.0801.

Step 1: Determine Initial Concentrations

Initially, the concentration of NOCl is given as 2.00 mol in a 1.00 L flask, which is 2.00 M. There are initially 0 moles of NO and Cl2, so both have initial concentrations of 0 M.

Step 2: Define Change in Concentration

As the system reaches equilibrium, NOCl decomposes producing NO and Cl2. According to the stoichiometry of the reaction, for every 2 moles of NOCl that decompose, 2 moles of NO and 1 mole of Cl2 are produced. Let x be the change in moles of NOCl. Thus, NO increases by x moles and Cl2 by x/2 moles.

Step 3: Calculate Equilibrium Concentrations

At equilibrium, there are 0.66 moles of NO, therefore \( x = 0.66 \). The equilibrium concentration of NOCl is \( [\mathrm{NOCl}] = 2.00 - 0.66 = 1.34 \text{ M} \), \([\mathrm{NO}] = 0.66\text{ M}\), and \([\mathrm{Cl}_2] = 0.33\text{ M}\) as it is \( x/2 = 0.33 \).

Step 4: Write the Equilibrium Expression

The equilibrium constant expression for the reaction is: \[ K_c = \frac{[\text{NO}]^2[\text{Cl}_2]}{[\text{NOCl}]^2} \]

Step 5: Substitute and Calculate Kc

Substituting the equilibrium concentrations into the expression:\[ K_c = \frac{(0.66)^2 (0.33)}{(1.34)^2} = \frac{0.4356 \times 0.33}{1.7956} = \frac{0.1438}{1.7956} \approx 0.0801 \].

Step 6: Conclusion

The equilibrium constant \( K_c \) for the decomposition of Nitrosyl Chloride at 462°C is approximately 0.0801.

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a state in chemical reactions where the concentrations of reactants and products no longer change over time. It's like reaching a balance where nothing seems to be happening because the forward and reverse reactions occur at the same rate.
This balance doesn't mean you've used up all your reactants; rather, it signifies that the conversion to products happens at the same pace as the reverse process, converting products back into reactants.
In the case of the decomposition of Nitrosyl chloride (NOCl), given by the reaction \( 2 \text{NOCl} (\text{g}) \rightleftharpoons 2 \text{NO} (\text{g}) + \text{Cl}_2 (\text{g}) \), the reaction reaches equilibrium when the concentrations of NOCl, NO, and Cl\(_2\) do not change anymore.
Understanding the concept of equilibrium is important for calculating the equilibrium constant, \( K_c \), which gives insight into the ratio of product concentrations to reactant concentrations at equilibrium.

Reaction Stoichiometry

Stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. It's like the recipe in a cookbook that tells you exactly how much of each ingredient you need.
For the decomposition of Nitrosyl chloride, we have the balanced equation: \( 2 \text{NOCl} (\text{g}) \rightarrow 2 \text{NO} (\text{g}) + \text{Cl}_2 (\text{g}) \).
This equation shows us that two moles of NOCl decompose to form two moles of NO and one mole of Cl\(_2\).
Stoichiometry helps us determine how much of each product will form when a certain amount of reactant reacts. In this case, if "\(x\)" is the change in moles of NOCl, then stoichiometry tells us that \(x\) moles of NO and \(x/2\) moles of Cl\(_2\) will be produced at equilibrium.
Understanding these relationships is crucial when seeking to calculate equilibrium concentrations.

Concentration Changes

Concentration changes refer to how the amounts of substances involved in a reaction vary as the reaction proceeds toward equilibrium. At the start of the reaction, you often begin with a certain concentration of reactants and none of the products. As the reaction progresses, reactants deplete while products accumulate.
Let's consider our example with Nitrosyl Chloride. Initially, the concentration of NOCl is 2.00 M, while both NO and Cl\(_2\) have a starting concentration of 0 M. As the reaction reaches equilibrium, NOCl decreases by \(x\) moles, producing \(x\) moles of NO and \(x/2\) moles of Cl\(_2\).

• The equilibrium concentration for NO is 0.66 M.
• Given that, Cl\(_2\) concentration becomes 0.33 M.
• NOCl reduces to an equilibrium concentration of 1.34 M.

Monitoring these concentration changes is key to understanding how to substitute the correct values into the equilibrium expression to find the equilibrium constant.