Question

Pure nitrosyl chloride (NOCl) gas was heated to \(240^{\circ} \mathrm{C}\) in a \(1.00-\mathrm{L}\) container. At equilibrium, the total pressure was 1.00 atm and the \(\mathrm{NOCl}\) pressure was 0.64 atm: $$ 2 \mathrm{NOCl}(g) \rightleftarrows 2 \mathrm{NO}(g)+\mathrm{Cl}_{2}(g) $$ (a) Calculate the partial pressures of \(\mathrm{NO}\) and \(\mathrm{Cl}_{2}\) in the system. (b) Calculate the equilibrium constant \(K_{P}\).

Short answer

(a) \(P_{\text{NO}} = 0.72\, \text{atm}\), \(P_{\text{Cl}_2} = 0.36\, \text{atm}\); (b) \(K_P \approx 0.90\).

Step-by-step solution

Calculate Partial Pressure of Decomposed NOCl

First, determine the change in pressure of \(\text{NOCl}\). The initial pressure was entirely \(\text{NOCl}\) with a pressure of \(0.64\, \text{atm}\) at equilibrium. The total pressure at equilibrium is \(1.00\, \text{atm}\), meaning the pressure change due to decomposition is \(1.00 - 0.64 = 0.36\, \text{atm}\).

Relate Pressure Change to NO and Cl2 Production

From the reaction \(2\text{NOCl} \rightleftarrows 2\text{NO} + \text{Cl}_2\), the decomposition of \(0.36\, \text{atm}\) of \(\text{NOCl}\) results in \(0.36\, \text{atm}\) of \(\text{Cl}_2\) and \(0.72\, \text{atm}\) of \(\text{NO}\), since two moles of \(\text{NO}\) are produced for every two moles of \(\text{NOCl}\) that decompose.

Calculate Equilibrium Constant Kp

The equilibrium constant \(K_P\) is calculated using \(K_P = \frac{(P_{\text{NO}})^2 \cdot P_{\text{Cl}_2}}{(P_{\text{NOCl}})^2}\). Substitute the equilibrium partial pressures:\[ K_P = \frac{(0.72)^2 \cdot 0.36}{(0.64)^2} \approx 0.90. \]

Key concepts

Partial Pressures

In the context of gases, partial pressure is the pressure that a gas in a mixture would exert if it occupied the entire volume by itself. It’s a crucial concept when studying chemical reactions involving gases, especially when dealing with equilibrium conditions. In the given exercise, nitrosyl chloride ( NOCl ) decomposes into nitric oxide ( NO ) and chlorine gas ( Cl_2 ). We were given initial and total equilibrium pressures to determine the partial pressures of the products— NO and Cl_2 .
To solve for partial pressures, we recognize the initial pressure from NOCl and its equilibrium state. From step-by-step calculations, we observe that the change in pressure indicates the amount of NO Cl that decomposed. This change also directly relates to the partial pressures of NO and Cl_2 at equilibrium. Using a stoichiometry from the balanced equation, we deduced that for every mole of NOCl that decomposes, two moles of NO and one mole of Cl_2 are formed. Thus, by understanding this relationship, we establish the partial pressures necessary to analyze the equilibrium state of the system.

Chemical Equilibrium

Chemical equilibrium occurs in a reversible reaction when the rate of the forward reaction equals the rate of the reverse reaction, causing the concentrations of reactants and products to remain constant over time. This steady state is critical for understanding the dynamic nature of chemical systems, as it showcases how reactions can "settle," though molecules continually react.
In our scenario involving 2 ext{NOCl} ightleftarrows 2 ext{NO} + ext{Cl}_2 , the chemical equilibrium helps predict how much NOCl will remain as reactants and how much will transform into NO and Cl_2. The concept of equilibrium doesn't mean the amounts are equal, but rather steady. Understanding equilibrium concepts is essential in solving for the equilibrium constant, K_P , a crucial value to quantify the balance point of a reaction under specific conditions.

• K_P tells us about the ratio of product pressures to reactant pressures at equilibrium at constant temperature.
• It provides insight into whether a reaction favors the formation of products or reactants.

Changes in conditions, like temperature or pressure, can shift this equilibrium, a principle described by Le Chatelier's principle.

Reaction Stoichiometry

Reaction stoichiometry explores the quantitative relationship between the reactants and the products in a chemical reaction. By utilizing the balanced chemical equation, we can determine how reactants like NOCl convert into products like NO and Cl_2 in our given reaction.
The chemical equation 2 ext{NOCl} ightleftarrows 2 ext{NO} + ext{Cl}_2 provides a stoichiometric guide: 2 moles of NOCl yield 2 moles of NO and 1 mole of Cl_2. This tells us that stoichiometry is essential in deducing the amounts of substances involved, especially under equilibrium conditions.

• This stoichiometric relationship was used to calculate the partial pressures of NO and Cl_2 from the decomposed amount of NOCl.
• It allows for the determination of unknown quantities when some information, like initial pressures, is provided.
• Accurate stoichiometric calculations enable the prediction of yield and the efficient use of reactants in chemical processes.

By mastering stoichiometry, students can navigate through predictions and calculations effectively, which are crucial for comprehensive analyses in chemical reactions.