When 9.25 g of ClF3 was introduced into an empty 2.00-L container at 700.0 K, 19.8% of the ClF3 decomposed to give an equilibrium mixture of ClF3, ClF, and F2. ClF3 (g) ⇌ ClF (g) + F2 (g). (a) What is the value of the equilibrium constant Kc at 700.0 K? (b) What is the value of the equilibrium constant Kp at 700.0 K? (c) In a separate experiment, 39.4 g of ClF3 was introduced into an empty 2.00-L container at 700.0 K. What are the concentrations of ClF3, ClF, and F2 when the mixture reaches equilibrium?
Verified step by step guidance
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Step 1: Calculate the initial concentration of ClF3. Use the formula: \( \text{Concentration} = \frac{\text{moles}}{\text{volume}} \). First, convert the mass of ClF3 to moles using its molar mass.
Step 2: Determine the change in concentration due to decomposition. Since 19.8% of ClF3 decomposes, calculate the moles of ClF3 that decomposed and the moles of ClF and F2 formed.
Step 3: Write the expression for the equilibrium constant \( K_c \) using the equilibrium concentrations of ClF3, ClF, and F2. \( K_c = \frac{[\text{ClF}][\text{F}_2]}{[\text{ClF}_3]} \). Substitute the equilibrium concentrations into this expression.
Step 4: Relate \( K_c \) to \( K_p \) using the equation \( K_p = K_c(RT)^{\Delta n} \), where \( \Delta n \) is the change in moles of gas, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
Step 5: For the separate experiment, calculate the initial concentration of ClF3 with the new mass. Use the same decomposition percentage to find the equilibrium concentrations of ClF3, ClF, and F2, and apply the equilibrium constant to verify the concentrations.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Equilibrium Constant (Kc and Kp)
The equilibrium constant (Kc) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. Kp is similar but is used for gases and is based on partial pressures instead of concentrations. The relationship between Kc and Kp is given by the equation Kp = Kc(RT)^(Δn), where Δn is the change in moles of gas. Understanding these constants is crucial for analyzing chemical equilibria.
Stoichiometry involves the quantitative relationships between the reactants and products in a chemical reaction. In the given reaction, ClF3 decomposes into ClF and F2, and the stoichiometric coefficients indicate the molar ratios of these species. This concept is essential for calculating the amounts of each substance at equilibrium based on the initial amounts and the extent of the reaction.
Decomposition refers to the process where a compound breaks down into simpler products, which in this case is ClF3 breaking down into ClF and F2. The extent of decomposition is influenced by temperature and pressure, and the system will reach a state of dynamic equilibrium where the rates of the forward and reverse reactions are equal. Understanding how to determine the equilibrium concentrations from the initial amounts and the percentage decomposed is vital for solving the problem.
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