This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
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Here are the solutions to the problems. Question 1 Equilibrium constant expression: For the reaction C(s) + CO_2(g) + 2Cl_2(g) 2COCl_2(g), the equilibrium constant expression K_c is: K_c = ([COCl_2(g)]^2)/([CO_2(g)][Cl_2(g)]^2) (Note: Solids like C(s) are not included in the equilibrium constant expression.) Calculation of the equilibrium constant: Given reactions: 1. C(s) + CO_2(g) 2CO(g) with K_c1 = 1.4 × 10^12 2. CO(g) + Cl_2(g) COCl_2(g) with K_c2 = 5.5 × 10^1 Target reaction: C(s) + CO_2(g) + 2Cl_2(g) 2COCl_2(g) Step 1: Manipulate the given reactions to obtain the target reaction. Multiply reaction (2) by 2: 2CO(g) + 2Cl_2(g) 2COCl_2(g) The new equilibrium constant for this reaction is (K_c2)^2. Step 2: Add reaction (1) and the modified reaction (2). (C(s) + CO_2(g) 2CO(g)) + (2CO(g) + 2Cl_2(g) 2COCl_2(g)) Summing these gives: C(s) + CO_2(g) + 2CO(g) + 2Cl_2(g) 2CO(g) + 2COCl_2(g) Canceling 2CO(g) from both sides yields the target reaction: C(s) + CO_2(g) + 2Cl_2(g) 2COCl_2(g) Step 3: Calculate the overall equilibrium constant. When reactions are added, their equilibrium constants are multiplied. K_c = K_c1 × (K_c2)^2 K_c = (1.4 × 10^12) × (5.5 × 10^1)^2 K_c = (1.4 × 10^12) × (30.25 × 10^2) K_c = (1.4 × 10^12) × (3.025 × 10^3) K_c = (1.4 × 3.025) × 10^12+3 K_c = 4.235 × 10^15 The equilibrium constant for the reaction is 4.235 × 10^15. Question 2 Given reaction: H_2(g) + Br_2(g) 2HBr(g) with K_p = 7.1 × 10^4 at 700 K. a) For the reaction 2HBr(g) H_2(g) + Br_2(g): Step 1: Identify the relationship between the given reaction and the target reaction. This reaction is the reverse of the original reaction. Step 2: Calculate the new K_p. When a reaction is reversed, the new equilibrium constant is the reciprocal of the original. K_p' = (1)/(K_p) K_p' = (1)/(7.1 × 10^4) K_p' ≈ 1.408 × 10^-5 The value of K_p is 1.408 × 10^-5. b) For the reaction (1)/(2)H_2(g) + (1)/(2)Br_2(g) HBr(g): Step 1: Identify the relationship between the given reaction and the target reaction. This reaction is the original reaction multiplied by a factor of (1)/(2). Step 2: Calculate the new K_p. When a reaction is multiplied by a factor 'n', the new equilibrium constant is the original constant raised to the power 'n'. Here, n = (1)/(2). K_p'' = (K_p)^1/2 = sqrt(K_p) K_p'' = sqrt(7.1 × 10^4) K_p'' = sqrt(71000) K_p'' ≈ 266.458 The value of K_p is 266.458. Question 3 Calculate a value for the equilibrium constant for the reaction: O_2(g) + O(g) O_3(g) Given information: 1. NO_2(g) NO(g) + O(g) with K_c1 = 6.8 × 10^-49 2. O_3(g) + NO(g) NO_2(g) + O_2(g) with K_c2 = 5.8 × 10^-34 Target reaction: O_2(g) + O(g) O_3(g) Step 1: Manipulate the given reactions