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.
ScanSolve AI Answer
C Step 1: Identify the given values and the unknown. We are given: • Volume of oxygen (V_O_2) = 30 cm³ • Time for oxygen to diffuse (t_O_2) = 7 s • Volume of chlorine (V_Cl_2) = 60 cm³ • Time for chlorine to diffuse (t_Cl_2) = ? Step 2: Determine the molar masses of oxygen (O_2) and chlorine (Cl_2). • Molar mass of Oxygen (O) = 16.00 g/mol • Molar mass of O_2 (M_O_2) = 2 × 16.00 = 32.00 g/mol • Molar mass of Chlorine (Cl) = 35.45 g/mol • Molar mass of Cl_2 (M_Cl_2) = 2 × 35.45 = 70.90 g/mol Step 3: Apply Graham's Law of Diffusion. Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. The rate of diffusion can be expressed as volume diffused per unit time (V/t). Rate_O_2Rate_Cl_2 = sqrt(M_Cl_2)M_O_2 Substituting the rate with volume and time: V_O_2/t_O_2V_Cl_2/t_Cl_2 = sqrt(M_Cl_2)M_O_2 Step 4: Substitute the known values into the equation. 30 cm^3 / 7 s60 cm^3 / t_Cl_2 = sqrt(70.90 g/mol)32.00 g/mol Step 5: Simplify both sides of the equation. First, simplify the right side: sqrt((70.90)/(32.00)) = sqrt(2.215625) ≈ 1.4885 Next, simplify the left side: (30/7)/(60/t_Cl_2) = (30)/(7) × t_Cl_260 = 30 × t_Cl_27 × 60 = t_Cl_27 × 2 = t_Cl_214 Step 6: Solve for t_Cl_2. t_Cl_214 = 1.4885 t_Cl_2 = 14 × 1.4885 t_Cl_2 ≈ 20.839 s Rounding to the nearest whole number, the time taken for chlorine to diffuse is approximately 21 s. Comparing this result with the given options: A 12s B 14s C 21s D 30s The calculated value is closest to option C. The final answer is 21s.