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
Step 1: Identify the given values and the unknown. We are given: • Volume of oxygen (V_O_2) = 300 cm³ • Time for oxygen to diffuse (t_O_2) = 73 s • Volume of chlorine (V_Cl_2) = 600 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. 300 cm^3 / 73 s600 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: (300/73)/(600/t_Cl_2) = (300)/(73) × t_Cl_2600 = 300 × t_Cl_273 × 600 = t_Cl_273 × 2 = t_Cl_2146 Step 6: Solve for t_Cl_2. t_Cl_2146 = 1.4885 t_Cl_2 = 146 × 1.4885 t_Cl_2 ≈ 217.321 s Rounding to three significant figures, the time taken for chlorine to diffuse is: t_Cl_2 ≈ 217 s The time it will take for 600 cm³ of chlorine to diffuse through the same plug is approximately 217 s.