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
Hey veale, good to see you again. Here are the solutions to your questions: 1) We will use Graham's Law of Diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. (r_1)/(r_2) = sqrt((M_2)/(M_1)) Given: Rate of unknown gas (r_1) = 47.15 cm^3/sec Rate of oxygen (r_2) = 60.40 cm^3/sec Relative molecular mass of oxygen (M_2) = 2 × 16 = 32 g/mol (since oxygen is diatomic, O_2) Assumption: The question asks for the relative molecular mass of the unknown gas, as the molecular mass of oxygen is a known constant. Step 1: Substitute the given values into Graham's Law. (47.15)/(60.40) = sqrt((32)/(M_1)) Step 2: Square both sides of the equation to remove the square root. ((47.15)/(60.40))^2 = (32)/(M_1) (0.780629)^2 ≈ 0.60938 = (32)/(M_1) Step 3: Solve for M_1. M_1 = (32)/(0.60938) M_1 ≈ 52.51 g/mol The relative molecular mass of the unknown gas is approximately 52.51 g/mol. If the question literally meant the relative molecular mass of oxygen, then it is simply 2 × 16 = 32 g/mol. However, this would make the diffusion rates irrelevant. 2) We will again use Graham's Law of Diffusion. r_H_2r_O_2 = sqrt(M_O_2)M_H_2 Given: Volume of hydrogen (H_2) = 450 cm^3 Time for hydrogen (H_2) = 25 sec Molecular mass of hydrogen (M_H_2) = 2 × 1 = 2 g/mol Molecular mass of oxygen (M_O_2) = 2 × 16 = 32 g/mol Volume of oxygen (O_2) = 450 cm^3 (same volume) Time for oxygen (t_O_2) = ? Step 1: Calculate the rate of diffusion for hydrogen. r_H_2 = VolumeTime = 450 cm^325 sec = 18 cm^3/sec Step 2: Express the rate of oxygen in terms of its unknown time. r_O_2 = 450 cm^3t_O_2 Step 3: Substitute the rates and molecular masses into Graham's Law. (18)/(450)t_O_2 = sqrt((32)/(2)) 18 · t_O_2450 = sqrt(16) 18 · t_O_2450 = 4 Step 4: Solve for t_O_2. 18 · t_O_2 = 4 × 450 18 · t_O_2 = 1800 t_O_2 = (1800)/(18) t_O_2 = 100 sec It would take 100 seconds for the same volume of oxygen to diffuse. The final answers are: 1) The relative molecular mass of the unknown gas is 52.51 g/mol. 2) The time taken for oxygen to diffuse is 100 seconds. Send me the next one 📸