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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You're on a roll — Step 1: State Graham's Law of Diffusion and calculate the molar mass of sulphur dioxide. Graham's Law of Diffusion 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)) Where r_1 and r_2 are the rates of diffusion of gas 1 and gas 2, and M_1 and M_2 are their respective molar masses. The molar mass of sulphur dioxide (SO_2): Molar mass of S = 32.06 g/mol Molar mass of O = 15.999 g/mol Molar mass of SO_2 = 32.06 + (2 × 15.999) = 64.058 g/mol Step 2: Set up the equation using the given diffusion rates. Let the hydrocarbon be gas 1 and sulphur dioxide be gas 2. Given that the hydrocarbon diffuses twice as quickly as sulphur dioxide: r_hydrocarbon = 2 × r_SO_2 So, r_hydrocarbonr_SO_2 = 2 Using Graham's Law: 2 = sqrt(M_SO)_2M_hydrocarbon 2 = sqrt(64.058 g/mol)M_hydrocarbon Step 3: Solve for the molar mass of the hydrocarbon. Square both sides of the equation: 2^2 = 64.058 g/molM_hydrocarbon 4 = 64.058 g/molM_hydrocarbon Rearrange to solve for M_hydrocarbon: M_hydrocarbon = 64.058 g/mol4 M_hydrocarbon = 16.0145 g/mol Step 4: Determine the molecular formula of the hydrocarbon. The general formula for the hydrocarbon is C_nH_2n+2. The molar mass of carbon (C) is 12.011 g/mol. The molar mass of hydrogen (H) is 1.008 g/mol. So, the molar mass of C_nH_2n+2 is: (n × 12.011) + ((2n+2) × 1.008) = 16.0145 12.011n + 2.016n + 2.016 = 16.0145 14.027n + 2.016 = 16.0145 14.027n = 16.0145 - 2.016 14.027n = 13.9985 n = (13.9985)/(14.027) ≈ 0.9979 ≈ 1 Since 'n' must be an integer, n=1. Substitute n=1 into the formula C_nH_2n+2: C_1H_(2 × 1)+2 = CH_4 The molecular formula of the hydrocarbon is CH_4. Got more? Send 'em 📸