This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given values and convert units. Temperature, T = 300 K Molar mass of hydrogen (H₂), M = 2.016 g/mol Ideal gas constant, R = 8.314 J mol^-1 K^-1 Convert the molar mass from g/mol to kg/mol: M = 2.016 g/mol × 1 kg1000 g = 0.002016 kg/mol Step 2: Use the formula for the root mean square (RMS) speed of a gas. The formula is: v_rms = sqrt((3RT)/(M)) Step 3: Substitute the values into the formula and calculate. v_rms = sqrt(3 × 8.314 J mol)^-1 K^-1 × 300 K0.002016 kg mol^-1 v_rms = sqrt(7482.6 J mol)^-10.002016 kg mol^-1 Since 1 J = 1 kg m^2 s^-2, the units simplify to m^2 s^-2: v_rms = sqrt(7482.6 kg m)^2 s^-20.002016 kg v_rms = sqrt(3711607.142857 m)^2 s^-2 v_rms ≈ 1926.558 m/s Step 4: Round the answer to an appropriate number of significant figures (e.g., 4 significant figures). v_rms ≈ 1927 m/s The root mean square speed of hydrogen molecules at 300 K is: 1927 m/s