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
Hey ThegirlGodishelping🥰💙🫠, good to see you again. Here are the calculations for the given problem: a) The mean translational kinetic energy of the molecules Step 1: Convert the temperature from Celsius to Kelvin. T = 27^ C + 273.15 = 300.15 K Step 2: Calculate the mean translational kinetic energy using the formula E_k = (3)/(2) k_B T, where k_B is the Boltzmann constant (1.38 × 10^-23 J/K). E_k = (3)/(2) (1.38 × 10^-23 J/K) (300.15 K) E_k = 1.5 × 1.38 × 10^-23 × 300.15 J E_k = 6.21 × 10^-21 J The mean translational kinetic energy of the molecules is 6.21 × 10^-21 J. b) The root-mean-squared speed of the oxygen molecules Step 3: Calculate the mass of an oxygen molecule. The mass of a hydrogen molecule is 3.34 × 10^-27 Kg, and an oxygen molecule is 16 times more massive. m_O = 16 × (3.34 × 10^-27 Kg) m_O = 53.44 × 10^-27 Kg Step 4: Calculate the root-mean-squared speed (v_rms) for oxygen molecules using the formula v_rms = sqrt((3 k_B T)/(m_O)). v_rms,O = sqrt(3 × (1.38 × 10^-23) J/K) × (300.15 K)53.44 × 10^-27 Kg v_rms,O = sqrt(1242.621 × 10^-23)53.44 × 10^-27 m/s v_rms,O = sqrt(23.25339 × 10^4) m/s v_rms,O = sqrt(232533.9) m/s v_rms,O = 482 m/s The root-mean-squared speed of the oxygen molecules is 482 m/s. Send me the next one 📸