10.59 What is the root-mean-square speed of the N2(g) molecule at 100. K and at 500. K?
10.60 What is the root-mean-square speed of the CO2(g) molecule at 125 K and at 650. K?
10.61 At what temperature would the root-mean-square speed of the NO(g) molecule equal the root-mean-square speed of the N2(g) molecule at 300. K?
10.62 At what temperature would the root-mean-square speed of the F 2(g) molecule equal the root-mean-square speed of the Cl(g) molecule at 400. K?

Understanding Root-Mean-Square Speed (urms) The root-mean-square speed is a measure of the average speed of gas molecules. It's calculated using the following equation:urms = √(3RT/M) Where:urms is the root-mean-square speed (m/s)R is the ideal gas constant (8.314 J/mol·K)T is the temperature (in Kelvin)M is the molar mass of the gas (in kg/mol) Calculations10.59 N2(g)Molar mass of N2 = 28.02 g/mol = 0.02802 kg/molAt 100 K:urms = √(3 * 8.314 J/mol·K * 100 K / 0.02802 kg/mol)urms ≈ 296 m/s- At 500 K:urms = √(3 * 8.314 J/mol·K * 500 K / 0.02802 kg/mol)urms ≈ 661 m/s 10.60 CO2(g)Molar mass of CO2 = 44.01 g/mol = 0.04401 kg/molAt 125 K:urms = √(3 * 8.314 J/mol·K * 125 K / 0.04401 kg/mol)urms ≈ 265 m/sAt 650 K:urms = √(3 * 8.314 J/mol·K * 650 K / 0.04401 kg/mol)urms ≈ 578 m/s 10.61 NO(g) and N2(g)We need to find the temperature at which the urms of NO is equal to the urms of N2 at 300 K.First, calculate the urms of N2 at 300 K: urms (N2) = √(3 * 8.314 J/mol·K * 300 K / 0.02802 kg/mol) urms (N2) ≈ 517 m/sNow, set up the equation for NO and N2 with equal urms: √(3RTNO/MNO) = √(3RTN2/MN2)Since urms is the same, we can cancel out the square root and the 3R: TNO/MNO = TN2/MN2Molar mass of NO = 30.01 g/mol = 0.03001 kg/molSolve for TNO: TNO = (TN2 * MNO) / MN2 TNO = (300 K * 0.03001 kg/mol) / 0.02802 kg/mol TNO ≈ 321 K 10.62 F2(g) and Cl(g)We need to find the temperature at which the urms of F2 is equal to the urms of Cl at 400 K.First, calculate the urms of Cl at 400 K: urms (Cl) = √(3 * 8.314 J/mol·K * 400 K / 0.03545 kg/mol) urms (Cl) ≈ 544 m/sNow, set up the equation for F2 and Cl with equal urms: √(3RTF2/MF2) = √(3RTCl/MCl)Since urms is the same, we can cancel out the square root and the 3R: TF2/MF2 = TCl/MClMolar mass of F2 = 38.00 g/mol = 0.03800 kg/molSolve for TF2: TF2 = (TCl * MF2) / MCl TF2 = (400 K * 0.03800 kg/mol) / 0.03545 kg/mol TF2 ≈ 428 KSummary:1. N2Temperature: 100 Kurms: 296 m/s 2. N2Temperature: 500 Kurms: 661 m/s3. CO2Temperature: 125 Kurms: 265 m/s4. CO2Temperature: 650 Kurms: 578 m/s5. NOTemperature: 321 Kurms: 517 m/s6. F2temperature: 428 Kurms: 544 m/s

Answered by alixzamarirapacon | 2024-10-20