I. Filling the blanks The number of particles in a cubic millimeter of a gas at temperature 273 K and 1.00 atm pressure is 2.69x10. To get a feeling for the order of magnitude of this number the age of the universe in seconds assuming it is 15 billion years old is 4.37x107 ntIon The number of particles is N=nN PV=nRT .、1×1013×105×1×10°×602×103 N=nN-Pv =269×106 8.315×273 The age of the universe in seconds is 15×10°×365×24×60×60=437×10(s) 2. A sample of oxygen gas (O2)is at temperature 300 K and 1.00 atm pressure. One molecule, with a speed equal to the rms speed, makes a head-on elastic collision with your nose. Ouch! The magnitude of the impulse imparted to your schnozzle is 5.- Kg m/s Solution The speed of an oxygen molecule is 3R/y/2=3×8315×300y2=483.59m/s) 32×10 Using the Impulse-Momentum Theorem, the magnitude of the impulse imparted to the schnozzle M2×32×10-3×483.59 Ⅰ=△P=2mv=2 =514×102(Kgm/s) 6.02×10 3. When helium atoms have an rms speed equal to the escape speed from the surface of the earth (escape=11.2 km/s), the temperature is_2.01x10K Ition According to the problem vm=(.-) 50=M201240)x4=201k 3×8.315 4 The rms speed of hydrogen gas(H2)at temperature 300 K in the atmosphere is- 1.93x10-km/ Compare it with the escape speed from the Earth(11. 2 km/s). Since hydrogen is the least massive gas, hydrogen molecules will have the highest rms speeds at a given temperature. How can this calculation explain why there is essentially no hydrogen gas in the atmosphere of the earth?II. Filling the Blanks 1. The number of particles in a cubic millimeter of a gas at temperature 273 K and 1.00 atm pressure is 2.69×1016 . To get a feeling for the order of magnitude of this number, the age of the universe in seconds assuming it is 15 billion years old is 4.37×1017 s . Solution: The number of particles is A N = nN Q PV = nRT 16 5 9 23 2.69 10 8.315 273 1 1.013 10 1 10 6.02 10 = × × × × × × × × ∴ = = = − A NA RT PV N nN The age of the universe in seconds is 15 10 365 24 60 60 4.37 10 (s) 9 17 × × × × × = × 2. A sample of oxygen gas (O2) is at temperature 300 K and 1.00 atm pressure. One molecule, with a speed equal to the rms speed, makes a head-on elastic collision with your nose. Ouch! The magnitude of the impulse imparted to your schnozzle is 5.14×10-23 Kg m/s . Solution: The speed of an oxygen molecule is ) 483.59(m/s) 32 10 3 8.315 300 ) ( 3 ( 1/ 2 3 1/ 2 = × × × = = = − M RT v vrms Using the Impulse-Momentum Theorem, the magnitude of the impulse imparted to the schnozzle is 5.14 10 (Kg m/s) 6.02 10 2 32 10 483.59 2 2 23 23 3 = × ⋅ × × × × = ∆ = = = − − − v N M I P mv A 3. When helium atoms have an rms speed equal to the escape speed from the surface of the Earth (vescape = 11.2 km/s), the temperature is 2.01×104 K . Solution: According to the problem 1/ 2 ) 3 ( M RT vrms = So the temperature is 2.01 10 (K) 3 8.315 (11.2 10 ) 4 10 3 4 2 3 2 3 = × × × × × = = − R v M T rms 4 The rms speed of hydrogen gas (H2) at temperature 300 K in the atmosphere is 1.93×103 km/s . Compare it with the escape speed from the Earth (11.2 km/s). Since hydrogen is the least massive gas, hydrogen molecules will have the highest rms speeds at a given temperature. How can this calculation explain why there is essentially no hydrogen gas in the atmosphere of the Earth?