Question

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A sample of Oxygen occupies 33.6 L under STP conditions. Find: a) How many moles of gas are in the sample? b) How many molecules are there in the gas? c) What is the average kinetic energy of a molecule? d) What is the total kinetic energy? e). what is the rms speed of oxygen molecules at this temperature? Problem 4

Answer 1

The molar volume of a gas at STP is equal to 22.4 L for 1 mole of any ideal gas. (T = 273.15 k P = 1 atm) (a) 1 mol occupies 22.4 L No. of moles in 33.6 L = 1.5 moles (b) 1 moles contains 6.022 times 10^23 atoms/molecules 1.5 mole contains 1.5 times 6.022 times 10^23 = 9.033 times 10^23 molecules (c) A molecule of Oxygen is diatomic At STP, the average kinetic energy per molecule = 3/2 KT k = Boltzmann constant = 3/2 times 1.38 times 10^- 23 times 273.15 K.E = 5.65 times 10^- 21 g \r\n (b) Total kinetic energy is average kinetic energy of a molecule multiplied by number of molecules in the sample Total kinetic energy = 3/2 NKT N = 9.033 times 10^23 Total K.E = 5.65 times 10^- 21 times 9.033 times 10^23 g = 51.03 times 10^2 = 5103 g = 5.1 kJ/mol (e) rms speed = squareroot 3 RT/M M = molecular mass For Oxygen M = 0.032 kg/mol T = 273 K R = 8.314 kg m^2/s^2/k mol = squareroot 3 times 8.314 times 273/0.032 V_rms = 461.3 m/s