A spherical balloon with a radius of 10.4 cm is filled with oxygen gas at atmosp

Question

A spherical balloon with a radius of 10.4 cm is filled with oxygen gas at atmospheric pressure and at a temperature of 13.8°C. (a) What is the number of molecules of oxygen in the balloon? 6.40 Incorrect: Your answer is incorrect. Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. molecules (b) What is the average kinetic energy of oxygen in the balloon? 5.94e-21 Correct: Your answer is correct. J (c) What is the rms speed of oxygen in the balloon? m/s

Explanation / Answer

(a) Use the formula, T = 273+13.8 = 286.8 K

PV = n R T
1 x ( 4/3 ) x pi x (0.104)^3 = n x 0.0821 x 286.8 where n= moles of O2

=> n = 2.0007x10^-4 moles

So, no. of molecules = 2.0007x10^-4x6.022x10^23 = 1.205x10^20

(b) Average kinetic energy of oxygen in the ballon = (3/2)*Kb*T*n = 1.5*1.38x10^-23*286.6*2.0007x10^-4 = 1186.94x10^-27 = 1.19x10^-24 J

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