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In a gas at standard temperature and pressure, what is the length of the side of a cube that contains a number of molecules equal to the population of the earth (about 7.0 billion people at present)? Express your answer using two significant figures. Answer is in meters.
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Given temperature , T = standard temperature = 273 K

Given pressure , P = Standard pressure = 100kPa = 105 Pa

Given number of molecules = 7 billion = 7*109 molecules

Number of molecules in 1 mole = 6.02*1023 molecules,

So, number of moles, n = (7*109)/(6.02*1023) = 1.16*10-14

Using ideal gas equation and putting R = 8.314 JK-1mol-1 , we get :

PV = nRT, we get :

V = nRT/P = 1.16*10-14*8.314*273/105 = 263.2*10-18 m3

So, (side)3 = 263.2*10-18

So, side = (263.2*10-18)1/3 = 6.4*10-6 m
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