Question

How many atoms of helium gas fill a spherical balloon of diameter 30.0 cm at 20.08 oC and 1.00atm? What is the average kinetic energy of the helium?

Answer 1

$V=(4/3)\pi r^3=(4/3)\cdot3.14\cdot 0.3^3=0.113(m^3)$

$pV=\nu RT\to pV=\frac{N}{N_A} RT\to$

$N=\frac{pVN_A}{RT}=\frac{101325\cdot 0.113\cdot 6.02\cdot10^{23}}{8.31\cdot 293.08}=2.83\cdot10^{24}$ atoms. Answer

The average kinetic energy of motion of a helium molecule

$E_{avg}=\frac{3}{2}kT=\frac{3}{2}\cdot 1.38\cdot 10^{-23}\cdot 293.08=607\cdot10^{-23}\ (J)$