Answer:
4.58×10²³ atoms
5.94×10⁻²¹ J
1340 m/s
Explanation:
Use ideal gas law to find moles of gas.
PV = nRT
(1.266 atm × 101300 Pa/atm) (4/3 π (0.15 m)³) = n (8.31451 J/mol/K) (14 + 273) K
n = 0.760 mol
Use Avogadro's number to find number of atoms.
(0.760 mol) (6.02214×10²³ atom/mol) = 4.58×10²³ atoms
Average kinetic energy per molecule is:
KE = 3/2 kT
KE = 3/2 (1.38066×10⁻²³ J/K) (14 + 273) K
KE = 5.94×10⁻²¹ J
RMS speed of each atom is:
KE = 1/2 mv²
5.94×10⁻²¹ J/atom = 1/2 (0.004 kg/mol) (1 mol / 6.02214×10²³ atom) v²
v = 1340 m/s
