A.)Consider neon, a noble gas whose molecules consist of single atoms of atomic

Question

A.)Consider neon, a noble gas whose molecules
consist of single atoms of atomic mass0.02 kg/mol.
Avogadro’s number is 6.02 × 1023 mol-1,
and Boltzmann’s constant is 1.38×10-23 J/K.
What is the average kinetic energy of a
neon atom when the gas is at a temperature
of 270 K?
Answer in units of J.

B.)What is the root-mean-square speed of a neon
atom under such conditions?
Answer in units of m/s.

C.) The internal energy of a monoatomic ideal gas
such as neon is simply the total kinetic energy
of all its atoms.
What is the internal energy of 5 liters of
neon at a temperature of 270 K and pressure
of 1.17 atm?
Answer in units of J.

Explanation / Answer

A. average kinetic energy for monatomic gas is (3/2)kT =

(1.5)(1.38 * 10-23 J/K)(270 K) = 5.589 * 10-21 J

B. To get RMS speed equate (1/2)mv2 = 5.589 * 10-21 J

mass m of a neon atom is (0.0201797 kg/mol)/(6.02 * 1023 atom/mol)  = 3.351 * 10-26 kg

Using that mass and solving for v, v = 577.6 m/s

C. molar gas volume is 22.414 l/mol at 273K and 1 atm; at 270K and 1.17 atm using V = nRT/P, molar gas volume is (22.414)(270/273)/1.17 = 18.947 l/mol

therefore 5 l is 0.2639 mol or 1.59 * 1023 atoms; total energy is 888 J

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