Any help on this three part question would be great! The molecular mass of heliu

Question

Any help on this three part question would be great!

The molecular mass of helium is 4 g/mol, the Boltzmann's constant is 1.38066 Times 10-23 J/K, the universal gas constant is 8.31451 J/K mol, and Avogadro's number is 6.02214 Times 1023 1/mol. Given: 1 atm = 101300 Pa. How many atoms of helium gas are required to fill a balloon to diameter 38 cm at 56 degrees C and 1.734 atm? What is the average kinetic energy of each helium atom? Answer in units of J What is the rms speed of each helium atom? Answer in units of m/s

Explanation / Answer

1)

Here ,

volume of tank , V = 3.141 * 4 * (38/2)^3/3

V = 28725.4 cm^3 = 28.73 Litre

using ideal gas equation

PV = n*RT

28.73 * 1.734 = n * (56 + 273) * 0.0821

n = 1.85

the number of moles is 1.85

2)

Kinetic energy = 1.5 kT

Kinetic energy = 1.5 * 1.38 *10^-23 * (56 + 273)

Kinetic energy = 6.81 *10^-21 J

C)

For Vrms

0.5 * m * Vrms^2 = KE

0.5 * 4 * 1.67 *10^-27 * Vrms^2 = 6.81 *10^-21

Vrms = 1427.2 m/s

the rms speed is 1427.2 m/s

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