3.899*10^23 for a is incorrect 1443.1856 for c is incorrect I have no idea what

Question

3.899*10^23 for a is incorrect
1443.1856 for c is incorrect
I have no idea what I'm doing wrong

a) The molecular mass of helium is 4 g/mol,
the Boltzmann’s constant is 1.38066 ×
10-23 J/K, the universal gas constant is
8.31451 J/K · mol, and Avogadro’s number
is 6.02214 × 1023 1/mol. Given: 1 atm =
101300 Pa.
How many atoms of helium gas are required
to fill a balloon to diameter 31 cm at 49C and
1.799 atm?

b) What is the average kinetic energy of each
helium atom?
Answer in units of J

c) What is the rms speed of each helium atom?
Answer in units of m/s

Explanation / Answer

Molecular mass of He is M = 4g/mol The Boltzmann’s constant is k = 1.38066*10^-23 J/K The universal gas constant is R = 8.31451 J/K · mol Avogadro’s number is N = 6.02214*10^23 /mol 1 atm = 101300 Pa 1) Applying ideal gas law PV = nkT n is number of particles of gas P = 1.799 atm = 182238.7 Pa V = 4/3 p(0.155)^3 = 0.0155 m^3 temperature of the gas is T = 49 C = 322 K The number of He atoms in the balloon is n = PV/kT = (182238.7 Pa) *(0.0155 m^3) / (1.38066*10^-23 J/K) * (322 K) = 6.35*10^23 ---------------------------------------------------------------------------------------------------------------- (2) The average kinetic energy of each He atom KEatom = (3/2)*kT KEatom = 1.5(1.38066*10^-23 J/K) * 322 K KEatom = 6.67*10^-21 J ------------------------------------------------------------------------------------------------------------------ (3) Root Men Square speed is given by vrms = v(3RT/M) vrms = v[3*(8.31451 J/K · mol)(322 K)/(0.004 kg/mol)] vrms = 1417 m/s

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