Gas Laws (Space Shuttle)

Gas pressure outside the space shuttle is approximately $1*10^{-14}$ at a temperature of approximately $1$ K. If the gas is almost entirely hydrogen atoms (H, not H2), what volume of space is occupied by 1 mol of atoms? (answer in L)

Part two:

What is the density of H gas in atoms per liter? (answer in atoms/L)

The equation of perfect gases is

$P*V = n*R*T$ where P is the pressure of the gas, V its volume, n the number of moles of gas, R is the gas constant ($8.31 J/(mol*K)$) the Boltzmann constant and T the absolute temperature

(given the pressure in p=10^-14 N/m^2)

$V = n*R*T/P = 8.314*1/10^{-14} = 8.314*10^{14} m^3$

In normal conditions 1 mol of perfect gas (hydrogen) occupies 22.4 liter

density $= 1/22.4$ mole/Liter = $6.023*10^{23}/22.4$ atoms/liter $= 0,269*10^{23}$ atoms/Liter