Question

A high vacuum pump can achieve pressures of 10^-11 atm. How many particles are there per cm^3 at this pressure? (Take 1atm= 101,000 Pa)

Answer 1

Real gas at low pressure can be assumed as an ideal gas. For an ideal gas we have (Ideal gas law):
PV=nRT which can be expressed as:
n/V =P/RT
where, n is the amount of gas in moles. we can convert the moles to the number of atoms using Avogadro's number (n mol=n mol* 6.022*10^23atom/1mol) and R is gas constant.

R=8.314472 cm^3 MPa/mol.K

P=10^-11 atm *101000 Pa= 1.01*10^-12 MPa

so by substituting the given values in the equation we have,

n/V=1.01*10^(-12) MPa / (8.314472 cm^3 MPa/mol.K *292K) = 4.1601*10^(-16) mole/cm3

multiply with 6.022*10^23

= 25.05 * 10^7 atom/cm3