Question

An expensive vacuum system can achieve a pressure as low as 1.03 ✕ 10−7 N/m2 at 22°C. How many atoms are there in a cubic centimeter at this pressure and temperature? atoms =

Answer 1

25 300 000 atom / cm³

Step-by-step explanation:

Given:

p = 1.03·10⁻⁷ N/m²

t = 22⁺C

_____________

n - ?

1)

Temperature in Kelvin:

T = 273 + t = 273 + 22 = 295 K

2)

Basic equation of molecular kinetic theory:

p = n·k·T

k = 1.38·10⁻²³ J/K - Boltzmann constant

n = p / (k·T)

n = 1.03·10⁻⁷ / (1.38·10⁻²³·295) ≈ 2.53·10¹³ atom / m³

or

n = 2.53·10¹³ ·1·10⁶ = 2.53·10⁷ atom / cm³

or

n = 25 300 000 atom / cm³