Question

An expensive vacuum system can achieve a pressure as low as 1.53 ✕ 10−7 N/m2 at 26°C. How many atoms are there in a cubic centimeter at this pressure and temperature?

Answer 1

The value is
`N = 3.708*10^(7) \ \ atoms`

Step-by-step explanation:

From the question we are told that

The pressure is
`P = 1.53 *10^(-7) \ N/m^2`

The temperature is
`T = 26 + 273 = 299 \ K`

The volume is 1 cubic cm =
`1 * 10^(-6) m^3`

Generally according to the ideal gas law we have that

`PV = NkT`

here k is the Boltzmann constant with a value
`k = 1.38 *10^(-23) \ J/K`

=>
`N = (PV)/( k T)`

=>
`N = ( 1.53 *10^(-7) * (1* 10^(-6)))/( 1.38*10^(-23) * 299)`

=>
`N = 3.708*10^(7) \ \ atoms`