Question

An expensive vacuum system can achieve a pressure as low as 1.00 × 10 − 8 N / m 2 at 19.5 °C . How many atoms are there in a cubic centimeter at this pressure and temperature?

Answer 1

Answer:

2475042

Explanation:

P = Pressure = [/tex]1\times 10^{-8}\ N/m^2[/tex]

V = Volume = 1 cm³

T = Temperature = 19.5 °C

R = Gas constant = 8.341 J/mol K

$N_A$ = Avogadro's number = $6.022\times 10^{23}$

n = Amount of substance

From ideal gas law we have

$PV=nRT\\\Rightarrow n=\frac{PV}{RT}\\\Rightarrow n=\frac{1\times 10^{-8}\times 1\times 10^{-6}}{8.314(273.15+19.5)}\\\Rightarrow n=4.11\times 10^{-18}$

Number of atoms is given by

$n\times N_A\\ =4.11\times 10^{-18}\times 6.022\times 10^{23}\\ =2475042\ atoms$

The number of atoms in this vacuum is 2475042