#### Answer

(a) The pressure in the vacuum chamber is a fraction of $1.3\times 10^{-13}$ of the atmospheric pressure.
(b) The number of molecules is $1.23\times 10^{11}$

#### Work Step by Step

(a) We can convert the pressure in the vacuum chamber to units of atm.
$P = (1.0\times 10^{-10}~mm~Hg)(\frac{1~atm}{760~mm~Hg})$
$P = 1.3\times 10^{-13}~atm$
The pressure in the vacuum chamber is a fraction of $1.3\times 10^{-13}$ of the atmospheric pressure.
(b) We can find the volume of the cylinder.
$V = \pi~R^2~h$
$V = (\pi)(0.20~m)^2(0.30~m)$
$V = 0.0377~m^3$
We can find the number of molecules.
$PV = NkT$
$N = \frac{PV}{kT}$
$N = \frac{(1.3\times 10^{-13}~atm)(\frac{1.013\times 10^5~Pa)}{1~atm})(0.0377~m^3)}{(1.38\times 10^{-23}~J/K)(293~K)}$
$N = 1.23\times 10^{11}~molecules$
The number of molecules is $1.23\times 10^{11}$.