vacuum question?

Question

Current vacuum technology can achieve a pressure of
1.0 x 10^(-10) of Hg. At this pressure, and at a temperature of 30.0 degrees C, how many molecules are in 5.00 cm cubed ?

Answer 1

I assume it was mm of Hg.
At STP (Standard Temperature and Pressure), 1 liter of gas contains N avogadro molecules, which is 1 mole. T = 0 C, P = 760 mm Hg.

If you were to expand 1 mole of gas to the pressure of 10E-10 mm Hg:
P1V1 = P2V2,
760 *1 Liter = 10E-10*x liters
x = 760*10^10 liters

Now, if you were to warm up this gas from 0 C to 30 C
V1/T1 = V2/T2
760*10^10/273 = V2/303
V2 = 843.5 *10^10

Now you can use proportion:
The volume of 843.5*10^10 * 10^3 cm^3 contains 6*10^23 molecules;
5 cm^3 contains n molecules

843.5*10^10/6*10^23 = 5/n

Find n:
n = 3.5 10E8