The best laboratory vacuum has a pressure of about 1.00 x 10^-18 atm, or 1.01 x 10^-13 pa. how many gas molecules are in 9.28 cm^3 in such a vacuum at 332 k?

204.5 molecules

Explanation:

Pressure, P = 1.01 x 10^-13 Pa

Volume, V = 9.28 cm^3 = 9.28 x 10^-6 m^3

Temperature, T = 332 K

Gas constant, R = 8.314 in MKS system

Let n be the number of moles

Use ideal gas equation

P x V = n x R x T

1.01 x 10^-13 x 9.28 x 10^-6 = n x 8.314 x 332

n = 3.396 x 10^-22

According to the Avagadro's law

1 mole of the substance contains = 6.023 x 10^23 molecules

so, 3.396 x 10^-22 moles contains = 6.023 x 10^23 x 3.396 x 10^-22

                                                         = 204.5 molecules

the force required to move the cart is divided by three or 33.33 n.