(a) An ideal gas occupies a volume of 1.8 cm3 at 20°C and atmospheric pressure. Determine the number of molecules of gas in the container.

molecules

(b) If the pressure of the 1.8-cm3 volume is reduced to 2.4 ✕ 10−11 Pa (an extremely good vacuum) while the temperature remains constant, how many moles of gas remain in the container? mol

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we know that PV = nRT ; therefore n = PV/RT
P = 1.00 atm ; V = 1.8 cm³ =0.0018 Liters ; R = 0.0821 L atm/mole K
T = 20°C = 293.15K

n = (1.00) x (0.0018) / [ (0.0821) x (293.15K) ]
n = 7.48x10^(-5) moles

7.48x10^(-5) x (6.022x10^23 / 1 ) = 4.50x10^(19) molecules.

(B) P = 2.4 x10 ^(-11) Pa = 2.4 x10^(-11) x 9.9 × 10^{-6} atm = 23.76 x 10^(-17) atm

; V = 1.8 cm³ =0.0018 Liters ; R = 0.0821 L atm/mole K

n = (23.76 x 10^(-17)) x (0.0018) / [ (0.0821) x (293.15K) ]
n =0.00177 x10^(-17) or 1.77 x 10^(-20) moles

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