##### (a) An ideal gas occupies a volume of 1.8 cm3 at 20°C and atmospheric pressure.

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(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?

Jun 21st, 2015

Thank you for the opportunity to help you with your question!

PV = nRT
n = PV/RT

P = 1.00 atm
V = 1.8 cm³ = 1.8 cm³ x (1 mL / 1 cm³) x (1 L / 1000 mL) = 0.0018 L
R = 0.0821 Latm/moleK
T = 20C = 20+273.15 = 293.15K

n = (1.00 atm) x (0.0018 L) / [ (0.0821 Latm/moleK) x (293.15K) ]
n = 7.48x10^-5 moles..

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

you should probably only have 2 sig figs since 1.8 has 2 and 20 has at most 2.....

# molecules = 4.5x10^19

b)

using the same formula, we get

1atm=10^5 Pa

2.4 ✕ 10−11 Pa= ?

= 2.4 X10−11 / 10^5 atm

n = (2.4 ✕ 10−11/10^5) x (0.0018 L) / [ (0.0821 Latm/moleK) x (293.15K) ]

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 21st, 2015

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Jun 21st, 2015
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Jun 21st, 2015
May 29th, 2017
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