# HW1_key - HW#1 Key 6 Q Research in surface science is...

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HW #1 Key 1/21/2011 6. Q. Research in surface science is carried out using ultra-high vacuum chambers that can sustain pressures as low as 10 -12 torr. How many molecules are there in a 1.00cm 3 volume inside such an apparatus at 298K? What is the corresponding molar volume 𝑉 at this pressure and temperature? A. Assume Ideal gas behavior, 𝑃𝑉 𝑅𝑇 = ? Inserting the appropriate constants for the units, 10 12 𝑡?𝑟𝑟 (1.00 ?? 3 ) 82.058 ?? 3 ∗ ?𝑡? ∗ ??? 1 ∗ 𝐾 1 760 𝑡?𝑟𝑟 ∗ ?𝑡? 1 (298 𝐾 ) = ? Gives 3.24x10 4 molecules in 1 cubic centimeter inside the apparatus. The molar volume, 𝑉 = 𝑉 ? where n is the number of moles, or our solution from above divided by Avogadro’s number is 𝑉 = 1.00 ?? 3 5.38 10 20 ??? = 1.86 10 19 ?? 3 ∗ ??? 1 11. Q. It takes 0.3625 g of nitrogen to fill a glass container at 298.2K and 0.0100 bar pressure. It takes 0.9175 g of an unknown homonuclear diatomic gas to fill the same bulb under the same condidtion, what is the gas?

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