Chemistry: The Central Science (13th Edition)

Published by Prentice Hall
ISBN 10: 0321910419
ISBN 13: 978-0-32191-041-7

Chapter 10 - Gases - Exercises - Page 437: 10.66

Answer

2.13 x 10^{16} molecules Ne 2.13 x 10^{16} molecules He 1.770 x 10^{23} molecules Xe

Work Step by Step

PV=nRT given: P= 500 torr 500 torr ÷ 760 torr = .65789 atm P= .65789 atm given: dimensions of tv screen are 0.900 mm x 0.300 mm x 10.0 mm to find V: multiply the lengths to get the V 0.900 mm x 0.300 mm x 10.0 mm = 2.70 mm^{3} convert to L 2.70 mm^{3} ÷ 10 = .270 cm^{3} .270 cm^{3} = .270 mL .270 mL ÷ 1000 = 2.7 x 10^{-6} V= 2.7 x 10^{-6} You are making an assumption for T because it is in a room, you are assuming it is room temperature. 21 °C + 273= 294 K T = 294 K Now that we have P, V, and T, we can find total n (moles): (.65789 mol)(2.7 x 10^{-6} L)= n (0.0820582 Lxatm/Kxmol)(294) solve for n total and get n= 7.36 x 10^{-8} given: Xe is 4%. So multiply n total by .04 to get mol Xe 7.36 x 10^{-8} x .04 = 2.944 10^{-9} mol Xe to get mol Ne and He we multiply total n by 48% because it's given that their mole ratio is 1:1 and Xe has the other 4% 7.36 x 10^{-8} x .48 = 3.53 x 0^{16} mol He 7.36 x 10^{-8} x .48 = 3.53 x 0^{16} mol Ne Just multiply the mol of Xe, He, and Ne by Avogadro's number to get number of molecules 2.944 x 10^{-9} mol Xe x 6.02 x 10^{23}= 1.770 x 10^{23} molecules Xe 3.53 x 0^{16} mol He = 2.13 x 10^{16} molecules He 3.53 x 0^{16} mol Ne = 2.13 x 10^{16} molecules Ne
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