A plasma-screen TV contains thousands of tiny cells filled with a mixture of Xe,

Question

A plasma-screen TV contains thousands of tiny cells filled with a mixture of Xe, Ne, and Hegases that emits light of specific wavelengths when a voltage is applied. A particular plasma cell, 0.900 mm×0.300mm×10.0mm, contains 4.00%Xe in a 1:1 Ne : He mixture at a total pressure of 500. torr.
Assumptions: In order to calculate total moles of gas and total atoms, we assumed a reasonable room temperature. Since '4.00% Xe' was not defined, we conveniently assumed mole percent. The 1:1 relationship of Ne to He is assumed to be by volume and not by mass. Part A) Calculate the number of Xe atoms in the cell. Part B) Calculate the number of Ne atoms in the cell. Part C) Calculate the number of He atoms in the cell.

Explanation / Answer

First calculate the volume as follows:

V total = 0.900 mm×0.300mm×10.0mm

V total = 2.7mm^3
Now, convert to Liters

2.7mm ^3 = 2.7 * 10^-6 Liters

and here pressure = 500. torr

convert the unit of pressure from torr to atm,
(500 torr) * (1 atm ÷ 760 torr) =0 .658 atm

room temperature is assumed to be 25 degrees celcius, or 298 K


apply ideal gas equation
PV = nRT
Therefore, n = PV ÷ RT,

n = [(2.7*10^-6 Liters)(0.658 atm)] ÷ [(0.08206)(298)]
n = 7.27 * 10^-8

this number reflects total moles present in plasma.

and given that, contains 4.00%Xe in a 1:1 Ne : He mixture



(a) To find Xe atoms, multiply the n value by 4 percent. So,

Moles of Xe=
(7.27 * 10^-8 )(4%) = 2.91*10^-9,

To calculate the number of moles , multiply by Avogadro's number as follows:

[(2.91 *10^-9)(6.022*10^23)] = 1.75*10^15 Xe atoms

now calculate the total number of moles of Ne and He in the mixture as follows:

total number of moles – number of Xe
7.27 * 10^-8 - 2.91*10^-9 = 6.679*10^-8

As Ne and He are in a 1:1 ratio, divide this number by two.
6.979*10^-8 ÷ 2 = 3.4895*10-8 moles

To calculate the number of moles , multiply by Avogadro's number as follows:

[(3.4895*10-8 moles)(6.022*10^23)] = 2.10*10^16
thus atoms of Ne = atoms of He = 2.10*10^16

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