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