J.R. S. answered • 11/12/20

Ph.D. University Professor with 10+ years Tutoring Experience

To find the grams of a gas (Ne), we can use the ideal gas law PV = nRT and solve for n (moles) and then convert that to moles. To do that in the present problem, we will first have to find the volume (V) of the sign.

Consider the sign to be a cylinder and the volume is V = π r^{2} h where π is pi, r is the radius and h is the height.

π = 3.1416

r = 1/2 x 2.5 cm = 1.25 cm

h = 5.5 m x 100 cm / m 550 cm

V = (3.1416)(1.25 cm)^{2}(550 cm) = 2699.8 cm3

Now, using the ideal gas law, we can find moles (n):

PV = nRT

n = PV/RT

P = pressure in atm = 1.78 torr x 1 atm/760 torr = 0.00234 atm

V = volume in liters = 2699.8 cm3 = 2.6998 L

R = gas constant = 0.0821 Latm/Kmol

T = temperature in K = 35 + 273 = 308K

n = (0.00234)(2.6998) / (0.0821)(308)

n = 2.498x10^{-4} moles of Ne

grams of Ne = 2.498x10^{-4} moles of Ne x 20.2 g Ne/mol = 5.0x10^{-3} g Ne