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 r2 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