A neon sign is made of glass tubing whose inside diameter is 2.5 cm
and whose length is 5.5 m
.If the sign contains neon at a pressure of 1.74 torr
at 38 ∘C
, how many grams of neon are in the sign? (The volume of a cylinder is πr2h
.)
To find the number of grams of neon in the sign, we first need to calculate the volume of neon gas using the ideal gas law:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the pressure to atm:
1.74 torr = 1.74/760 atm = 0.00228 atm
Next, we calculate the volume of the neon gas in the sign:
r = 2.5 cm / 2 = 1.25 cm = 0.0125 m
h = 5.5 m
V = π(0.0125 m)^2 * 5.5 m
V ≈ 0.0027 m^3
Now we can rearrange the ideal gas law to solve for the number of moles:
n = PV / RT
n = (0.00228 atm)(0.0027 m^3) / (0.0821 L atm / K mol)(311 K)
n ≈ 0.00023 mol
Finally, we can calculate the mass of neon in the sign using the molar mass of neon (20.18 g/mol):
mass = n * molar mass
mass = 0.00023 mol * 20.18 g/mol
mass ≈ 0.0047 g
Therefore, there are approximately 0.0047 grams of neon in the neon sign.