Respuesta :
The question is incomplete, here is the complete question:
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 1.75 torr at 38°C, how many grams of neon are in the sign? (The volume of a cylinder is πr²h.) Express your answer using two significant figures.
Answer: The mass of neon in the sign is [tex]4.8\times 10^{-3}g[/tex]
Explanation:
The equation used to calculate the volume of cylinder is:
[tex]V=\pi r^2h[/tex]
where,
V = volume of neon sign
r = radius of the neon sign = [tex]\frac{d}{2}=\frac{2.5cm}{2}=1.25cm=1.25\times 10^{-2}m[/tex] (Conversion factor: 1 m = 100 cm)
h = length/ height of the neon sign = 5.5 m
Putting values in above equation, we get:
[tex]V=(3.14)\times (1.25\times 10^{-2})^2\times 5.5\\\\V=2.69\times 10^{-3}m^3=2.69L[/tex] (Conversion factor: [tex]1m^3=1000L[/tex] )
To calculate the number of moles, we use the equation given by ideal gas equation:
PV = nRT
Or,
[tex]PV=\frac{w}{M}RT[/tex]
where,
P = Pressure of the gas = 1.75 torr
V = Volume of the gas = 2.69 L
w = Weight of the gas = ?
M = Molar mass of neon gas = 20 g/mol
R = Gas constant = [tex]62.364\text{ L. torr }mol^{-1}K^{-1}[/tex]
T = Temperature of the gas = [tex]38^oC=[38+273]K=311K[/tex]
Putting values in above equation, we get:
[tex]1.75torr\times 2.69L=\frac{w}{20g/mol}\times 62.364\text{ L. torr }mol^{-1}K^{-1}\times 311K\\\\w=\frac{1.75\times 2.69\times 20}{62.364\times 311}=4.8\times 10^{-3}g[/tex]
Hence, the mass of neon in the sign is [tex]4.8\times 10^{-3}g[/tex]
