A neon sign is made of glass tubing with an inside
diameter of 12.7 mm and length of 16.0 m. If the
sign contains neon at a pressure of 7.56 torr at 33°C,
how much neon is in the sign?
volume= area*length=PI (.0127/2)^2 * 16
moles= PV/RT
To find out how much neon is in the sign, we need to calculate the volume of the sign and then use the ideal gas law to determine the amount of neon.
1. Calculate the volume of the sign:
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the radius of the cylinder and h is the height. In this case, the inside diameter of the glass tubing is given, so we need to find the radius first:
Radius (r) = Diameter/2 = 12.7 mm / 2 = 6.35 mm = 0.00635 m
Now we can calculate the volume of the sign:
Volume (V) = π * r^2 * h
= π * (0.00635 m)^2 * 16.0 m
≈ 0.001016 m^3 (rounded to 4 decimal places)
2. Use the ideal gas law to find the amount of neon:
The ideal gas law formula is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, convert the temperature from Celsius to Kelvin:
Temperature (T) = 33°C + 273.15 = 306.15 K
Rearrange the ideal gas law formula to solve for n:
n = PV / RT
The pressure (P) is given as 7.56 torr, but we need to convert it to the SI unit of pressure (Pascal) for consistency:
1 torr = 133.3224 Pascal
Pressure (P) = 7.56 torr * 133.3224 Pascal/torr
≈ 1007.32 Pascal (rounded to 2 decimal places)
Now we can substitute the values into the formula:
n = (1007.32 Pascal) * (0.001016 m^3) / [(8.314 J/(mol·K)) * (306.15 K)]
Calculating this expression will give us the number of moles of neon in the sign.
Please note that the ideal gas law assumes ideal conditions, so the calculation may not be extremely precise in real-world situations.