Depending on your job or other aspects of your lifestyle, you may occasionally or regularly work with pressurized cylinders containing one or more kinds of gas. "Gas" in this context is not short for "gasoline," but instead refers to any substance in a gaseous, as opposed to solid or liquid, state. One popular example is the hydrocarbon fuel propane.
Occasionally, you might have to find the weight of the gas inside the cylinder. One crude way to do this would be to weigh the cylinder containing the gas in question, discharge all of the gas and weigh the cylinder again; the difference in values would be the mass of the gas, assuming no air could flow into the container and add mass that would throw off the calculation. This, however, would be an obvious waste of chemical resources.
Is there a better way? Indeed, and it teaches you a little physics and chemistry in the bargain.
The Standard Gas Cylinder
The purpose of storing compressed gases in cylinders and other containers is straightforward: It allows for more of a substance to be transported and stored in a smaller physical volume than would be required if the gas in question were allowed to distribute itself naturally, as do the gas molecules and other particles making up the air in the atmosphere around you.
This, unfortunately, entails a trade-off: Compressing gases (that is, reducing their volume) entails a proportional increase in pressure, assuming all other variables, such as temperature, are held constant. This is explored further in a later section.
Gas cylinders therefore have internal pressures higher than atmospheric pressure, which is 14.7 pounds per square inch (psi) at Earth's surface. The substances they contain must have boiling points below 20 degrees Celsius (68 degrees Fahrenheit) in order to be considered gases, for otherwise they would remain solids above "room temperature" or so.
The Ideal Gas Law
The ideal gas law states that:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles of gas present, R is a constant and T is the temperature in Kelvin (K). In a situation in which T and n are constant but P and V can change, such as when a valve is opened in a gas-containing cylinder, this means that the product of P and V is a constant throughout the process. In symbols:
P1V1 = P2V2
Calculating the Volume of Compressed Gas
Say you have a cylinder of nitrogen stored at normal temperature (20 C) and pressure (14.7 psi) labeled with a volume of 29.5 L and an internal pressure of 2,200 psi. What is the "natural" volume of nitrogen gas?
If the gas were released, it would disperse throughout the environment, and its pressure would become equal to atmospheric pressure. You can therefore use the relationship derived above where P1 = 2,200 psi, V1 = 29.5 L and P2 = 14.7 psi to find V2:
(2,200)(29.5)/(14.7) = V2 = 4,415 L
Calculating the Mass of the Gas: Is the Mass of the Cylinder Needed?
To calculate the mass of this volume of gas, you need to know its density under normal conditions. For this information, consult a page such as the one in the resources.
Nitrogen (N2) has a molecular mass of 28.0 g/mol and a density of 1.17 kg/m3 = 1.17 g/L at 20 C. Since density is mass divided by volume, mass equals volume times density; in this case:
(4,415 L)(1.17 g/L) = 5,165 g = 5.165 kg
- This is about 11.5 pounds of nitrogen (1 kg = 2.204 lb).
And, as you can see, the answer to the question about the mass of the cylinder is no! All you need is some practical chemistry knowledge and a little perseverance.