Two identical pressure cylinders show the same pressure on the gauge. They both are at room temperature. One contains methane (CH4) and the other contains Nitrogen (N2). Use what you know about gas laws to explain how to tell which is by weighing the cylinders.

Answer 1

To determine which cylinder contains methane (CH4) and which contains nitrogen (N2), you can make use of the ideal gas law equation:

PV = nRT

Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas

Since the cylinders are identical and show the same pressure on the gauge, we can assume that they have the same volume, pressure, and temperature. Therefore, the only difference between the two is the number of moles of gas present in each cylinder.

Assuming both cylinders are at the same room temperature, the gases will have the same temperature (T). The ideal gas law equation shows a direct relationship between the number of moles (n) and the mass of the gas (m), given the molar mass (M) of the gas:

m = n * M

Since we are using identical cylinders, the cylinder containing the gas with a higher molar mass will have a greater mass. Hence, to determine which cylinder contains methane and which contains nitrogen, you can weigh the cylinders. The cylinder with a higher mass will contain the gas with a higher molar mass, which in this case will be methane (CH4) since the molar mass of methane is greater than that of nitrogen.