Two identical pressure cylinders show the same pressure on the gauge. They both are at room temperature. One contains methane (CH) 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 and which contains nitrogen by weighing them, we can make use of the ideal gas law.

The ideal gas law states that the pressure (P), volume (V), and temperature (T) of a gas are related by the equation PV = nRT, where n is the number of moles of the gas and R is the ideal gas constant.

Since the two cylinders have the same pressure and are at the same temperature, we can deduce that their volumes and number of moles of gas are also equal, given that the cylinders are identical.

Now, let's focus on the number of moles of gas (n) in each cylinder. The number of moles of gas can be calculated using the equation n = m/M, where m is the mass of the gas and M is the molar mass of the gas.

Since the cylinders are identical and the volumes are equal, we can assume that the masses of the gases will also be equal. Therefore, the cylinder with the gas that has a lower molar mass will contain a larger number of moles compared to the other cylinder.

Knowing this, we can conclude that the cylinder containing methane (CH) will be lighter than the cylinder containing nitrogen (N2) due to methane's lower molar mass compared to nitrogen. Hence, the lighter cylinder will contain methane, while the heavier cylinder will contain nitrogen.