If an unlabeled tank of gas is found in a storeroom, how can the

Question

molar mass of the gas be determined to help identify the gas?

Answer 1

To determine the molar mass of an unlabeled gas in a tank, you can use several methods. Here’s a common approach using the Ideal Gas Law, which relates the pressure, volume, temperature, and amount of gas:

Method: Ideal Gas Law

1. Gather Equipment: You will need a gas syringe or a container of known volume, a pressure gauge, a thermometer, and possibly a scale (if you want to measure mass).

2. Measure the Volume: Use a gas syringe or a container of known volume to collect a known volume (V) of the gas from the tank.

3. Measure Temperature: Measure the temperature (T) of the gas in Kelvin. To convert Celsius to Kelvin, use the formula: \[ T(K) = T(°C) + 273.15 \]

4. Measure Pressure: Use the pressure gauge to measure the pressure (P) of the gas in atmospheres (atm) or another suitable unit.

5. Apply the Ideal Gas Law: The Ideal Gas Law is given by: \[ PV = nRT \] where:

   • \( P \) = pressure (in atm),
   • \( V \) = volume (in liters),
   • \( n \) = number of moles of gas,
   • \( R \) = ideal gas constant (0.0821 L·atm/(K·mol)),
   • \( T \) = temperature (in Kelvin).

6. Calculate Moles (n): Rearranging the Ideal Gas Law gives you: \[ n = \frac{PV}{RT} \]

7. Determine Mass of Collected Gas: If you can safely weigh the gas (for example, by weighing the gas tank before and after emptying a known amount), do so to get the mass (m) of the gas.

8. Calculate Molar Mass (M): Molar mass (M) is given by: \[ M = \frac{m}{n} \] where:

   • \( m \) = mass of the gas (in grams),
   • \( n \) = number of moles (calculated in the previous step).

Summary Steps:

1. Draw a known volume of gas from the tank.
2. Measure the pressure and temperature of the gas.
3. Use the Ideal Gas Law to calculate the number of moles.
4. Measure the mass of the gas collected.
5. Calculate the molar mass using the mass and the number of moles.

Notes:

• It’s important to handle the gas safely, ensuring proper ventilation and use of personal protective equipment when necessary.
• Some gases may have specific handling or safety concerns based on their properties.
• If you have access to other analytical tools (like gas chromatography), these can provide more detailed identification of the gas.