A common method to determine the molar mass of a volatile liquid utilizes the ideal gas law. Since volatile liquids easily transition into a gaseous state, we can use their properties as a gas to calculate the molar mass.
Using the Ideal Gas Law
The core principle involves using the ideal gas law, 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 in Kelvin.
To find molar mass, we need to know the mass of the substance and the number of moles. The ideal gas law helps us find the number of moles. Then we can use this to determine molar mass.
Steps to Determine Molar Mass
Here's a step-by-step approach:
- Vaporize the Liquid: Heat a known mass of the volatile liquid in a container until it is completely vaporized. Ensure the volume is controlled by the container size.
- Measure Pressure (P): Measure the pressure of the vapor inside the container. This is typically done with a pressure sensor.
- Measure Volume (V): Determine the volume of the container, which is equal to the volume of the gas.
- Measure Temperature (T): Measure the temperature of the gas inside the container.
- Calculate Moles (n): Using the ideal gas law (PV=nRT), rearrange the equation to solve for n: n = PV/RT.
- Calculate Molar Mass (M): Molar mass (M) is equal to the mass of the vapor (m) divided by the number of moles (n), M = m/n.
Example Scenario:
Let's say we have a volatile liquid and we perform the following measurements:
- Mass of liquid vaporized = 0.200 g
- Volume of the vapor = 0.100 L
- Pressure of the vapor = 1.0 atm
- Temperature of the vapor = 373 K (100 °C)
- Ideal gas constant, R = 0.0821 L atm / (mol K)
Now, we will use the ideal gas law to find the number of moles.
n = (1.0 atm 0.100 L) / (0.0821 L atm/(mol K) 373 K) = 0.00326 mol
Next, we can calculate the molar mass:
Molar Mass = 0.200 g / 0.00326 mol = 61.35 g/mol
Therefore, the molar mass of the volatile liquid is approximately 61.35 g/mol.
Practical Considerations
- Leakage: Make sure that the container has no leaks when you are working with the volatile liquid.
- Complete Vaporization: Ensure that all of the liquid has vaporized for accurate results.
- Temperature Control: Maintain a consistent temperature during the experiment.
- Choice of Container: Select a container suitable for the temperature and pressure of the experiment.
This method effectively uses the properties of gases to determine the molar mass of substances that are easily vaporized.
