The vapour density of a gas is calculated by comparing its density to that of hydrogen. It essentially tells you how much heavier a given volume of a gas is compared to the same volume of hydrogen under the same conditions of temperature and pressure.
Definition
Vapour density is defined as the ratio of the mass of a certain volume of a substance to the mass of the same volume of hydrogen. Mathematically:
Vapour Density = (Mass of n molecules of gas) / (Mass of n molecules of Hydrogen gas)
Calculating Vapour Density
Here's how you can calculate vapour density using different methods:
1. Using Molar Mass:
A convenient relationship exists between vapour density and the molar mass of a gas:
Vapour Density = (Molar Mass of the Gas) / 2
This is because the molar mass of hydrogen gas (H2) is approximately 2 g/mol.
Example: Calculate the vapour density of oxygen gas (O2).
- Molar mass of O2 = 32 g/mol
- Vapour Density = 32 / 2 = 16
Therefore, the vapour density of oxygen gas is 16.
2. Using the Ideal Gas Law (Indirectly):
While not a direct calculation, you can use the ideal gas law (PV=nRT) to determine the density of both the gas in question and hydrogen gas under the same conditions, and then calculate the ratio. This approach is more complex and generally unnecessary if the molar mass is known. However, it's useful in situations where you experimentally determine the density of both gases.
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Determine the density of the unknown gas (ρgas) experimentally. You'll need to measure the mass and volume of the gas at a specific temperature and pressure.
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Determine the density of hydrogen gas (ρH2) at the same temperature and pressure. This can be done experimentally or calculated using the ideal gas law and the molar mass of hydrogen.
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Calculate the vapour density:
Vapour Density = ρgas / ρH2
Key Considerations:
- Temperature and Pressure: Vapour density is temperature and pressure dependent. Make sure both the gas and hydrogen are measured under the same conditions.
- Ideal Gas Behavior: The simple molar mass relationship assumes ideal gas behavior. This approximation is generally valid at low pressures and high temperatures.
Summary:
The easiest and most common way to calculate vapour density is using the formula: Vapour Density = (Molar Mass of the Gas) / 2. This provides a quick and accurate estimation under most conditions. If you don't know the molar mass, you can calculate the density of the gas and hydrogen gas under the same conditions and find their ratio to obtain the vapour density.
