You can find molecular mass from density by using the ideal gas law and rearranging it to solve for molar mass (which is numerically equivalent to molecular mass).
Here's how:
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Start with the Ideal Gas Law: PV = nRT
- P = Pressure
- V = Volume
- n = Number of moles
- R = Ideal gas constant
- T = Temperature
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Relate moles to mass and molar mass: n = m/M
- m = mass
- M = molar mass (what we want to find)
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Substitute n = m/M into the Ideal Gas Law: PV = (m/M)RT
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Rearrange to solve for Molar Mass (M): M = (mRT) / PV
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Recognize density: Density (ρ) = m/V
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Substitute ρ = m/V into the equation: M = (ρRT) / P
Therefore, the final equation to calculate molecular mass (M) from density (ρ) is:
M = (ρRT) / P
Where:
- M = Molar Mass (g/mol)
- ρ = Density (g/L or kg/m3, depending on R's units)
- R = Ideal Gas Constant (0.0821 L·atm/mol·K or 8.314 J/mol·K, depending on the units of P, V, and T)
- T = Temperature (Kelvin)
- P = Pressure (atm or Pascals, depending on R's units)
Example:
Let's say you have a gas with a density of 2.1 g/L at a pressure of 1 atm and a temperature of 273 K. We will use R = 0.0821 L·atm/mol·K.
M = (2.1 g/L 0.0821 L·atm/mol·K 273 K) / 1 atm
M ≈ 47.04 g/mol
Therefore, the molecular mass of the gas is approximately 47.04 g/mol.
In summary, by manipulating the ideal gas law and incorporating the definition of density, you can calculate the molecular mass of a gas if you know its density, pressure, and temperature.
