Can we determine the molecular mass of an unknown gas if we know the pressure temperature and volume of gas along with mass of gas
The correct answer and explanation is:
Correct Answer: Yes, the molecular mass (molar mass) of an unknown gas can be determined if the pressure, temperature, volume, and mass of the gas are known.
Explanation:
To determine the molecular mass of a gas, the Ideal Gas Law is used: PV=nRTPV = nRT
Where:
- PP = pressure (in atm)
- VV = volume (in liters)
- nn = number of moles
- RR = universal gas constant (0.0821 L·atm/mol·K)
- TT = temperature (in Kelvin)
The number of moles nn can also be written as: n=mMn = \frac{m}{M}
Where:
- mm = mass of the gas (in grams)
- MM = molecular (molar) mass (in g/mol)
Substituting into the ideal gas law: PV=mMRTPV = \frac{m}{M}RT
Rearranging to solve for molecular mass MM: M=mRTPVM = \frac{mRT}{PV}
Thus, with the mass mm of the gas, the pressure PP, the volume VV, and the temperature TT, the molecular mass MM can be calculated directly.
Example:
Suppose a sample of gas has:
- Mass = 2.5 g
- Pressure = 1 atm
- Volume = 2 L
- Temperature = 300 K
Using the equation: M=2.5×0.0821×3001×2=61.5752=30.79 g/molM = \frac{2.5 \times 0.0821 \times 300}{1 \times 2} = \frac{61.575}{2} = 30.79 \text{ g/mol}
So, the molecular mass of the gas is approximately 30.79 g/mol.
This method is reliable for ideal gases and gives a good estimate even for many real gases under moderate conditions.