The density of an elemental gas is 2.14 kg/m3 at STP. What is its approximate molecular weight?
To find the approximate molecular weight of the elemental gas, we need to use the Ideal Gas Law equation. The Ideal Gas Law equation is given as:
PV = nRT
Where:
- P is the pressure
- V is the volume
- n is the number of moles
- R is the ideal gas constant (8.314 J/(mol·K))
- T is the temperature
At STP (Standard Temperature and Pressure), the pressure is 1 atmosphere (atm) and the temperature is 273.15 Kelvin (K). The volume is not provided in the question, as it is not necessary for finding the molecular weight.
Given that the density of the gas at STP is 2.14 kg/m^3, we can rewrite it in terms of molar mass (molecular weight) and molar volume to relate it to the Ideal Gas Law.
Density = molar mass / molar volume
Since density is mass per unit volume, we can rearrange the equation to find molar mass:
molar mass = density * molar volume
Now, we can calculate the molar volume at STP using the ideal gas law:
PV = nRT
(1 atm) * (V) = (1 mol) * (8.314 J/(mol·K)) * (273.15 K)
V = (8.314 J/(mol·K)) * (273.15 K) / (1 atm)
V ≈ 22.414 L
Converting the molar volume to cubic meters:
V = 22.414 L * (0.001 m^3 / 1 L)
V ≈ 0.022414 m^3
Now, we can substitute the values into the equation for molar mass:
molar mass = 2.14 kg/m^3 * 0.022414 m^3
molar mass ≈ 0.0479 kg/mol
Therefore, the approximate molecular weight of the elemental gas is approximately 0.0479 kg/mol.