Question

Question #b9c49

Answer 1

The molecular weight (molecular mass) of the gas is:

`M_{gas} = 16,1 color(white) "."g cdot mol^{- 1}`.

Explanation:

According to Avogadro's hypothesis equal volumes of gas, measured under the same pressure and temperature conditions, will contain the same number of particles. From this hypothesis, a series of laws is derived that leads to the definition of mol and molar volume.

The molar volume of a gas is the volume occupied by one mole of said gas under certain conditions of pressure and temperature. We must remember that under normal conditions (i.e., pressure equal to `1` atm and temperature of `0` °C, or `273.15` K), `1` mole of any gas occupies a volume of `22.4` L (more exactly `22.413962` L, according to the NIST physics lab: http://physics.nist.gov/cgi-bin/cuu/Value?mvolstd).

Therefore, if we have a `1` L bottle filled with a gas, we will have:

`n = V/V_m = {1 color(white) "."L}/{22.4 color(white) "."L cdot mol^{- 1}} = 0.0446 color(white) "."mol`,

if we assume that we are in normal conditions.

Knowing this, we can find the molecular mass by dividing the mass of gas between the number of moles:

`M_{gas} = m/n = {113.52 - 112.8}/0.0446 color(white) "."g cdot mol^{-1}`,

i.e.

`M_{gas} = 16,1 color(white) "."g cdot mol^{- 1}`.