Question #b9c49

1 Answer
Mar 10, 2017

Answer:

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}#.