# Question b9c49

Mar 10, 2017

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

${M}_{g a s} = 16 , 1 \textcolor{w h i t e}{\text{.}} g \cdot m o {l}^{- 1}$.

#### 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:

${M}_{g a s} = \frac{m}{n} = \frac{113.52 - 112.8}{0.0446} \textcolor{w h i t e}{\text{.}} g \cdot m o {l}^{- 1}$,

i.e.

${M}_{g a s} = 16 , 1 \textcolor{w h i t e}{\text{.}} g \cdot m o {l}^{- 1}$.