Question

An experiment shows that a 252 mL gas sample has a mass of 0.433 g at a pressure of 760 mm Hg and a temperature of 34 degrees C. What is the molar mass of the gas?

Answer 1

Molar mass is `43.3 color(white) {.}g cdot mol^{- 1}`.

Explanation:

Gas law's shows that:

`p cdot V = n cdot R cdot T`,

where `p` is the pressure of gas, `V` it's volume, `n` the amount of gas, in mols, `R` is the constant of gases, and `T` is the absolute temperature of the gas.

In I.S. units, `R approx 8.31 color(white) {.} J cdot mol^{- 1} cdot K^{- 1}`.

Done molar mass is given by:

`M_r = m/n`

we can write gas law's in the next form:

`p cdot V = m/M_r cdot R cdot T`,

and we obtain:

`M_r = {m cdot R cdot T}/{p cdot V} = {0.433 g cdot 8.31 J cdot mol^{- 1} cdot K^{- 1} cdot (34 + 273,15) K}/{760/760 cdot 1.013 cdot 10^5 Pa cdot 252 cdot 10^{- 6} m^3} =`
`= 43.3 g cdot mol^{- 1}`