Question

Question #e9ae8

Answer 1

`(77.95" g")/"mole"`

Explanation:

Let `R =` The Gas Constant `= 62.363` L Torr K`"^-1` mole`"^-1`

Given: `P = 400" torr"` and `T = 127" C"^@ = 400" "K`

The Ideal Gas law is:

`PV = nRT`

We are not given the volume but we do not need it; the reason will soon become obvious. Solve for the Volume per Moles:

`V/n = (RT)/P`

`V/n = ((62.363" L Torr K"^-1" mole"^-1)(400" K"))/(400" Torr")`

I am taking an extra step to show you that the Numbers for temperature and pressure cancel and and their units are canceled by the gas constant:

`V/n = ((62.363" L "cancel("Torr")cancel(K^-1)" mole"^-1)(cancel(400)cancel(" K")))/(cancel(400)cancel(" Torr"))`

No matter what Volume or number of moles we pick, at this temperature and pressure, the following ratio is true:

`(62.363" L")/"mole" = V/n`

We are given the mass density: `(1.25" g")/"L"`

To find the Molar Mass, we use the Factor-Label Method (a.k.a. Dimensional Analysis):

`(1.25" g")/cancel("L")(62.363cancel(" L"))/"mole" = 77.95" g"/"mole"`