Question #e9ae8

1 Answer
Dec 11, 2016

Answer:

#(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"#