Physics help-ideal gas laws?

Question

If I'm looking for the density of an ideal gas where M=34.1 kg/kmol at 300.15 Kelvin and 2 atm, what value do I use for r? As in what units (L*mmHg*K ^-1*what?) and what is the actual number? Is there any way to get the 34.1 kg/kmol to however many moles there are?

Answer 1

Actually most of the information you need to answer the question is right in the question. we just need to play with the classical gass formula.

pV=nRT

pV = (mass/ molecular weight)RT

from here on ( will denote MW as M)

-multiply both sides by M

pMV=mRT

-divide both sides by the volume

pM= (m/v)RT

and if you recall, m/v is the formula for density D. So, now just solve for density:

pM/RT = D

As for R, since your pressure is given in atm we will use the constant that contains that unit R= 0.082315 L*atm/mol*K.

D = (2 atm*34.1 Kg/mol) / (0.082315*300.15 K)

D=2.76 kg/kL =2.76 g/L

Answer 2

From http://en.wikipedia.org/wiki/Ideal_gas_l...

"The state of an amount of gas is determined by its pressure, volume, and temperature according to the equation:

PV = nRT

where

P is the absolute pressure of the gas,

V is the volume of the gas,

n is the number of moles of gas,

R is the universal gas constant,

T is the absolute temperature.

The value of the ideal gas constant, R, is found to be as follows.

R =  8.314472 J / (mol K)"

If you have grams and kg/kmol, then you can find moles rather handily, if you know how units work. If a substance were, for example, 5 g / mol, that would mean that 1 mole has a mass of 5 grams -- it would also mean that 5 grams of that mass is 1 mole of it. So, if you had 1 gram of it, you would have a fifth of a mole of it -- 0.2 mol. Same principle here: 34.1 kg/kmol would be just 34.1 g / mol, which means that 1 mole weighs 34.1 grams. et cetera.

A millimeter of mercury (mm Hg), or a "torr," is equal to 133.322 pascals -- the SI unit for pressure. One pascal is equal to one newton per square meter.

Answer 3

Using the last set of numbers.

You are given that M  =  34.1Kg / Kmol

M is therefore   34.1 gm / mol, and you have 1.216gm of gas

No. of moles (n)  is therefore  =  1.216 / 34.1   =   0.03566

Gas constant (R) is 8.31 joules / deg K

Temperature of the gas (T)   =   291.15 degree K.

Pressure of the gas is the same as  due to a depth of 755 mm of mercury

Pressure (P)  =    depth  x  density  x  9.81

                 =       0.755  x  13600  x  9.81   =   1.0073 x 10^5 N / m^2

Apply the general gas equation:-

                   P  x  V   =   n   x   R   x   T

So volume of gas,  V   =    n*R*T / P

Yoy have just to substitute the values obtained above into this equation, and the volume will be in m^3   (  8.57 x 10^-4 )

1 m^3   =   1000 litre   =   10^6 cm^3  if you want to convert