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### Topic: Second virial coefficient  (Read 15514 times)

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#### Suze

• Guest ##### Second virial coefficient
« on: April 08, 2005, 08:32:47 AM »
I don't seem to be getting anywhere with this problem:

The second virial coefficient B' can be obtained from measurements of the density (d) of a gas at a series of pressures. Show that the graph of p/d against p should be a straight line with slope proportional to B'. Find the values of B and B'at 298K... and I've been given six pressure values with corresponding densities.

I've plotted p/d vs p but don't see how that helps. I've plotted Z vs p and don't see how that helps. I've tried using pVm=RT(1+B/Vm) but don't get the correct value for B. I've tried using pVm=RT(1+B'p) but don't get the correct value for B'. I know B=B'RT but that's not useful until I've found one of the second virial coefficients.

Please could somebody help me with this?? #### Donaldson Tan ##### Re:Second virial coefficient
« Reply #1 on: April 08, 2005, 03:19:09 PM »
pv = RT + Bp where B is a function of temperature and v is molar volume

the above relationship holds sufficiently well for p < 5bar

d = M/v where M is the molar mass
pv - Bp = RT
p(v - B) = RT
v - B = RT/p
v = B + RT/p
d = M/v where M is the molar mass
d = M/(B + RT/p) = Mp/(Bp + RT)
d/p = M/(Bp + RT)
p/d = (Bp + RT)/M = Bp/M + RT/M
p/d = (B/M)p + RT/M

from the above equation, it can be seen the gradient of the graph for p/d against p is a function of B. note: density is varied with pressure at constant temeprature.
« Last Edit: April 08, 2005, 03:20:06 PM by geodome »
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

#### Suze

• Guest ##### Re:Second virial coefficient
« Reply #2 on: April 11, 2005, 08:25:11 AM »
I understand the manipulation of 'pV=RT + Bp' and 'd=M/V' to get an equation in the form of 'y = mx + c', and after plotting the graph of p/d vs p, I multiply the gradient by M (molar mass) but still don't get the answer printed in my textbook.
Here are the given pressure and density values:
p /Torr         91.74     188.98     277.3     452.8     639.3     760
d /(g L-1)     0.225      0.456      0.664     1.062     1.468    1.734

I get: B = 2.119 L mol-1, B' = 1.140E-4 Torr-1 = 1.5003E-7 atm-1
The printed answer is: B = -4.4 L mol-1, B = -0.18 atm-1

Please could someone check if my answer is correct or if I have a problem with my method?? #### Donaldson Tan ##### Re:Second virial coefficient
« Reply #3 on: April 11, 2005, 08:46:05 PM »
what is the molar mass of the gas? i used the data to directly calculate the gradient, which is 439.93 Tor L / g
« Last Edit: April 11, 2005, 11:38:39 PM by geodome »
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

#### Suze

• Guest ##### Re:Second virial coefficient
« Reply #4 on: April 12, 2005, 02:49:36 AM »
Sorry, I forgot to say the gas is dimethyl ether so the molar mass is 46.0682 g mol-1.

If the gradient is the y-value divided by the x-value, shouldn't the units of the gradient be Torr g-1 L / Torr = g-1 L, and then multiplied by 46.0682 g mol-1 to give 'x' L mol-1 ?

So at least neither of us get a minus value which the printed answer is....

#### Donaldson Tan ##### Re:Second virial coefficient
« Reply #5 on: April 12, 2005, 02:05:59 PM »
at what temperature was the measurement taken?
"Say you're in a [chemical] plant and there's a snake on the floor. What are you going to do? Call a consultant? Get a meeting together to talk about which color is the snake? Employees should do one thing: walk over there and you step on the friggin� snake." - Jean-Pierre Garnier, CEO of Glaxosmithkline, June 2006

#### Suze

• Guest ##### Re:Second virial coefficient
« Reply #6 on: April 13, 2005, 09:15:33 AM »
I'm really sorry - I keep leaving vital information out!!! The measurements were taken at 25 deg C.