[edge]

Exactly 2 moles of n-octane are placed in a tank of 45.5dm3 at 182.3 oc. Calculate the presure of the gas using (i) the ideal gas low, (ii) the van der Waals equation with the constants a=37.32 atm dm6mol-2,b=0.2368dm3mol-1,and (iii) the law of corresponding states with the compressibility factor Z=0.95.

I'm still fresh with the gas pressure calculation
Thus can't really get an idea to solve the problem.
Thanks for any advice to solve my doubts.

[billnotgatez]

one should attempt to solve and then we can help

can you post the equations for each of the questions
and then maybe you can see where to substitute the values

[edge]

thanks a lot for your hint, billnotgatez.

(i)
The answer of pressure of gas in ideal gas law is 1.643 atm , am I right?

I get the answer based on the following way:

PV=nRT

P(45.5L)=2mol*0.0821LatmK-1mol-1*(182.3+273.15)K

P=1.643atm

(ii)
I just trying to solve the problem two with the following solution:

[P+a(n/v)2](v/n-b)=RT

[P+37.32(2/45.5)2](45.5/2-0.2368)=0.0821*(182.3+273.15)

P=1.5886 atm

 

Do you have any idea regarding the (iii) question to calculate the pressure of gas?

Why the gas pressure in three different situation, (i), (ii), (iii)?

 

Really thanks for your advice.

[billnotgatez]

I can not easily do the math right now but it looks good for the first one.

Why the gas pressure in three different situation, (i), (ii), (iii)?

 hint - is n-octane an IDEAL gas

[edge]

Thanks for your reply, billnotgatez.

I able to write out the following equation:
2 C8H18(l) + 25 O2(g) 16 CO2(g) + 18 H2O(g)

Unfortunately, I still can't get any hint regarding my question
Do you have any idea to calculate the gas pressure in (iii) the law of corresponding states with the compressibility factor Z=0.95 ?
I can't solve this problem as well.
Thanks.

[fledarmus]

Try this for your part iii)

http://en.wikipedia.org/wiki/Compressibility_factor

You might also try looking up "real gas" on wikipedia

[fledarmus]

As for why the three equations give different pressures, you need to consider the underlying assumptions behind the equations, especially the ideal gas law. The ideal gas law is an approximation derived by assuming: 1) that the individual molecules can be treated as points with no volume, and that the entire volume is taken up by distance between the molecules; and 2) that there are no attractive or repulsive forces between the individual molecules which would tend to pull them closer together or push them further apart.

The question for you is, under what circumstances would these assumptions be valid or invalid? And if the assumptions are not valid, what sort of factors would need to be added to your ideal gas equation to make it more accurately reflect your real world situation?

[edge]

Many thanks for advice, fledarmus

For the (iii),
I'm calculate the gas pressure based on this equation:
Z=PV/RT
The answer for (iii) is 1.51atm.

Do you have any idea why the gas pressure in ideal gas law is highest while in (iii) is slowest?
I'm still a little bit confusing regarding "the underlying assumption behind the equation"
Many thanks for advice. 

[fledarmus]

For the "underlying assumptions behind the equation" -

The two main assumptions behind the ideal gas law are that there are no attractive forces between the molecules of the gas and that the molecules occupy no volume. If you look at your van der Waal's equation, [P+a(n/v)2](v/n-b)=RT, you will notice that if both a and b are zero, it reduces to PV/n=RT, the ideal gas equation. A quick look at a table of constants (for example http://en.wikipedia.org/wiki/Van_der_Waals_constants_(data_page)) will show you that molecules which are very small and have little interaction (for example, Helium) have constants very close to zero, meaning they behave in a very similar manner to ideal gases. Large molecules with strong attractive forces, for example bromobenzene, have large constants and differ significantly from ideal gases.

The molecules of all pure neutral compounds have some form of attractive force, including zwitterionic charge interactions, hydrogen bonding, dipole moments, London forces, and so forth. This means that at relatively large volumes, the pressure that you measure in a real gas will always be somewhat less than you would expect from the Ideal Gas Law, due to the fact that the molecules are pulling together. This reduces the amount of force pressing against the sides of the container.

Acting against this is the fact that the free space between the molecules is slightly less than predicted by the Ideal Gas Law. The molecules aren't single points - they do occupy some volume. Imagine two baseballs being thrown at each other - when they are twenty feet away, you can pretty much ignore the volume of the baseball when you are calculating how far they will have to travel to hit each other, but when they are five inches away, that volume becomes significant. In the van der Waal's equation, as you increase the number of moles of gas in a given volume, you are packing the molecules closer together and both the molecular interactions and the actual volume of the molecule become more significant.

Compressibility factors are another way to measure the reduced pressure (or temperature) that you see in real gases from what you would expect from an ideal gas. Again, since all neutral molecules have some attractive force, the pressure that you measure will always be slightly less than the pressure that the ideal gas law will predict. Compressibility factors use indirect measurements of the attractive forces between molecules by calculating from the critical point, which is the combination of temperature and pressure at which a stable mixture of gas, liquid, and solid of the same molecule can be maintained. The stronger the attractive forces between molecules, the higher the temperature at which gas and liquid would be in equilibrium, for example.

So the Ideal Gas Law should always give you the highest estimate of pressure for a pure neutral compound in its gas form. The Real Gas equations all have various mechanisms to correct this measurement and obtain a number closer to what the measured pressure will be.

A little long winded, I know, but I hope this helps.