[newbie!]

need help with some questions for a course i'm doing called surface chemistry.

Q1)The adsorption of carbon monoxide on mica at 90 K gave the following results:-

P x 105/atm          1.38    5.96   7.17    10.4   13.9
Vads104 /dm3       1.3      1.63   1.68    1.78   1.83

a) Plot the isotherm, i.e. P versus V.   Which of the 5 isotherm types does the data conform to?   Is there any evidence for multilayer adsorption?
ok so i can do that ovbs just plot a graph. p is x axis v is y axis.
i got a resulting increasing then leveling off so i picked it would be isotherm type 1
(i can upload a pic of my graph if you like?)

b)Using a graphical method, show that these data fit the Langmuir adsorption isotherm and evaluate the parameters a and Vm.  What is the one main deficiency of the Langmuir theory.
here i am stuck. in my notes we have like 8 different equations all under the heading for langmuir, so i dont know which one to use for a start.
i was thinking it might be ap=V/Vm(1-V/Vm) but both my unknows are in that equations so i guess i have to get some info from the graph as well, not sure what though?

[newbie!]

Q2) A sample of activated carbon has surface area 1000 m2 g-1.   Assuming that monolayer coverage is complete, what is the volume of ammonia that would be adsorbed on 0.25 g at 25 °C and 1 atm?   The NH3 molecule may be approximated to a sphere of radius 1.5 x 10-10 m.   In your calculation you may assume that adsorbed NH3 molecules just touch each other in a plane, with the centres of four adjacent spheres at the corners of a square.
i know its forum policy to show my working but i literally have no clue. this may as well be written in hindi to me. in class we've been talking about BET, langmuir, temkin and freundlick isotherms but i have no idea....?

[fledarmus]

Q2) A sample of activated carbon has surface area 1000 m2 g-1.   Assuming that monolayer coverage is complete, what is the volume of ammonia that would be adsorbed on 0.25 g at 25 °C and 1 atm?   The NH3 molecule may be approximated to a sphere of radius 1.5 x 10-10 m.   In your calculation you may assume that adsorbed NH3 molecules just touch each other in a plane, with the centres of four adjacent spheres at the corners of a square.
i know its forum policy to show my working but i literally have no clue. this may as well be written in hindi to me. in class we've been talking about BET, langmuir, temkin and freundlick isotherms but i have no idea....?

This is actually a geometry problem. How many spheres of radius 1.5 x 10-10 m can be placed in a square arrangement on the surface available on 0.25 g of carbon having 100 m2 g-1 surface area? Then you can take that number of molecules and back-calculate to find the volume they would normally occupy.

[newbie!]

so i would divide the surface area (1000 m2 g-1) by the radius of spheres (1.5 x 10-10 m)?

in my notes i have the dispersion equation: D= no. surface atoms/ total no. atoms.

but it gives the mass of carbon so where does that come in?

[newbie!]

Q3)
started trying to solve it using the equation: using the idea y=mx+c where p/v(Po-P) is y, (c-1)/VmC is m, P/Po is x and 1/VmC is C which gave 8.16 = (c-1)/VmC x 10.4 + then i get lost...

[fledarmus]

so i would divide the surface area (1000 m2 g-1) by the radius of spheres (1.5 x 10-10 m)?

Not quite. You need to divide the surface area by the area of the surface occupied by a single NH₃ molecule. A radius is not an area. As a hint - draw the problem. Draw a surface with four spheres arranged in a square as indicated by the problem. How much area would each sphere occupy?

in my notes i have the dispersion equation: D= no. surface atoms/ total no. atoms.

but it gives the mass of carbon so where does that come in?

The surface area of your carbon has already been given to you. It is 1000m² per gram. How many grams of carbon do you have? So what is the total surface area of carbon?

[newbie!]

so each half the volume of each sphere would occupy 1/4 of the surface area of the square?
i drew 2 pics (sorry paint is s#*$ i cba scanning my actual drawings)

the red shaded show the part of the sphere that has actually entered the cube, the other unshaded part would be the half that lies outside the cube.

and ahh so the total surface area of carbon is 0.25 x 1000 = 250m^2 ?

[fledarmus]

You're getting close - the spheres don't actually go through the surface, they merely sit on top of it, so in your right hand picture the line needs to go underneath the spheres rather than through them.

However, your left hand picture is sufficient for your purposes. You now have four spheres in a square. What is the area of the square? That is the amount of surface area covered by four molecules of ammonia.

And yes, you've got the total surface area of carbon right 

Now that you know the amount of surface area of the carbon, and the amount occupied by four molecules of ammonia, it shouldn't be difficult to find the total number of molecules of ammonia absorbed and back-calculate to the volume of ammonia gas.

[newbie!]

the area of the square would be - assuming atoms are touching) (4r)^2 ?

then to find the total number of ammonia molecules absorbed i will multiply something by avagadro's number?