[ashish]

here is the graph and question ..

https://postimg.org/image/rvgo30l81/

can anyone please help in understanding what the graph represents ??

on y-axis it says 1/moles adsorbed .

does it means 5000 molecules/mole adsorbed ??

[mjc123]

No, it means 1/moles adsorbed = 5000 mol^-1, i.e. moles adsorbed = 1/5000 = 0.0002 mol.
Why does it plot 1/moles adsorbed vs. 1/concentration rather than moles adsorbed vs. concentration? What do you know about the form of the Langmuir isotherm, and why would that make this a useful way of plotting the data?

[ashish]

No, it means 1/moles adsorbed = 5000 mol^-1, i.e. moles adsorbed = 1/5000 = 0.0002 mol.
Why does it plot 1/moles adsorbed vs. 1/concentration rather than moles adsorbed vs. concentration? What do you know about the form of the Langmuir isotherm, and why would that make this a useful way of plotting the data?

hi...thanks for answering and clearing my first confusion ....i know we have to somehow find the volume of surfactant needed to cover 1 g of ZrO2 because that volume will give the no.of surfactant molecules and then we have to multiply that many no.of molecules with the area of one single molecule which is given in the question as 0.25 nm^2 ....and that will be the area of 1 g of ZrO2

so on x-axis ....it is 1/surfactant = 0.1
so surfactant = 1/0.1 = 10 moles/L (as 1dm^3 = 1L)

and next one will be 1/0.2 = 5 moles/L

and on y axis - first one is 0.0002 moles

second one will be 1/10000 = 0.0001 moles

as concentration of surfactant is decreasing ....no of molecules getting adsorbed on the colloid is decreasing .

suppose we take the first data ...i.e.  10 moles/L and 0.0002 moles

no.of molecules getting adsorbed on 10 g = 0.0002 X 6.022 X 10^23 = 1.204 X 10^20 molecule

area of 1 molecule = 0.25 nm^2

so area of 1.204 X 10^20 molecules = 1.204 X 10^20 X 0.25 X 10^-18 = 30.1 m^2


similarly if we take the second data....0.0001 mole and 5 mole/L

no.of molecules getting adsorbed = 0.0001 X 6.022 X 10^23 = 6.022 X 10^19

and area of 6.022 X 10^19 molecules = 6.022 X 10^19 X 0.25 X 10^-18 = 15.055 m^2

how to move from here ...if you could give furthur suggestion it will be really helpful

[ashish]

Why does it plot 1/moles adsorbed vs. 1/concentration rather than moles adsorbed vs. concentratio?

i think its because the numbers are small like 0.0001 and 0.0002  thats why it has inverted it .

[sjb]

i think its because the numbers are small like 0.0001 and 0.0002  thats why it has inverted it .

Certainly one reason, but what formulae do you know that describe the Langmuir isotherm?

[ashish]

i think its because the numbers are small like 0.0001 and 0.0002  thats why it has inverted it .

Certainly one reason, but what formulae do you know that describe the Langmuir isotherm?

hi...i have seen theta = kp/1+kp

where theta = fraction of sites ocuupied i.e. no.of adsorption sites occupied / no.of adsorption sites available

k is = ka/kd (adsorpion const/desorption const)

its another version is V/Vmono = kp/1+kp

where V = volume of gas adsorbed and Vmono is the volume adsorbed at sufficiently high gas pressure so as to give a compete coverage of surface with a single layer of gaseous molecules

it can be rearranged to p/V = 1/kVmono + p/Vmono

and now a plot is made between p/v and p we would get a linear plot with solpe equal to 1/Vmono and intercept 1/kVmono

but this question is not like that ....how should i proceed now ??

pls help

[ashish]

i think its because the numbers are small like 0.0001 and 0.0002  thats why it has inverted it .

Certainly one reason, but what formulae do you know that describe the Langmuir isotherm?

hi.....just found one website

http://www2.stetson.edu/~wgrubbs/datadriven/langmuir/langmuirwtg.html

i think equation 7 given there is of the form similar to asked in this question ....but how will i find the slope and intercept ??

[mjc123]

Not easily from that graph, is the answer. You can get a decent idea of the slope, but the intercept is very small, indeed to my eye it goes through the origin. They should either give you the numerical data, or at least a larger and better drawn graph than that.