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Vapor in air diffusion
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SAMPLE CALCULATION 

 

OBSERVATION TABLE - IN AIR AT  328K

 

  

 

Now we plot a graph between (x-x0) and time/(x-x0)

 

(x-x0) vs time/(x-x0) plot

 

Then for the data above we have the least square equation as :

y = 26.17x + 1159

From the graph slope S is = 2.617*10^7 sec/m^2

Operating temperature T = 328K

Vapor pressure or carbon tetrachloride can be obtained from the equation :

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»V«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mi mathvariant=¨bold¨»exp«/mi»«mo»(«/mo»«msub»«mi mathvariant=¨bold¨»C«/mi»«mn»1«/mn»«/msub»«mo»§nbsp;«/mo»«mo»+«/mo»«mfrac»«msub»«mi mathvariant=¨bold¨»C«/mi»«mn»2«/mn»«/msub»«mi mathvariant=¨bold¨»T«/mi»«/mfrac»«mo»§nbsp;«/mo»«mo»+«/mo»«msub»«mi mathvariant=¨bold¨»C«/mi»«mn»3«/mn»«/msub»«mi mathvariant=¨bold¨»ln«/mi»«mo»(«/mo»«mi mathvariant=¨bold¨»T«/mi»«mo»)«/mo»«mo»+«/mo»«msub»«mi mathvariant=¨bold¨»C«/mi»«mn»4«/mn»«/msub»«mo»§nbsp;«/mo»«mo»+«/mo»«msub»«mi mathvariant=¨bold¨»C«/mi»«mn»5«/mn»«/msub»«mo»§nbsp;«/mo»«mo»)«/mo»«/math»

 

Where T is in K and vapor pressure is in Pascal.

For carbon tetrachloride : C1=78.441 , C2=-6128.1 , C3=-8.5766 , C4=6.8465*10(-6) , C5=2

With these values of constants we have the vapor pressure to be 49512.55 pascal =49.512 kN/m2

Total pressure P = 101.32 kN/m2

Kilogram molecular volume of a gas = 22.4 m3 at 273.15 K

Molecular weight of carbon tetrachloride = 154 kg/mol

Density of carbon tetrachloride at 321K = 1540 kg/ m3

Total concentration

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»C«/mi»«mi mathvariant=¨bold¨»T«/mi»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mn»1«/mn»«mo»§#215;«/mo»«mn»273«/mn»«mo».«/mo»«mn»15«/mn»«/mrow»«mrow»«mn»22«/mn»«mo».«/mo»«mn»4«/mn»«mo»§#215;«/mo»«mi mathvariant=¨bold¨»T«/mi»«/mrow»«/mfrac»«/math»

=.03716kmol/m^3

 

Concentration of carbon tetrachloride

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»C«/mi»«mrow»«mi mathvariant=¨bold¨»A«/mi»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«mo»§nbsp;«/mo»«/mrow»«/msub»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«msub»«mi mathvariant=¨bold¨»C«/mi»«mi mathvariant=¨bold¨»T«/mi»«/msub»«mo»§#215;«/mo»«mi mathvariant=¨bold¨»V«/mi»«/mrow»«mi mathvariant=¨bold¨»P«/mi»«/mfrac»«/math»

=.01816 kmol/m3

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»C«/mi»«msub»«mi mathvariant=¨bold¨»B«/mi»«mn»1«/mn»«/msub»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«mfrac»«mrow»«mn»273«/mn»«mo».«/mo»«mn»15«/mn»«/mrow»«mrow»«mn»22«/mn»«mo».«/mo»«mn»4«/mn»«mo»§#215;«/mo»«mi mathvariant=¨bold¨»T«/mi»«/mrow»«/mfrac»«/math»

= .0372kmol/m3

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»C«/mi»«msub»«mi mathvariant=¨bold¨»B«/mi»«mn»2«/mn»«/msub»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mo»§nbsp;«/mo»«msub»«mi mathvariant=¨bold¨»C«/mi»«msub»«mi mathvariant=¨bold¨»B«/mi»«mn»1«/mn»«/msub»«/msub»«mfrac»«mrow»«mi mathvariant=¨bold¨»P«/mi»«mo»-«/mo»«mi mathvariant=¨bold¨»V«/mi»«/mrow»«mi mathvariant=¨bold¨»P«/mi»«/mfrac»«/math»

=.01902 kmol/m3

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»C«/mi»«msub»«mi mathvariant=¨bold¨»B«/mi»«mi mathvariant=¨bold¨»M«/mi»«/msub»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mrow»«msub»«mi mathvariant=¨bold¨»C«/mi»«msub»«mi mathvariant=¨bold¨»B«/mi»«mn»1«/mn»«/msub»«/msub»«mo»§nbsp;«/mo»«mo»-«/mo»«mo»§nbsp;«/mo»«msub»«mi mathvariant=¨bold¨»C«/mi»«msub»«mi mathvariant=¨bold¨»B«/mi»«mn»2«/mn»«/msub»«/msub»«/mrow»«mrow»«mi mathvariant=¨bold¨»ln«/mi»«mfenced»«mfrac»«msub»«mi mathvariant=¨bold¨»C«/mi»«msub»«mi mathvariant=¨bold¨»B«/mi»«mn»1«/mn»«/msub»«/msub»«msub»«mi mathvariant=¨bold¨»C«/mi»«msub»«mi mathvariant=¨bold¨»B«/mi»«mn»2«/mn»«/msub»«/msub»«/mfrac»«/mfenced»«/mrow»«/mfrac»«/math»

=.0271 kmol/m3

 

Diffusion co-efficient

 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«mi mathvariant=¨bold¨»D«/mi»«mrow»«mi mathvariant=¨bold¨»A«/mi»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«/msub»«mo»§nbsp;«/mo»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨bold-italic¨»§#929;«/mi»«msub»«mi mathvariant=¨bold¨»C«/mi»«msub»«mi mathvariant=¨bold¨»B«/mi»«mi mathvariant=¨bold¨»M«/mi»«/msub»«/msub»«/mrow»«mrow»«mn»2«/mn»«msub»«mi mathvariant=¨bold¨»M«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«msub»«mi mathvariant=¨bold¨»C«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«msub»«mi mathvariant=¨bold¨»C«/mi»«mi mathvariant=¨bold¨»T«/mi»«/msub»«mi mathvariant=¨bold¨»S«/mi»«/mrow»«/mfrac»«/math»

=7.67*10(-6) m2/sec

 

 

Similarly repeating the experiments at different temperature we get different values for diffusion co-efficient.Thus it is seen that the diffusion coefficient is a function of time and it increases with increase in temperature.

Plot a T vs D*P on a log - log plot.

Finally from the plot we have

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨»D«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo»§#215;«/mo»«msup»«mi mathvariant=¨bold¨»T«/mi»«mi mathvariant=¨bold¨»b«/mi»«/msup»«/math»

where b is a parameter that denotes temperature dependence and theoritically it should lie between 1.5 to 1.8

 

 

 

 

 

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