The data below relate to the adsorption of N2 on rutile (TiO2) at 75 K. Confirm...

The data below relate to the adsorption of N2 on rutile (TiO2) at 75 K. Confirm
that they fit a BET isotherm in the range of pressures reported, and determine Vmon
and c.

p/kPa 0.160 1.87 6.11 11.67 17.02 21.92 27.29
V/cm3 235 559 649 719 790 860 950

At 75 K, p* = 76.0 kPa. The volumes have been corrected to 1.00 atm and 273 K and
refer to 1.00 g of substrate

how do I know the intercept without graph excel in exam ?

Solutions

Expert Solution

The equation that follows BET adsorption isotherm is

On rearranging the equation becomes

Now if we plot z/(1-z)V vs z then it will be straight line y = mx + c where m = slope = 1/cVmono and intercept = (c-1)/cVmono

Setting up the table

Now if you want to calculate without excel first calculate the slope

Since this is an equation of straight line y = mx + c

here m = y2-y1 / x2 - x1

so take any two values

I am taking 1st two values

y2 = 0.35 y1 = 0.035

x2 = 24.6 ; x1 = 2.11

so m = (0.35 - 0.035) / (24.6 - 2.11) = 1.3 * 10^-2

now take first values of x and y and put the value of m

y = 0.035 and x = 2.11

and m = 1.3 * 10^-2

0.035 = 1.3 * 10^-2 * 2.11 + c

on solving intercept c = 0.0075

From this we conclude that (c − 1)/cVmon will be calculated from the slope of a plot of the expression of the equation which is on the left versus z, and cVmon can be obtained by the value of the intercept at z = 0. Combining these results we will get c and Vmon.

On obtaining the solutions we get c = 310 and Vmon = 811 mm³

queen_honey_blossom answered 2 months ago

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