Question

The mass of gas adsorbed, \[x\] , per unit mass of adsorbate, \[m\] was measured at various pressures, \[p\] . A graph between \[\log [x/m]\] and between \[\log p\] gives a straight line with slope equal to 2 and the intercept equal to \[0.4771\] . The value of \[[x/m]\] at pressure of 4 atm is: ( Given \[\log 3 = 0.4771\] )

Answer 1

Hint: Adsorption is a phenomenon in which the atoms of a molecule in a substance adhere to a surface. The adsorption can occur in solid, liquid, or gases, and the materials that exhibit this property are termed adsorbents.

Formula used: In the question mentioned above, we have the following values:
Mass of gas adsorbed is \[x\]
Per unit mass of adsorbate is \[m\]
Pressure is denoted as \[p\]
Slope of graph between \[\log [x/m]\] and \[\log p\] was equal to 2
Intercept C was equal to \[0.4771\]
The formula we will use to calculate the value of \[[x/m]\] at 4 atm is
\[(\dfrac{x}{m}) = K{p^{1/n}}\]

Complete Step by Step Solution:
By using the formula mentioned above, we will get
\[(\dfrac{x}{m}) = K{p^{1/n}}\]
\[\log (\dfrac{x}{m}) = {\log _{(k)}} + (\dfrac{1}{n})\log p\]
\[y = c + mx\]
\[Intercept\,C = {\log _k} = 0.4771\]
\[Slope = \dfrac{1}{n} = \,2\]
\[k = 3\]
\[(\dfrac{x}{m}) = k{(p)^{1/n}}\] at \[p = 4\,atm\]
\[ = 3{(4)^2}\]
\[(\dfrac{x}{m}) = 3 \times 16\]
\[ = 48\]
Hence, the value of \[[x/m]\] at the pressure of 4 atm will be 48.

Note: Adsorption is entirely a surface phenomenon and it results in the formation of a film over the surface. This process has been of a lot of significance in our day-to-day life as well. It has various applications such as in heterogeneous catalysts, activated charcoal, synthetic resins, water purification, helps in increasing the storage capacity of the carbide-derived carbons and capturing and usage of heat that is wasted for air conditioning. This process has also been of great importance in our body as proteins, more commonly albumin is transferred in the body with this process.