Adsorption of a gas on a surface follows Freundlich adsorption isotherm. Plot of log(x/m) versus log p gives a straight line with slope equal to 0.5, then what is the relationship between adsorption and pressure?

The Freundlich adsorption isotherm is given by the equation:

x/m = kP^(1/n)

where:

x/m is the mass of gas adsorbed per gram of adsorbent
k is the Freundlich constant
P is the pressure of the gas
1/n is a constant which is less than 1

Taking logarithm on both sides, we get:

log(x/m) = log k + (1/n)log P

This equation is of the form y = mx + c, where y = log(x/m), x = log P, m = 1/n, and c = log k. This represents a straight line with a slope of 1/n.

Given that the slope of the plot of log(x/m) versus log P is 0.5, we have:

1/n = 0.5

n = 2

Substituting this value of n into the Freundlich adsorption isotherm equation, we get:

x/m = kP^(1/2)

x/m = k√P

This shows that the adsorption (x/m) is proportional to the square root of the pressure (P).