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For adsorption of gas on solid surface, the plots of log x/m vs. log P is linear with a slope equal to:
  • a)
    K
  • b)
    log K
  • c)
    1/nK
  • d)
    1/n ( n being interger)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
For adsorption of gas on solid surface, the plots of log x/m vs. log P...
The empirical relation x/m = kp1/n put forward by Freundlich is known as Freundlich adsorption isotherm. Taking logarithm

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For adsorption of gas on solid surface, the plots of log x/m vs. log P...
Explanation:

Adsorption is the process of accumulation of molecules or particles on the surface of a material. The amount of gas adsorbed on a solid surface is proportional to the pressure of the gas at constant temperature. The relationship between the amount of gas adsorbed and the pressure of the gas can be expressed by the Langmuir adsorption isotherm equation given below:

x/m = K P / (1 + K P)

where x is the amount of gas adsorbed, m is the mass of the adsorbent, P is the pressure of the gas, K is the adsorption equilibrium constant, and 1/K is the Langmuir adsorption constant.

The plot of log x/m vs. log P is linear with a slope equal to 1/n, where n is an integer. This can be explained as follows:

- Taking logarithm of both sides of the Langmuir adsorption isotherm equation, we get:

log (x/m) = log K + log P - log (1 + K P)

- Comparing this equation with the equation of a straight line, y = mx + c, we can see that the slope of the line is 1/n, where n is the order of the reaction. For the Langmuir adsorption isotherm equation, n = 1, hence the slope is 1.

- Therefore, the plot of log x/m vs. log P is a straight line with a slope equal to 1, which means that the adsorption process follows a first-order reaction.

- This relationship is useful in determining the adsorption equilibrium constant and the surface area of the adsorbent. By measuring the amount of gas adsorbed at different pressures and plotting the data on a log-log scale, the slope of the line can be determined, which gives the value of 1/nK.

- Thus, the plot of log x/m vs. log P is a powerful tool for studying the adsorption process and characterizing the adsorbent.
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For adsorption of gas on solid surface, the plots of log x/m vs. log P...
For the adsorption of a gas on a solid x/m ​= kp1/n. This equation is known as Freundlich Adsorption Isotherm.
On taking logarithm on both sides, we obtain, logx/m ​= logk+ 1/n​logp
∴ plot of log(x/m) versus log p will be linear with slope = 1/n​ .
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