This is a multiple-choice question with one or more correct options about surface properties. Let's analyze each statement.

Statement A: Adsorption is accompanied by decrease in ethalpy and decrease in entropy of the system

1. Thermodynamics of Adsorption: Adsorption is the process where gas or liquid molecules (adsorbate) adhere to the surface of a solid or liquid (adsorbent). This is a spontaneous process.
2. Enthalpy Change ($\\\Delta H$): When adsorbate molecules are attracted to the adsorbent surface, new bonds (like van der Waals forces in physisorption or chemical bonds in chemisorption) are formed. Bond formation is an exothermic process, which means heat is released. Therefore, the enthalpy of the system decreases, and $\\\Delta H$ is negative.
3. Entropy Change ($\\\Delta S$): Before adsorption, the adsorbate molecules are free to move around (especially in the gas phase). After adsorption, they are held on the surface, restricting their movement. This leads to a more ordered state, so the randomness or entropy of the system decreases. Thus, $\\\Delta S$ is negative.
4. Gibbs Free Energy ($\\\Delta G$): For a process to be spontaneous, the change in Gibbs free energy must be negative ($\\\Delta G < 0$). The Gibbs-Helmholtz equation is $\\\Delta G = \\\Delta H - T\\\Delta S$. Since $\\\Delta H$ is negative and $\\\Delta S$ is negative, the term $-T\\\Delta S$ is positive. For $\\\Delta G$ to be negative, the magnitude of the negative enthalpy change must be greater than the positive $T\\\Delta S$ term ($|\\\Delta H| > |T\\\Delta S|$).

Conclusion: Statement A is correct. Adsorption is an exothermic process ($\\\Delta H < 0$) and leads to a decrease in entropy ($\\\Delta S < 0$).

Statement B: The critical temperatures of ethane and nitrogen are $563K$ and $126K,$ respectively. The adsorption of ethane will be more than that of nitrogen on same amount of activated charcoal at a given temperature

1. Critical Temperature ($T_c$) and Adsorption: The critical temperature of a gas is the temperature above which it cannot be liquefied, no matter how much pressure is applied. A higher critical temperature indicates stronger intermolecular forces of attraction, making the gas easier to liquefy.
2. Extent of Physisorption: Physical adsorption (physisorption) relies on weak van der Waals forces. Gases that are more easily liquefiable are more readily adsorbed on a surface. This is because the same intermolecular forces responsible for liquefaction are also responsible for physisorption.
3. Comparison: Given $T_c(\\text{ethane}) = 563K$ and $T_c(\\text{nitrogen}) = 126K$. Since the critical temperature of ethane is much higher than that of nitrogen, ethane is much more easily liquefiable than nitrogen.
4. Conclusion: Consequently, at a given temperature and pressure, ethane will be adsorbed to a greater extent than nitrogen on the same amount of activated charcoal. Statement B is correct.

Statement C: Cloud is an emulsion type of colloid in which liquid is dispersed phase and gas is dispersion medium

1. Definition of a Cloud: A cloud is a colloidal system consisting of tiny liquid water droplets or ice crystals (dispersed phase) suspended in the air (dispersion medium).
2. Types of Colloids:
   • Emulsion: A colloid in which both the dispersed phase and the dispersion medium are liquids (e.g., milk).
   • Aerosol: A colloid in which the dispersion medium is a gas. If the dispersed phase is a liquid, it's a liquid aerosol. If the dispersed phase is a solid, it's a solid aerosol.
3. Classification of Cloud: Since a cloud consists of a liquid (water droplets) dispersed in a gas (air), it is classified as a liquid aerosol, not an emulsion.

Conclusion: Statement C is incorrect because it misclassifies a cloud as an emulsion.

Statement D: Brownian motion of colloidal particles does not depend on the size of the particles but depends on viscosity of the solution

1. Brownian Motion: This is the random, zig-zag movement of colloidal particles suspended in a dispersion medium. It is caused by the unbalanced bombardment of the colloidal particles by the smaller, fast-moving molecules of the dispersion medium.
2. Factors Affecting Brownian Motion:
   • Size of Particles: Brownian motion is more pronounced for smaller particles. Larger particles experience more uniform bombardment from all sides, which tends to cancel out, resulting in less movement. Thus, Brownian motion is inversely related to the size of the colloidal particles. The statement that it does not depend on size is incorrect.
   • Viscosity of the Solution: A more viscous medium offers more resistance to the movement of particles. Therefore, Brownian motion decreases as the viscosity of the solution increases. The statement that it depends on viscosity is correct.
   • Temperature: Higher temperature leads to faster movement of medium molecules, more energetic collisions, and thus more rapid Brownian motion.

Conclusion: Since one part of the statement (