Identify the correct statements from the following.
$(i)$ In the oxidation of oxalic acid with $KMnO_4$ in acid medium, $Mn^{2+}$ acts as an autocatalyst.
$(ii)$ $CdS$ colloidal solution can be precipitated by the addition of $Cl^{-}$ ions.
$(iii)$ The gold numbers of three protective colloids $(A, B, C)$ are $0.03$, $25$, and $0.25$ respectively. Their protective power follows the order $A > C > B$.
$(iv)$ Physisorption is an irreversible process.

The correct statement$(s)$ about surface properties is(are):
$[A]$ Adsorption is accompanied by decrease in enthalpy and decrease in entropy of the system.
$[B]$ The critical temperatures of ethane and nitrogen are $563 \ K$ and $126 \ K$,respectively. The adsorption of ethane will be more than that of nitrogen on the same amount of activated charcoal at a given temperature.
$[C]$ Cloud is an emulsion type of colloid in which liquid is dispersed phase and gas is dispersion medium.
$[D]$ Brownian motion of colloidal particles does not depend on the size of the particles but depends on the viscosity of the solution.

Sodium thiosulphate is used in photography to :-

$0.27 \ g$ of a long chain fatty acid was dissolved in $100 \ cm^3$ of hexane. $10 \ mL$ of this solution was added dropwise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed. The distance from edge to centre of the watch glass is $10 \ cm$. What is the height of the monolayer? [Density of fatty acid $= 0.9 \ g \ cm^{-3}, \pi = 3$]

$A$ cube of edge length $1 \ cm$ is divided into smaller cubes of uniform size of length $1 \ nm$. Assuming that no voids are present, the ratio of total surface area of all the cubes of $1 \ nm$ edge length to the surface area of the initial cube is

Photographic films and plates have an essential ingredient of