At a given temperature, 0.45 g of acetic acid in 50 mL of water is shaken with 1.0 g of charcoal and the pH of the resulting solution is 3.0 . Assume, the adsorption of acetic acid from the aqueous solution by charcoal follows Freundlich isotherm,

$$ \frac{x}{m}=k C^{1 / n} $$

If the plot of $\log _{10}(x / m)$ against $\log _{10} C$ gives a straight line with slope 1 , the value of $k$ in $\mathrm{L} \mathrm{mol}^{-1}$ is $\_\_\_\_$ .

Given: The molar mass of acetic acid is $60 \mathrm{~g} \mathrm{~mol}^{-1}$.

The acid dissociation constant of acetic acid is $1.0 \times 10^{-5}$ at the given temperature.

$x$ is the mass (in grams) of acetic acid adsorbed.

$m$ is the mass (in grams) of charcoal.

$C$ is the equilibrium concentration of acetic acid in the solution after the adsorption is complete.

$k$ and $n$ are constants for acetic acid-charcoal system at the given temperature.

Adsorption of phenol from its aqueous solution on to fly ash obeys Freundlich isotherm. At a given temperature, from $10 \mathrm{mg} \mathrm{g}^{-1}$ and $16 \mathrm{mg} \mathrm{g}^{-1}$ aqueous phenol solutions, the concentrations of adsorbed phenol are measured to be $4 \mathrm{mg} \mathrm{g}^{-1}$ and $10 \mathrm{mg} \mathrm{g}^{-1}$, respectively. At this temperature, the concentration (in $\mathrm{mg} \mathrm{g}^{-1}$ ) of adsorbed phenol from $20 \mathrm{mg} \mathrm{g}^{-1}$ aqueous solution of phenol will be ______________.

Use: $\log _{10} 2=0.3$

To form a complete monolayer of acetic acid on $1 \mathrm{~g}$ of charcoal, $100 \mathrm{~mL}$ of $0.5 \mathrm{M}$ acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 $\mathrm{mL}$ of $1 \mathrm{M} \mathrm{NaOH}$ solution was required. If each molecule of acetic acid occupies $\mathbf{P} \times 10^{-23} \mathrm{~m}^2$ surface area on charcoal, the value of $\mathbf{P}$ is _____.

[Use given data: Surface area of charcoal $=1.5 \times 10^2 \mathrm{~m}^2 \mathrm{~g}^{-1}$; Avogadro's number $\left(\mathrm{N}_{\mathrm{A}}\right)=6.0 \times 10^{23}$ $\left.\mathrm{mol}^{-1}\right]$

Nitrogen gas is absorbed on 20% surface sites. On heating N$$_2$$ gas evolved from sites and was collected at 0.01 atm and 298 K in a container of volume 2.46 cm$$^3$$. Find out the number of surface sites occupied per molecule of N, if the density of surface sites is $$6.023\times10^{14}/\mathrm{cm^3}$$ and surface area is 1000 cm$$^2$$.