The Freundlich adsorption isotherm is an empirical relationship that describes the adsorption of gases or solutes onto a surface. It is represented by: \[ \frac{x}{m} = k p^{1/n} \] where $x$ is the mass of the adsorbate, $m$ is the mass of the adsorbent, $p$ is the pressure, and $k$ and $n$ are constants. The graphical representations are:
A: Correct, shows $\frac{x}{m}$ vs $p$ with a logarithmic relationship.
B: Correct, shows $\log \frac{x}{m}$ vs $\log p$ as a straight line.
D: Correct, shows a logarithmic relationship $\frac{x}{m}$ vs $p^{1/n}$.
C: Incorrect, as it shows a constant $\frac{x}{m}$, not related to Freundlich's isotherm. \end{itemize}
Thus, the correct representations are A, B, and D.
If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440th position in this arrangement is:
If the system of equations \[ x + 2y - 3z = 2, \quad 2x + \lambda y + 5z = 5, \quad 14x + 3y + \mu z = 33 \] has infinitely many solutions, then \( \lambda + \mu \) is equal to:}
The equilibrium constant for decomposition of $ H_2O $ (g) $ H_2O(g) \rightleftharpoons H_2(g) + \frac{1}{2} O_2(g) \quad (\Delta G^\circ = 92.34 \, \text{kJ mol}^{-1}) $ is $ 8.0 \times 10^{-3} $ at 2300 K and total pressure at equilibrium is 1 bar. Under this condition, the degree of dissociation ($ \alpha $) of water is _____ $\times 10^{-2}$ (nearest integer value). [Assume $ \alpha $ is negligible with respect to 1]