Surface Chemistry

The coagulating value of an electrolyte is defined as the minimum amount of the electrolyte required to coagulate a unit volume of the colloidal solution in a given time. In this problem, we are given that $20\ \mathrm{mL}$ of $0.5\ \mathrm{M}$ $\mathrm{NaCl}$ solution is required to coagulate $200\ \mathrm{mL}$ of $\mathrm{As}_2\mathrm{S}_3$ solution in 2 hours.

To find the coagulating value of $\mathrm{NaCl}$, we need to determine the amount of $\mathrm{NaCl}$ required to coagulate 1 liter (1000 mL) of the $\mathrm{As}_2\mathrm{S}_3$ solution in 2 hours. This can be calculated using the following formula:

$\text{Coagulating value} = \frac{\text{amount of electrolyte required to coagulate 1 L of sol in 2 hours}}{1\ \mathrm{L}}$

To find the amount of $\mathrm{NaCl}$ required to coagulate 200 mL of the $\mathrm{As}_2\mathrm{S}_3$ solution in 2 hours, we can use the formula for the number of moles of $\mathrm{NaCl}$ used:

$n_{\mathrm{NaCl}} = C_{\mathrm{NaCl}} \times V_{\mathrm{NaCl}}$

where $C_{\mathrm{NaCl}}$ is the concentration of $\mathrm{NaCl}$ in moles per liter, and $V_{\mathrm{NaCl}}$ is the volume of $\mathrm{NaCl}$ solution used in liters. Substituting the given values, we get:

$n_{\mathrm{NaCl}} = 0.5\ \mathrm{M} \times 0.02\ \mathrm{L} = 0.01\ \mathrm{mol}$

To find the amount of $\mathrm{NaCl}$ required to coagulate 1 L of the $\mathrm{As}_2\mathrm{S}_3$ solution, we need to scale up the amount of $\mathrm{NaCl}$ used by a factor of 5 (since 5 times the given volume of $\mathrm{NaCl}$ solution is required to make 1 L of the $\mathrm{As}_2\mathrm{S}_3$ solution). This gives:

$n_{\mathrm{NaCl}} = 0.01\ \mathrm{mol} \times 5 = 0.05\ \mathrm{mol}$

The coagulating value of $\mathrm{NaCl}$ can now be calculated as:

$\text{Coagulating value} = \frac{0.05\ \mathrm{mol}}{1\ \mathrm{L}} \times 1000 = 50\ \mathrm{mM}$

Therefore, the coagulating value of $\mathrm{NaCl}$ is $\boxed{50}$ (in millimoles per liter).

Let's analyze each statement about modern adsorption theory of heterogeneous catalysis:

A. The catalyst is diffused over the surface of reactants.

This statement is incorrect. In heterogeneous catalysis, the catalyst is usually a solid, and the reactants are in a different phase (gas or liquid). The reactants are adsorbed on the catalyst's surface, not the other way around.

B. Reactants are adsorbed on the surface of the catalyst.

This statement is correct. In the adsorption theory of heterogeneous catalysis, reactants are adsorbed onto the surface of the catalyst, where they undergo a chemical reaction.

C. Occurrence of chemical reaction on the catalyst's surface through formation of an intermediate.

This statement is correct. In the adsorption theory, the reaction takes place on the catalyst's surface through the formation of an intermediate species.

D. It is a combination of intermediate compound formation theory and the old adsorption theory.

This statement is correct. The modern adsorption theory of heterogeneous catalysis combines the concepts of intermediate compound formation and the old adsorption theory.

E. It explains the action of the catalyst as well as those of catalytic promoters and poisons.

The modern adsorption theory of heterogeneous catalysis does explain the action of the catalyst. However, the roles of catalytic promoters and poisons are not entirely explained by this theory. The NCERT textbook states that the modern adsorption theory explains the action of the catalyst but does not elaborate on the roles of promoters and poisons.

Therefore, considering the information provided by the NCERT textbook, point E is not entirely correct. There are three correct statements (B, C, and D) about the modern adsorption theory of heterogeneous catalysis.