Answer :
Let's address each part of your question one by one:
**Aqueous Solution of Sodium Chloride and Molten Sodium Chloride:**
An aqueous solution of sodium chloride cannot be used to produce sodium metal because water will undergo electrolysis along with the sodium chloride. In aqueous solution, electrolysis of water produces hydrogen gas at the cathode and oxygen gas at the anode instead of producing sodium metal, which would react violently with water.
**Derivation of the Relationship Between Kp and Kc:**
The equilibrium constant for a reaction in terms of partial pressures, Kp, is related to the equilibrium constant in terms of concentration, Kc, by the equation:
\[ K_p = K_c(RT)^{\Delta n} \]
where Δn is the difference in moles of gaseous products and reactants, R is the ideal gas constant, and T is the temperature in Kelvin.
For example, consider the synthesis of ammonia:
\[ N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g) \]
The Δn for this reaction is 2 - (1 + 3) = -2. Because Δn is negative, Kp will be less than Kc at a fixed temperature since we raise (RT) to a negative power, which yields a number smaller than one.
**Derivation of the Ideal Gas Equation PV = nRT:**
The ideal gas equation is an empirical law that describes the behavior of ideal gases. It is not derived from first principles but is based on experimental observations and can be stated as:
\[ PV = nRT \]
where P represents the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Conditions under which real gas behavior approaches that of an ideal gas include:
1. High temperature: At higher temperatures, the kinetic energy of the gas molecules is greater, and the effects of intermolecular forces become less significant.
2. Low pressure: At lower pressures, the volume occupied by the gas molecules themselves is negligible compared to the total volume of the container, and the distances between molecules are relatively large, making the interactions between molecules insignificant.
**Production of Hydrogen Chloride Gas Using Concentrated Sulfuric Acid:**
To produce hydrogen chloride gas in the laboratory, concentrated sulfuric acid (H2SO4) reacts with a chloride salt, such as sodium chloride (NaCl). The general reaction can be represented as:
\[ NaCl(s) + H_2SO_4(l) \rightarrow NaHSO_4(s) + HCl(g) \]
Hydrogen chloride gas is evolved, and sodium hydrogen sulfate is formed as the solid product.
