The conversion of sulfur dioxide \( \text{SO}_2 \) to sulfur trioxide \( \text{SO}_3 \) in the Contact Process is a key step in the production of sulfuric acid. This reaction occurs in the presence of a vanadium(V) oxide catalyst.
Step 1: Reaction Characteristics:
The reaction:
\[ 2\ \text{SO}_2 (g) + \text{O}_2 (g) \rightarrow 2\ \text{SO}_3 (g) \]
is known to be exothermic, releasing heat. The standard enthalpy change \( \Delta H^\circ \) for this reaction is negative, indicating that heat is released to the surroundings.
Step 2: Reversibility:
This reaction is also reversible. Under industrial conditions, it does not go to completion, and the formation of \( \text{SO}_3 \) can be reversed back to \( \text{SO}_2 \) and \( \text{O}_2 \) under certain conditions.
The use of a catalyst and optimized conditions such as temperature and pressure help shift the equilibrium towards the formation of more \( \text{SO}_3 \).
Step 3: Industrial Significance:
The exothermic nature of the reaction helps in maintaining operational efficiency, while its reversibility is critical for maximizing \( \text{SO}_3 \) yield through the recirculation of unreacted gases and careful control of reaction conditions.
An ideal monoatomic gas is contained inside a cylinder-piston assembly connected to a Hookean spring as shown in the figure. The piston is frictionless and massless. The spring constant is 10 kN/m. At the initial equilibrium state (shown in the figure), the spring is unstretched. The gas is expanded reversibly by adding 362.5 J of heat. At the final equilibrium state, the piston presses against the stoppers. Neglecting the heat loss to the surroundings, the final equilibrium temperature of the gas is __________ K (rounded off to the nearest integer).
The residence-time distribution (RTD) function of a reactor (in min$^{-1}$) is 
The mean residence time of the reactor is __________ min (rounded off to 2 decimal places).}
Ideal nonreacting gases A and B are contained inside a perfectly insulated chamber, separated by a thin partition, as shown in the figure. The partition is removed, and the two gases mix till final equilibrium is reached. The change in total entropy for the process is _________J/K (rounded off to 1 decimal place).
Given: Universal gas constant \( R = 8.314 \) J/(mol K), \( T_A = T_B = 273 \) K, \( P_A = P_B = 1 \) atm, \( V_B = 22.4 \) L, \( V_A = 3V_B \).
The following data is given for a ternary \(ABC\) gas mixture at 12 MPa and 308 K:
\(y_i\): mole fraction of component \(i\) in the gas mixture
\(\hat{\phi}_i\): fugacity coefficient of component \(i\) in the gas mixture at 12 MPa and 308 K
The fugacity of the gas mixture is __________ MPa (rounded off to 3 decimal places).