Question

1. a factory wants to produce ammonia (nh₃) as quickly as possible using the reaction: n₂ + 3h₂ → 2nh₃. design a plan to control this reaction for maximum speed. consider temperature, pressure, concentration, and catalysts.

Explanation:

• Temperature: Increase temperature. Higher temperature provides more kinetic energy to reactant molecules (\(N_2\) and \(H_2\)), increasing the frequency of effective collisions. According to the Arrhenius equation \(k = A e^{-\frac{E_a}{RT}}\), where \(k\) is the rate - constant, \(A\) is the pre - exponential factor, \(E_a\) is the activation energy, \(R\) is the gas constant and \(T\) is the temperature. As \(T\) increases, \(k\) increases.
• Pressure: Increase pressure. The reaction \(N_2+3H_2

ightarrow 2NH_3\) has \(4\) moles of reactants (\(1\) mole \(N_2 + 3\) moles \(H_2\)) and \(2\) moles of products. By Le - Chatelier's principle, increasing pressure (since \(P=\frac{nRT}{V}\), for a fixed \(V\) and \(T\), increasing \(n\) (by compressing the gases) increases \(P\)) shifts the equilibrium towards the side with fewer moles (product side). Also, higher pressure means higher concentration (since \(C=\frac{n}{V}\), for a fixed \(V\), higher \(n\) (due to compression) means higher \(C\)), and rate of reaction is proportional to concentration (for an elementary reaction, rate \(\propto [N_2][H_2]^3\)).

• Concentration: Increase the concentration of \(N_2\) and \(H_2\). According to the rate law (for the forward reaction, if we assume an elementary reaction, rate \(r = k[N_2][H_2]^3\)), higher concentrations of reactants lead to a higher rate of reaction as there are more reactant molecules per unit volume, increasing the collision frequency.
• Catalyst: Use a catalyst (e.g., iron - based catalyst). A catalyst lowers the activation energy (\(E_a\)) of the reaction. From the Arrhenius equation \(k = A e^{-\frac{E_a}{RT}}\), a lower \(E_a\) means a higher value of \(k\) (rate - constant) for a given \(T\). So, the reaction occurs at a faster rate.

Answer:

Increase temperature (to increase kinetic energy and rate - constant), increase pressure (to increase concentration and shift equilibrium towards products), increase the concentration of \(N_2\) and \(H_2\) (to increase collision frequency based on rate law), and use an iron - based catalyst (to lower activation energy and increase rate - constant).