Final answer:
The overall reaction described by the given mechanism is 2NO + Br2 ⟶ 2BrNO. To calculate the rate constant (k) for a reaction at 50.0 °C with an activation energy of 77.3 kJ/mol and a frequency factor of 3.50x10^11 s-1, we can use the Arrhenius equation: k = A * e^(-Ea/RT).
Step-by-step explanation:
The overall reaction that this mechanism describes can be obtained by adding up the elementary steps and canceling out intermediate species (Br2NO in this case) that do not appear in the final reaction equation. The first step adds Br2 to NO to form Br2NO, and the second step has Br2NO reacting with another NO to produce 2BrNO. Adding these up, the intermediates cancel out, leaving the overall reaction as:
2NO(g) + Br2(g) → 2BrNO(g)
To calculate the rate constant, k, for the reaction at 50.0 °C with an activation energy of 77.3 kJ/mol and a frequency factor of 3.50×1011 s−1, we use the Arrhenius equation:
k = A × exp(-Ea/(RT))
Where A is the frequency factor, Ea is the activation energy, R is the universal gas constant in appropriate units (8.314 J/mol·K), and T is the temperature in Kelvin. We will need to convert the given temperature to Kelvin and the activation energy to joules per mole before plugging into the equation:
50.0 °C = 323.15 K
77.3 kJ/mol = 77300 J/mol
Substitute these values into the Arrhenius equation to find k.