In a second-order reaction, the rate of the reaction is determined by the concentrations of the reactants raised to the power of 2. If both reactants, A and B, exhibit first-order behavior, it means that the rate depends on the individual concentrations of A and B.
To determine which reactant mixture will provide the highest initial rate, we need to compare the concentrations of A and B in each option.
Let's examine the given options:
(1) 0.1 mol of A and 0.1 mol of B in 0.2 liters of solvent
(2) 1.0 mol of A and 1.0 mol of B in one liter of solvent
(3) 0.2 mol of A and 0.2 mol of B in 0.1 liters of solvent
(4) 0.1 mol of A and 0.1 mol of B in 0.1 liters of solvent
To compare the concentrations, we need to consider the total moles of A and B divided by the volume of the solvent.
Let's calculate the concentrations for each option:
(1) Concentration of A = 0.1 mol / 0.2 L = 0.5 M
Concentration of B = 0.1 mol / 0.2 L = 0.5 M
(2) Concentration of A = 1.0 mol / 1 L = 1.0 M
Concentration of B = 1.0 mol / 1 L = 1.0 M
(3) Concentration of A = 0.2 mol / 0.1 L = 2.0 M
Concentration of B = 0.2 mol / 0.1 L = 2.0 M
(4) Concentration of A = 0.1 mol / 0.1 L = 1.0 M
Concentration of B = 0.1 mol / 0.1 L = 1.0 M
Comparing the concentrations, we can see that option (3) has the highest concentration of both reactants, A and B, with concentrations of 2.0 M.
Therefore, the reactant mixture in option (3) with 0.2 mol of A and 0.2 mol of B in 0.1 liters of solvent will provide the highest initial rate. |
