In a first-order reaction A B , if k is the rate constant and initial concentration of thereactant A is 0.5 M, then the half-life i

To determine the half-life of a first-order reaction A B, we need to use the rate constant (k) and the initial concentration of reactant A (0.5 M).

Step 1: Recall the first-order reaction rate equation: Rate = k[A]

Step 2: The half-life (t1/2) is the time it takes for the concentration of reactant A to decrease by half. Mathematically, it can be calculated using the equation: t1/2 = (0.693 / k)

Step 3: Substitute the given initial concentration of reactant A (0.5 M) into the rate equation: Rate = k[0.5]

Step 4: Rearrange the rate equation to solve for the rate constant (k): k = Rate / [0.5]

Step 5: Substitute the value of k into the half-life equation: t1/2 = (0.693 / (Rate / [0.5]))

Step 6: Simplify the equation: t1/2 = (0.693 * [0.5]) / Rate

Step 7: Calculate the half-life using the given rate constant (k) and initial concentration of reactant A (0.5 M).

Please note that the specific value of the rate constant (k) is not provided in the question, so you would need that information to calculate the half-life accurately.