Chemical Kinetics

Step 1: Understanding the relationship for first-order reactions.
For a first-order reaction, the relationship between the concentration of reactant at time and the half-life is given by the equation: where is the initial concentration, is the concentration at time , and is the rate constant.

Step 2: Using the information given.
At the end of 30 minutes, the reaction is 87.5% complete. This means only 12.5% of the original reactant remains. Thus, .

Step 3: Using the formula for first-order reactions.
For first-order reactions, the fraction remaining after time is given by: Taking the natural logarithm: Solving for :

Step 4: Calculating the half-life.
The half-life for a first-order reaction is given by: Substitute the value of :

Step 5: Conclusion.
Thus, the half-life of the reaction is 10 minutes, and the correct answer is 10.

To determine the order with respect to A, we compare the initial rates for the same concentration of [B]. The rate doubles as [A] doubles, indicating the order is 1 with respect to A