Two compounds A and B in a flask decompose independently to yield the same product P . The reaction for A is A P and for B is B 2P . Both reactions follow first-order kinetics. The half-life of A is 20 minutes and that of B is 40 minutes . If the initial amounts of A and B are 400 mmol and 200 mmol respectively, the total amount of product P formed after 40 minutes is ____ mmol .

Step-by-step solution

For compound A , the number of half-lives passed in 40 minutes is n_A = 40 20 = 2 . Amount of A remaining after 40 minutes = 400 2^2 = 100 mmol . Amount of A reacted = 400 - 100 = 300 mmol . From the stoichiometry A P , 1 mole of A gives 1 mole of P . Amount of P formed from A = 300 mmol . For compound B , the number of half-lives passed in 40 minutes is n_B = 40 40 = 1 . Amount of B remaining after 40 minutes = 200 2^1 = 100 mmol . Amount of B reacted = 200 - 100 = 100 mmol . From the stoichiometry B 2P , 1 mole o