In a given 1st order reaction A ---> products, the initial concentration of A is 0.40 M. What will be the concentration of A after 15 seconds if the half-life of the reaction is 3 seconds?
Same song, third verse.
To determine the concentration of A after 15 seconds, we need to use the concept of half-life. The half-life is the time taken for the concentration of a reactant to decrease by half.
Given that the half-life of the reaction is 3 seconds, we can calculate the number of half-lives that occur in 15 seconds by dividing the total time by the half-life:
Number of half-lives = Total time / Half-life
Number of half-lives = 15 seconds / 3 seconds
Number of half-lives = 5
Since each half-life divides the concentration by half, we can raise the fractional value of 1/2 to the power of the number of half-lives to find the fraction of the initial concentration remaining:
Fraction remaining = (1/2)^(Number of half-lives)
Fraction remaining = (1/2)^5
Fraction remaining ≈ 0.03125
Finally, we can multiply this fraction by the initial concentration of A to find the concentration of A after 15 seconds:
Concentration of A after 15 seconds = Fraction remaining * Initial concentration
Concentration of A after 15 seconds ≈ 0.03125 * 0.40 M
Concentration of A after 15 seconds ≈ 0.0125 M
Therefore, the concentration of A after 15 seconds is approximately 0.0125 M.