Determine the rate constant from the concentration-time dependence Time (s) [Rea

Question

Determine the rate constant from the concentration-time dependence Time (s) [Reactant] (M) 0.0 10 20 50 70 0.0350 0.0223 0.0142 0.0037 0.0015 Use Sl units, that is, seconds for time (not included in answer) Answer: Calculate the half-life (in s) of a first-order reaction if the concentration of the reactant is 0.0782 M 25.2 s after the reaction starts and is 0.0285 M 56.3 s after the reaction starts Answer Suppose the half-life is 50.8 s for a first order reaction and the reactant concentration is 0.0860 M 64.9 s after the reaction starts. How many seconds after the start of the reaction does it take for the reactant concentration to decrease to 0.0102 M? Answer:

Explanation / Answer

1)

let us check for first - order :

rate constant = 1/t ln (Ao / At)

k1 = 1/10 ln (0.0350 / 0.0223)

      = 0.0451 s-1

k2 = 1/ 20 ln (0.0350 / 0.0142)

     = 0.0451 s-1

here all rate constants are same. so this is confirmed to be first - order.

rate constant = 0.0451 s-1

2)

for first - order reaction :

K = 1 /(t2-t1) ln (a-x1/a-x2)

    = 1 / (56.3 - 25.2) ln (0.0782 / 0.0285)

    = 0.0326 s-1

half - life = 0.693 / k

              = 0.693 / 0.0326

hlaf -life = 21.4 s

3)

rate constant = 0.693 / half - life

                      = 0.693 / 50.8

                      = 0.0136 s

K = 1 /(t2-t1) ln (a-x1/a-x2)

0.0136 = 1 / (t2 - 64.9) ln (0.0860 / 0.0102)

t2 = 221.7

time taken = 221.7 s

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