Will NOT rate if all questions are not answered! 1. The reaction X products is f

Question

Will NOT rate if all questions are not answered!

1. The reaction X products is first-order, and the rate constant is 1.2 × 104 min1. If the original concentration of X is 1.35 M, how long (in hr) will it take the concentration of X to decrease by 85%?

2. What is its molarity after a reaction time of 27.0 h ?

_____ M?

3. Half-life equation for first-order reactions:

t1/2=0.693k  
where t1/2 is the half-life in seconds (s), and k is the rate constant in inverse seconds (s1).

Part A

What is the half-life of a first-order reaction with a rate constant of 5.70×104  s1?

Express your answer with the appropriate units.

4. What is the rate constant of a first-order reaction that takes 131 seconds for the reactant concentration to drop to half of its initial value?

5. A certain first-order reaction has a rate constant of 6.20×103 s1. How long will it take for the reactant concentration to drop to 18 of its initial value?

Explanation / Answer

1) we know that for first order reactoin

K = 1/t (ln [A0/At]

[A0] = 1.35

[At] = 0.15 X 1.35 (15% of A0]

K = 1.2 × 104 min1

ln [A0 / At] = ln (1/0.15) = 1.897

time = 1.897 / K = 1.897 / 1.2 X 10^-4 = 15808.33 minutes = 263.47 hours = 2.6 X 10^2 hours

    2) K = 1/t (ln [A0/At]

time = 27 hours = 27 X 60 minutes = 1620 minutes
  1.2 × 104 min1 = 1 / 1620 (ln A0 / At)

0.1944 = (ln A0 / At)

Taking antilog

1.215 = A0 / At

At = A0 / 1.215 = 1.35 / 1.215 = 1.111 M

     3)

A)

t1/2 = 0.693 / K

t1/2 = 0.693 / 5.7 X 10^-4 = 1215.79 seconds

4) The time required to drop to half concentration is also called as half life

t1/2 = 131 seconds

K = 0.693 / t1/2 = 0.693 / 131 = 0.00529 sec^-1

5) it should be 1/8th of its original value

Let original value = A0

At = A0 / 8

K =6.20×103 s1 = 1/t ln [A0 /At]

time = 2.079 / 6.20×103 = 335.39 seconds

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