Question

Question 18 of 27

A reactant decomposes with a half-life of 137137 s when its initial concentration is 0.1170.117 M. When the initial concentration is 0.6030.603 M, this same reactant decomposes with the same half-life of 137137 s.

What is the value and unit of the rate constant for this reaction?

?=k=

Not a valid number

tools

x10^y

Answer 1

Answer 2

 

1. Half-Life Independence: The half-life ($t_{1\mathrm{/}2}$) of the reactant is 137 seconds for both initial concentrations (0.117 M and 0.603 M).

• This indicates that the half-life does not depend on the initial concentration.

• 
  

2. Reaction Order:

   Since the half-life remains constant regardless of concentration, this is a first-order reaction.

3. 
   

• For a zero-order reaction, the half-life is proportional to the initial concentration.

• 
  

• For a first-order reaction, the half-life is independent of the initial concentration.

• 
  

• For a second-order reaction, the half-life is inversely proportional to the initial concentration.

• 
  

Formula for First-Order Half-Life:

For a first-order reaction, the half-life is related to the rate constant ($k$) by the formula:

$$t_{1\mathrm{/}2}=\frac{\ln (2)}{k}$$

Solving for $k$$k$:

1. Rearrange the formula to solve for $k$:

   $$k=\frac{\ln (2)}{t_{1\mathrm{/}2}}$$

2. Plug in the given half-life ($t_{1\mathrm{/}2}=137$ s):

   $$k=\frac{0.693}{137\text{ s}}$$

3. Calculate the value:

   $$k\approx 0.00506{\text{ s}}^{-1}$$

Answer is :

The rate constant for this reaction is:

$$k\approx 0.00506{\text{ s}}^{-1}$$