for a zero order how long will it take for the concentration of reactant tp fall to one eight is original value if it takes 15.5 minutes for concentration to be reduced to half its original value

To determine the time it takes for the concentration of a reactant to fall to one-eighth of its original value in a zero-order reaction, we can use the integrated rate equation for zero-order reactions.

The integrated rate equation for a zero-order reaction is given by:

[Reactant] = [Reactant]₀ - kt

Where:
[Reactant] is the concentration of the reactant at a given time,
[Reactant]₀ is the initial concentration of the reactant,
k is the rate constant, and
t is the time.

Given that it takes 15.5 minutes for the concentration to be reduced to half its original value, we can use this information to find the rate constant (k).

1. [Reactant] = [Reactant]₀ / 2
2. [Reactant]₀ - kt = [Reactant]₀ / 2

Simplifying the equation:

3. kt = [Reactant]₀ / 2

Now, let's calculate the value of k using the given information:

k = ([Reactant]₀ / 2) / t = ([Reactant]₀ / 2) / 15.5

Once you have calculated the value of k:

4. Substitute the given values into the integrated rate equation to solve for the time required for the concentration to fall to one-eighth of its original value.

[Reactant] = [Reactant]₀ - kt

[Reactant] = [Reactant]₀ - k * t_required

[Reactant] = [Reactant]₀ - k * t_required / 8

Since we want [Reactant] to be one-eighth of its original value, we have:

[Reactant] / 8 = [Reactant]₀ - k * t_required / 8

Simplify the equation:

[Reactant]₀ / 8 = [Reactant]₀ - k * t_required / 8

Now you can solve this equation for t_required, which represents the time it takes for the concentration of the reactant to fall to one-eighth of its original value.