Calculation of Time Required for 100% Completion of Zero Order Reaction

The time required for 100% completion of a zero order reaction depends on the rate constant (k) and the initial concentration of the reactant (a). There are different equations that can be used to calculate the time required for 100% completion of a zero order reaction, depending on the information given.

Equations for Time Required for 100% Completion of Zero Order Reaction

1. Time Required for 100% Completion of Zero Order Reaction with Rate Constant (k)

The equation to calculate the time required for 100% completion of a zero order reaction with rate constant (k) is:

t = a/k

where t is the time required for 100% completion of the reaction, a is the initial concentration of the reactant, and k is the rate constant.

2. Time Required for 100% Completion of Zero Order Reaction with Half-Life (t1/2)

The equation to calculate the time required for 100% completion of a zero order reaction with half-life (t1/2) is:

t = (t1/2) x ln(2)

where t is the time required for 100% completion of the reaction, and t1/2 is the half-life of the reaction.

3. Time Required for 100% Completion of Zero Order Reaction with Initial and Final Concentrations

The equation to calculate the time required for 100% completion of a zero order reaction with initial and final concentrations is:

t = (a - 0) / k

where t is the time required for 100% completion of the reaction, a is the initial concentration of the reactant, and 0 is the final concentration of the reactant.

Answer to the Question

The options given are:

1. ak
2. a/2k
3. a/k
4. 2k/a

Option 3, a/k, is the correct answer. This is because the equation for the time required for 100% completion of a zero order reaction is t = a/k. Therefore, the time required for 100% completion of a zero order reaction is directly proportional to the initial concentration of the reactant and inversely proportional to the rate constant.

Conclusion

The time required for 100% completion of a zero order reaction can be calculated using different equations, depending on the information given. In this case, the correct answer is option 3, a/k, which is derived from the equation t = a/k.

Option (3) a/ k
{A}={A}• - kt
{A}•= a
{A}= a - a = 0
so on putting values of {A}• and {A}
t = a / k