Hydrogen peroxide decomposes to water and oxygen according to the following reaction H 2 O 2(aq) → H 2 O + ½ O 2 (g) It’s rate of decomposition is measured by titrating samples of the solution with potassium permanganate (KMnO4) at certain intervals

This is an incomplete question, here is a complete question.

Hydrogen peroxide decomposes to water and oxygen according to the following reaction:

It’s rate of decomposition is measured by titrating samples of the solution with potassium permanganate at certain intervals.

Initial rate determinations at 40°C for the decomposition give the following data:

[H₂O₂] (M)      Initial Rate (mol/L min)

 0.10                  1.93 × 10⁻⁴

 0.20                 3.86 × 10⁻⁴

 0.30                 5.79 × 10⁻⁴

Calculate the half-life for the reaction at 40°C?

Answer : The half life for the reaction is, 3590.7 minutes

Explanation :

Rate law is defined as the expression which expresses the rate of the reaction in terms of molar concentration of the reactants with each term raised to the power their stoichiometric coefficient of that reactant in the balanced chemical equation.

For the given chemical equation:

Rate law expression for the reaction:

where,

a = order with respect to

Expression for rate law for first observation:

....(1)

Expression for rate law for second observation:

....(2)

Expression for rate law for third observation:

....(3)

Dividing 2 by 1, we get:

Thus, the rate law becomes:

Now, calculating the value of 'k' by using any expression.

Putting values in equation 1, we get:

Now we have to calculate the half-life for the reaction.

The expression used  is:

Thus, the half life for the reaction is, 3590.7 minutes

it is b that is the answer.