Decomposition of Hydrogen Peroxide

The decomposition of hydrogen peroxide (H2O2) follows first-order kinetics, which means that the rate of the reaction is directly proportional to the concentration of the reactant. The reaction can be represented as follows:

2H2O2(aq) → 2H2O(ell) + O2(g)

Volume of O2 Gas Liberated at STP in 20 minutes

Given that the volume of O2 gas liberated at STP (Standard Temperature and Pressure) in the first 20 minutes of the start of decomposition is 25.00 ml, we need to calculate the total volume of O2 gas collected in time, t > t1/2.

First Order Kinetics

In first-order kinetics, the rate of the reaction is proportional to the concentration of the reactant raised to the power of one. The rate equation can be written as follows:

Rate = k[H2O2]

Where:
- Rate is the rate of the reaction
- k is the rate constant
- [H2O2] is the concentration of hydrogen peroxide

Half-Life of the Decomposition Reaction

The half-life (t1/2) for the decomposition of hydrogen peroxide is given as 10 minutes. The half-life of a reaction is the time required for the concentration of the reactant to reduce to half of its initial value.

Calculating the Rate Constant (k)

To calculate the rate constant (k), we can use the half-life of the reaction. The half-life of a first-order reaction can be related to the rate constant using the equation:

t1/2 = 0.693 / k

Substituting the given half-life value of 10 minutes into the equation, we can solve for the rate constant:

10 = 0.693 / k
k = 0.693 / 10
k = 0.0693 min^-1

Calculating the Total Volume of O2 Gas Collected

To calculate the total volume of O2 gas collected in time, t > t1/2, we need to consider the rate of the reaction and the time interval.

Since the reaction follows first-order kinetics, the rate of the reaction can be determined using the rate constant (k) and the concentration of hydrogen peroxide at a given time.

Rate = k[H2O2]

In the given scenario, the initial volume of O2 gas liberated in the first 20 minutes is 25.00 ml. Let's assume that the concentration of hydrogen peroxide at this time is [H2O2]0.

To calculate the total volume of O2 gas collected in time, t > t1/2, we can integrate the rate equation with respect to time:

∫dV = ∫k[H2O2] dt

Where:
- dV is the change in volume of O2 gas (dV = V - V0)
- k is the rate constant
- [H2O2] is the concentration of hydrogen peroxide at a given time
- dt is the time interval

Integrating the equation from t = t1/2 to t = t, we get:

V - V0 = k∫[H2O2] dt

Since the concentration