Half life of a third order reaction 3C— products, where initial concentration is C, will bep?

Question

Answer

Half-life of a Third Order Reaction

A third-order reaction is a type of chemical reaction where the rate of reaction is proportional to the cube of the concentration of the reactant. The general form of a third-order reaction is:

3A → products

Half-life Definition

The half-life of a chemical reaction is the time required for the concentration of the reactant to decrease to half of its initial value. In mathematical terms, the half-life (t_1/2) is defined as:

t_1/2 = ln(2) / k

where k is the rate constant of the reaction.

Derivation of Half-life for Third Order Reaction

The rate law for a third-order reaction can be written as:

rate = k[A]³

Integrating this rate law with respect to time gives:

1/[A] = kt/2 + 1/[A]₀

where [A]₀ is the initial concentration of the reactant. Solving for t_1/2 (when [A] = [A]₀/2) gives:

t_1/2 = 1 / (k[A]₀)

This means that the half-life of a third-order reaction is inversely proportional to the initial concentration of the reactant.

Conclusion

In conclusion, the half-life of a third-order reaction is inversely proportional to the initial concentration of the reactant. This is because the rate of reaction is proportional to the cube of the concentration of the reactant. As the concentration of the reactant decreases, the rate of reaction also decreases, resulting in a longer half-life.

Similar Chemistry Doubts

Half-life for a third order reaction 3C → products, where Co is initial concentration of C will be 1/[zKCo2]. The value of ‘z’ is? [rounded up to two decimal places] Correct answer is between '0.65,0.67'. Can you explain this answer?

For the first order reaction2N2O5 (g) → 4NO2 (g)+ O2 (g)

For the first order reaction

The half-life of the chemical reaction, A →Product, for initial reactant concentrations of 0.1 and 0.4 mol L–1 are 200 and 50 s, respectively. The order of the reaction is

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