Question

Derive the expression for half life of nth order reaction

Answer 1

Answer:

The half-life for a general nth order reaction is given by the expression .

t(1/2) = {2^(n-1) - 1} / {k(n-1)([A]^(n-1))}

the integrated rate law will be given by

1/A^n-1=1/A0^n-1 +(n-1)kt

therefore t1/2 /t3/4=2^n-1 -1/4^n-1 -1

Explanation:

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Answer 2

The expression for half-life of nth order reaction is given in the explanation for each order of the reaction.

Explanation:

• The half-life period of a chemical reaction is defined as the time taken to determine the concentration of a given reactant reaching almost half of its initial concentration.
• It is the time taken for the reactant concentration to reach half of its value.
• It is denoted by $t_{1/2}$ and is usually expressed in seconds.
• For zero-order reaction the expression to determine the half-life period is $t1/2 = [R]0/2k$
• For first-order reaction the expression to determine the half-life period is $t1/2 = 0.693/k$
• For second-order reaction the expression to determine the half-life period is $t1/2 = 1/k[R]0$