Question

the half life of a substance in first order reaction is 15 minutes calculate the rate constant

Answer 1

We know, t 1/2 = 0.693/k

As, t 1/2 = 15, So the rate connstant will be,

k = 4.62 x 10 ^-2 /min

Answer 2

The value of the rate constant of the reaction is equal to 0.0462 min⁻¹.

Given:

The half-life of the substance in the first-order reaction is 15 minutes.

To Find:

The value of the rate constant of the reaction?

Solution:

→ The rate constant, or the specific rate constant of a reaction is defined as the proportionality constant that establishes the relationship between the concentrations of the reacting substances and the rate of the reaction.

→ For a reaction: aA + bB → cC + dD

The relationship between the rate of reaction (r) and the concentrations of the reactant is given as:

                            Rate of Reaction (r) = k [A]ᵃ [B]ᵇ

• where 'k' is a constant known as the rate constant of the reaction.

→ The relationship between the half-life and rate constant (k) of a first-order reaction is given as:

                               $\boldsymbol{Half-life\:(T_{1/2} )=\frac{0.693}{k} }$

→ In the given question:

The half-life of the substance in the first-order reaction is 15 minutes.

Let the rate constant of the reaction be 'k'.

                               $\boldsymbol{\because Half-life\:(T_{1/2} )=\frac{0.693}{k} }$

                               $\boldsymbol{\therefore 15=\frac{0.693}{k} }\\\\\boldsymbol{\therefore k=\frac{0.693}{15} }\\\\\boldsymbol{\therefore k=0.0462\:min^{-1} }$

→ The value of 'k' comes out to be equal to 0.0462 min⁻¹.

Hence the value of the rate constant of the reaction comes out to be equal to 0.0462 min⁻¹.

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