Question

प्रथम कोटि की अभिक्रिया के लिए वेग स्थिरांक का व्यंजक ज्ञात कीजिए।
Derived an expression for the rate constant of first order te​

Answer 1

Derive an expression for the rate constant of first order reaction.

solution : Let a chemical reaction occurs in first order kinetics such that, A ⇒ constant

initial concentration of substance is [A]₀ , final concentration of substance is [A]t and rate constant is k.

for first order reaction,

decrement rate in the concentration of A = k[A]

⇒- d[A]/dt = k[A]

⇒∫d[A]/[A] = - k∫dt

⇒ln[A] = -kt

⇒ln[A]t - ln[A]₀ = -kt

⇒kt = ln[A]₀ - ln[A]t

⇒kt = ln{[A]₀/[A]t}

⇒k = 1/t ln{[A]₀/[A]t}

⇒k = 2.303/t log{[A]₀/[A]t}

Therefore rate constant of the first order reaction is k = 2.303/t log{[A]₀/[A]t}.