A first order reaction takes 20 minutes for 25% decomposition. calculate the time when 75% of the reaction will be completed
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Hey !!
Given
Time t₁ = 20 min for 25% decomposition
Required
Time t₂ for 75% decomposition
Solution
Let 'k' be the rate constant of the reaction
CASE - 1
C = C₀ - 25 / 100 C₀ = 0.75 C₀
We know, for a first order reaction
t = 2.303 / k log C₀ / C
=> 20 = 2.303 / k log C₀ / 0.75 C₀
=> 2.303 / k log 100 C₀ / 75 C₀
=> k = 2.303 / 20 log (4/3) ----------> (1)
CASE - 2
C' = C₀ - 0.75 C₀ = 0.25 C₀
∴ t₂ = 2.303 / k log C₀ / C'
= 2.303 / k log C₀ × 100 / 0.25 C₀
=> t₂ = 2.303 / log 4
PUTTING THE VALUE OF 'K' FROM EQUATION (1)
t₂ = 2.303 × log 4
=> 2.303 / 20 log 4
=> 20 log 4 / log 4/3
=> 20 log 4 / log 4 - log 3
=> 20 × 0.6021 / 0.6021 - 0.4771
=> 20 × 0.0621 / 0.01250
=> 20 × 6021 / 1250
FINAL RESULT = 96.336 min
GOOD LUCK !!
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