It takes 41.0 min for the concentration of a reactant in a first-order reaction to drop...

It takes 41.0 min for the concentration of a reactant in a first-order reaction to drop from 0.430 M
to 0.310 M at 25.0 ^oC. How long will it take for the concentration to reach 0.126 Molar?

		153 min
		60.2 min
		87.2 min
		0.368 min
		71.3 min
		50.4 min
		5.20 x 10² min
		16.9 min

Solutions

Expert Solution

Consider a given reaction, A Products

For above first order reaction, we have k = [2.303 / t ] log [A] ₀ / [A] _t

Where, t is a time of reaction, k is a rate constant, [A] ₀ is a initial concentration of reactant at time t=0 s, [A] _t is a concentration of reactant at time t.

Here t =41.0 min, [A] ₀ = 0.430 M and [A] _t = 0.310 M .

k = ( 2.303 / 41.0 min ) log 0.430 / 0.310

k = 0.05617 min ^-1 log 0.430/0.310

k = 0.05617 min ^-1 ( 0.1421 )

k = 0.00798 min ^-1

Calculation of time required to reach the concentration to 0.126 Molar

We have, k = 0.00798 min ^-1, [A] ₀ = 0.430 M and [A] _t = 0.126 M .

we have k = [2.303 / t ] log [A] ₀ / [A] _t

0.00798 min ^-1 = ( 2.303 / t ) log 0.430 / 0.126

0.00798 min ^-1 = ( 2.303 / t ) 0.533

0.00798 min ^-1 = 1.228 / t

t = 1.228 / 0.00798 min ^-1

t = 153.8 min

ANSWER : 153 min

queen_honey_blossom answered 7 months ago

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