Given that the equation for a first-order rate law is In([A]_t/[A]_o) = -kt, Ple

Question

Given that the equation for a first-order rate law is In([A]_t/[A]_o) = -kt, Please answer the following questions: 2H_2O_2(aq) rightarrow 2H_2O(g) + O_2(g) The reaction is first-order with respect to H_2O_2. the rate constant for the consumption of H_2O_2 at 20 degreeC is 1.8 Times 10^-5S^-1s and the initial concentration ot H_2O_2 Is 0.30 M. a.) What is the concentration of H_2O_2 after 4h? b.) How long will it take the H_2O_2 concentration to drop to 0.12 M? c.) How long will it take for 90% of the H_2O_2 to decompose?

Explanation / Answer

Since this is first order

ln(a) = ln(a0) - kt

k = 1.8*10^-5

a0 = 0.30

then

for a = 0.12

apply formula

ln(0.12) = ln(0.3) - (1.8*10^-5)*t

solve for t

t = ln(0.12/0.3)/(-1.8*10^-5) = 50905.0 seconds = 14.140 hours

c)

for 90% to decompose, this means final concnetration is 10% original one

so

ln(0.1*0.30) = ln(0.30) - (1.8*10^-5)*t

t = ln(0.1)/(-1.8*10^-5) = 127921.39 seconds = 35.5 hours

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