Integrated Rate Laws

Question

The decomposition of hydrogen peroxide in dilute sodium hydroxide at 20 °C

H₂O₂(aq)H₂O(l) + ½ O₂(g)

is first order in H₂O₂ with a rate constant of 1.10×10^-3 min^-1.

If the initial concentration of H₂O₂ is 4.24×10^-2 M, the concentration of H₂O₂ will be 1.16×10^-2 M after min have passed.

Please include answer

Answer 1

For a first order reaction, the rate law equation is:

ln[A] = -kt + ln[A₀]

A = 1.16*10^-2 M

A₀ = 4.24*10^-2 M

k = 1.10*10^-3 1/min

rearrangement and plugging our values gives us:

ln[A] - ln[A₀] = -kt --> ln[A/A₀]/(-k) = t

t--> 1.178*10³ minutes

conversely we could also start from a first order differential equation:

dA/dt = -kA --> dA/A = -kdt

integrating both sides gives us:

lnA = -kt+C --> e^ln(A)= e^-kt+c --> A = e^{-kt+c =} A = A₀e^-kt (substituting A₀ for C).

we can plug and chug to arrive at the same answer.

Hope this helps!

-Andrew