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 5.68×10^-2 M, the concentration of H₂O₂ will be  M after 1800 minhave passed.

Answer 1

H₂O₂ (aq) ---->H₂O (l) + ½ O₂(g)

The initial concentration [A]_o of H₂O₂ is 5.68×10-2 M.

t = 1800 min

Rate constant k = 1.10×10-3 min-1.

A first order reaction has integrated rate law

ln[A]_t =−kt + ln[A]_o

Where [A_t] is the concentration at time t and [A]_o is the concentration at time 0, and k is the first-order rate constant

ln[A]_t = - 1.10×10-3 min-1*1800 + ln (5.68×10^-2)

ln[A]_t = - 1.10 × 10^-3 min-1*1800 + -2.86821895

ln[A]_t = - 1.98 + -2.86821895

ln[A]_t = - 4.8482189

[A]_t = e^(-4.8482189 )

[A]_t = 0.00784

   = 7.84 x 10^-3M

The concentration of H₂O₂ will be 7.84 x 10^-3M after 1800 min have passed.