Question

the decomposition of hydrogen peroxide H₂O_2, is first-order reaction. the half-life of of reaction is 17.0minutes.

a.) What is the rate constant of the reaction?

b.) If you had a bottle of H₂O₂, how long would it take for 80% to decompose?

Answer 1

The rate expression for first oder reaction =

=-dCA/dt= KCA

Where K= rate constant

which on integration and separation of variabled give -ln (1-XA)=Kt

XA =conversion= 1-CA/CAO, CAO= initial concentration and CAO= Concentration at time t and K= rate constant

for XA=0.5 that is the conversion t= t1/2 half life =17 minutes

-ln(1-XA)= -ln (0.5)= Kt1/2

given =0.693 = K t1/2

K= 0.693/ t1/2 = 0.693/17=0.0408 min-1

b) for 80% decomposition XA=0.8 time taken = t

-ln (1-0.8)= 0.0408*t

t= 39.44 minutes