Fixing the balanced equation:
2 H2O2 ----> 2 H2O + 1 O2
not
2 H2O ----> 2 H2O + 1 O2
Arrhenius equation
k = Ao exp (-Ea/RT)
Two runs:
k1 = Ao exp (-Ea1 / RT1)
k2 = Ao exp (-Ea2 / RT2)
Rearrangement:
k1 / exp (-Ea1 / RT1) = Ao
k2 / exp (-Ea2 / RT2) = Ao
since they both = Ao, they must = each other and ;
k1 / exp (-Ea1 / RT1) = Ao = k2 / exp (-Ea2 / RT2)
Rearrangement:
(k1 / k2) = exp(-Ea1 / RT1) / exp(-Ea2 / RT2)
Rearrangement: since n^a / n^b = n^(a-b)..
(k1 / k2) = exp (-Ea1 / RT1) - (-Ea2 / RT2) )
Rearrangement:
(k1 / k2) = exp ( (1/R) x (( Ea2 / T2) - (Ea1 / T2)) )
taking "ln" of both sides
ln(k1 / k2) = (1/R) x (Ea2/T2 - Ea1/T1)
rate1 = k1 x [H2O2]^n
rate2 = k2 x [H2O2]^n
rate1 / rate2 = k1 / k2
ln(k1 / k2) = (1/R) x (Ea2/T2 - Ea1/T1)
ln(rate1 / rate2) = (1/R) x (Ea2/T2 - Ea1/T1)
rate1 = rate2
T1 = ?
Ea1 = 75 kJ/mol
T2 = 25°C = 298K
Ea2 = 49 kJ/mol
ln(rate2 / rate2) = (1/R)
x (Ea2/T2 - Ea1/T1)
ln(1) = (1/R) x (Ea2/T2 - Ea1/T1)
0 = (1/R) x (Ea2/T2 - Ea1/T1)
0 = Ea2/T2 - Ea1/T1
Ea2/T2 = Ea1/T1
T1 = T2 x (Ea1 / Ea2) = 298K x (75 kJ/mol / 49kJ/mol) = 456K
= 183°C
