Question

Hydrogen peroxide decomposes spontaneously to yield water and oxygen gas according to the reaction equation 2h2o2(aq)⟶2h2o(l)+o2(g) the activation energy for this reaction is 75 kj·mol−1. the enzyme catalase, found in blood, lowers the activation energy to 8.0 kj·mol−1. at what temperature would the non-catalyzed reaction need to be run to have a rate equal to that of the enzyme-catalyzed reaction at 25 °c?

Answer 1

Answer:

the temperature of the non- catalyzed reaction is = 2793.75 K

Explanation:

The reaction of the spontaneous decomposition of hydrogen peroxide to give water and oxygen is given as:

$2H_2O_{2(aq)} ----> 2H_{2(l)} + O_2_{(g)}$

The activation energy of non-catalyzed reaction $E{a_1} = 75 kJ/mol$

The activation energy of metal catalyzed reaction $E{a_2} = 8 kJ/mol$

The temperature of metal catalyzed reaction $T_2 = 25^0C$ = (25+273)K = 298 K

The rate constant of the non-catalyzed reaction can be expressed as:

$k_1 = Ae^{{-Ea_1}/RT_1}$ ----- equation (1)

The rate constant of the metal catalyzed reaction can be expressed as:

$k_2 = Ae^{{-Ea_2}/RT_2}$

Then $k_1 = k_2$

$Ae^{{-Ea_1}/RT_1}=Ae^{{-Ea_2}/RT_2}$

$e^{{-Ea_1}/RT_1}=e^{{-Ea_2}/RT_2}$

$\frac{Ea_1}{RT_1}}=\frac{Ea_2}{RT_2}}$

$T_1 = \frac{Ea_1*T_2}{Ea_2}$

$T_1 = \frac{75*298}{8}$

$\\T_1 = 2793.75 \ K$

Thus; the temperature of the non- catalyzed reaction is = 2793.75 K