Hydrogen peroxide decomposes to water and oxygen as shown in the following react
ID: 24971 • Letter: H
Question
Hydrogen peroxide decomposes to water and oxygen as shown in the following reaction: 2H2O2<-->2H2O+O2The activation energy for the uncatalyzed reaction at 20 degree celsius is 18 kcal/mol, and the standard free energy change for this reaction is -200 kcal/mol. The reaction can be catalyzed by ferris ions (Ea=13 kcal/mol) or by the enzyme catalase (Ea=7 kcal/mol), an iron-containing enzyme.
A)Draw the activation energy diagram(x-axis=reaction progress;y-axis=energy) for the uncatalyzed versions of this reaction under stardard conditions.be sure to label Ea and dalta G.
B)The reaction shown above occurs approximately 30,000 times faster when catalyzed by ferric ions versus no catalyst, and approximately 100,000,000 times faster in the presence of catalase versus the uncatalyzed reaction. Assume that 1 microgram of catalase can decompose a certian amount of H2O2 in 1 minute at 25 degree celsius. How long would it take (in hours) for the same quantity of H2)2 to decompose in the presence of an amount of ferric ions equivalent to the iron content in the catalase?
C) How long would it take (in hours) for the same quantity of H2O2 to decompose in the absence of a catalyst.
Explanation / Answer
A) One molecule of catalase weighs, on average: 68,900 amu (atomic mass units), quoting James Sumner and collaborator Nils Gralen (University of Uppsala, Sweden) who first determined it and published it in their landmark 1938 article. Each molecule, like hemoglobin, holds 4 heme groups, each with one atom of iron in its ferric state. One amu = 1.66053 X 10^-24 g (grams) = 1.66053 X 10^-18 g (micrograms). Iron weighs, on average 55.847 amu (times 1.66053 X 10^-18 micrograms/amu) = 9.27356189 X 10^-17 g for atom of Fe. If catalase has 4 Fe atoms, its content of Fe is 4 times the latter amount = 3.70942476 X 10^-16 g 3.71 X 10^-16 g of Fe. One mol of catalase contains an Avogadro's number multiplying this amount of Fe: (6.0221415 X 10^23) (3.70942476 X 10^-16) = 2.233868079 X 10^8 g 2.2339 X 10^8 g = 1 mole, and 18 kcal/mol. But 1 g of catalase is (1 X 10^-6 g /1.66053 X 10^-24 g/mol) = 6.022173643 X 10^17 moles, each with 18 kcal, for a total of 1.083991256 X 10^19 kcal. The amount of iron in that much catalase is (2.233868079 X 10^8)(1.083991256 X 10^19) = 2.421493464 X 10^27, which has to be divided by the Avogadro's number to see how many moles of Fe it makes = 402.0984004 moles 402 moles, each with 13 kcal, for a total of (13 kcal/mol)(402 mol) = 5226 kcal. Compare that with (18 kcal/mol)(6.022 X 10^17 mol) = 1.08396 X 10^19 kcal. The ratio is (1.08396 X 10^19)/(5226) = 2.074167623 X 10^15 2.074 TRILLION times as fast. If catalase does it in 1 minute, this amount of Fe would do it in 2.074 trillion minutes, which divided by 60 minutes per hour equals: 34 trillion hours.
B) 100,000,000 minutes = 100 million minutes = 1,666,667 hours (notice that this is faster than with the small amount of ferric ions used before, but that is because we did not use enough iron)
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