The estimated half-life for P-O bonds is 1.3 x 105 a (a = annum = year). Approximately 10⁹ such bonds are present in a strand of DNA. How long (in terms of its half life) would a single strand of DNA survive with NO cleavage (in the absence of DNA repair enzymes)?
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- The half-life for the (first-order) radioactive decay of 14Cis 5730 a (1 a is the Sl unit 1 annum, for 1 year); the nuclideem its ~ particles, high-energy electrons, w ith an energy of0.16 MeV). An archaeological sample contained wood thathad only 69 per cent of the 14C found in living trees. What isits age?Americium-241 is used in smoke detectors. It has a first-order rate constant for radioactive decay of k = 1.6 * 10-3 yr-1. By contrast, iodine-125, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day-1. (a) What are the half-lives of these two isotopes? (b) Which one decays at a faster rate?Enzymes are remarkably efficient catalysts that can increase reaction rates by as many as 20 orders of magnitude.(a) How does an enzyme affect the transition state of a reac-tion, and how does this effect increase the reaction rate?(b) What characteristics of enzymes give them this tremendous effectiveness as catalysts?
- Americium-241 is used in smoke detectors. It hasa first-order rate constant for radioactive decay ofk = 1.6 x 10-3 yr-1. By contrast, iodine-125, which isused to test for thyroid functioning, has a rate constantfor radioactive decay of k = 0.011 day-1. (a) What are thehalf-lives of these two isotopes? (b) Which one decays ata faster rate? (c) How much of a 1.00-mg sample of eachisotope remains after three half-lives? (d) How much of a1.00-mg sample of each isotope remains after 4 days?The estimated half life for P—O bonds Is 1.3 x 10^5 a ( 1 a is the SI unit 1 annum for 1 year). Approximately 10^9 such bonds are present in a strand of DNA. How long would a single strand of DNA survive with no cleave in a absence of repair enzymes.The acid-catalyzed hydrolysis of sucrose occurs by the fol-lowing overall reaction whose kinetic data are given below:C₁₂H₂₂O₁₁(s) H₂O(l) →C₆H₁₂O₆(aq) C₆H₁₂O₆(aq) (a) Determine the rate constant and the half-life of the reaction.(b) How long does it take to hydrolyze 75% of the sucrose?(c) Other studies have shown that this reaction is actually sec-ond order overall but appears to follow first-order kinetics.(Such a reaction is called a pseudo–first-order reaction.) Sug-gest a reason for this apparent first-order behavior.
- The gas-phase decomposition of ozone is thought to oc- cur by the following two-step mechanism. Step 1: 03(8) = 02(8) + O(g) (fast) Step 2: 0(8) + O,(8) → 202(8) (slow) (a) Write the balanced equation for the overall reaction. (b) Derive the rate law that is consistent with this mecha- nism. (Hint: The product appears in the rate law.) (c) Is O a catalyst or an intermediate? (d) If instead the reaction occurred in a single step, would the rate law change? If so, what would it be?Technetium (Tc) is a by-product of the spontaneous fission of Uranium-238 and as such is of particular interest to the nuclear sector. The most common isotope is 99Tc which is unstable and decays by emission of a beta particle,with a half-life of t½ = 2.11 x 105 years. A 99Tc sample is characterised and is found to contain 0.1 mol of the radionuclide. Determine the time required for the amount of technetium to reduce by 1% of this valueThe equilibrium constant for the attachment of a substrate to the active site of an enzyme was measured as 200. In a separate experiment, the rate constant for the secondorder attachment was found to be 1.5 x 108 dm3 mol-1 s- 1. What is the rate constant for the loss of the unreacted substratefrom the active site?
- ate constant mol/(L -s) falf-life -Consider the following chain mechanism(a) AH →A•+ H• K1(b) A → B• + C K2(c) B• + H• → P K3Identify the steps in the chain and use the steady-state approximation to determine therate of formation of product(a) Initiation(b) Propagation product(c) TerminationThe enzyme-catalyzed conversion of a substrate at 298 K has a Michaelis constant of 0.032 M and a maximum rate of 4.25 x 10-4 M/s when the enzyme concentration is 3.60 x 10-9 M. Calculate the catalytic efficiency ofthe enzyme (catalytic efficiency = k2/Km).