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Chemistry LibreTexts

Homework 4 (Due 4/15/16)

  • Page ID
    47373
  • Name: ______________________________

    Section: _____________________________

    Student ID#:__________________________

    Q4.1

    Compounds A and B both decay by first-order kinetics. The half-life of A is 20 minutes and the half-life of B is 48 minutes. If a container initially contains equal concentrations of compounds A and B, after how long will the concentration of B be twice that of A?

    Q4.2

    If a reaction has come to thermodynamic equilibrium, can we say anything in particular about the system's kinetics?

    Q4.3

    Chemical reactions occur when reactants collide. What are two factors that may prevent a collision from producing a chemical reaction?

    Q4.4

    How does an increase in temperature affect rate of reaction? Explain this effect in terms of the collision theory of the reaction rate.

    Q4.5

    An elevated level of the enzyme alkaline phosphatase (ALP) in the serum is an indication of possible liver or bone disorder. The level of serum ALP is so low that it is very difficult to measure directly. However, ALP catalyzes a number of reactions, and its relative concentration can be determined by measuring the rate of one of these reactions under controlled conditions. One such reaction is the conversion of p-nitrophenyl phosphate (PNPP) to p-nitrophenoxide ion (PNP) and phosphate ion. Control of temperature during the test is very important; the rate of the reaction increases 1.47 times if the temperature changes from 30 °C to 37 °C. What is the activation energy for the ALP–catalyzed conversion of PNPP to PNP and phosphate?

    Q4.6

    The hydrolysis of the sugar sucrose to the sugars glucose and fructose,

    \[\ce{C12H22O11 + H2O ⟶ C6H12O6 + C6H12O6}\]

    follows a first-order rate equation for the disappearance of sucrose: Rate = k[C12H22O11] (The products of the reaction, glucose and fructose, have the same molecular formulas but differ in the arrangement of the atoms in their molecules.)

    1. In neutral solution, k = 2.1 × 10−11 s−1 at 27 °C and 8.5 × 10−11 s−1 at 37 °C. Determine the activation energy, the frequency factor, and the rate constant for this equation at 47 °C (assuming the kinetics remain consistent with the Arrhenius equation at this temperature).
    2. When a solution of sucrose with an initial concentration of 0.150 M reaches equilibrium, the concentration of sucrose is 1.65 × 10−7 M. How long will it take the solution to reach equilibrium at 27 °C in the absence of a catalyst? Because the concentration of sucrose at equilibrium is so low, assume that the reaction is irreversible.
    3. Why does assuming that the reaction is irreversible simplify the calculation in part (b)?