Case Study in Environmental Chemistry

Authors: Sarunya Hengpraprom and Cindy Lee, Environmental Engineering and Science, Clemson University.

Hydrolysis: Hydrolysis is a bond breaking and bond forming process in which a molecule R-X, where X is a leaving group, reacts with water (H₂O) or hydroxide ion (OH^-) forming a new R-O bond and cleaving a R-X bond in the original molecule. The products of hydrolysis reaction are usually less of an environmental concern than the parent compounds because they are usually transformed into more polar compounds which are less hydrophobic than the original molecules and therefore behave differently in the environment (16).

Hydrolysis can be usually defined by a simple pseudo-first order reaction:

where
[C] is the molar concentration of the chemical,
k_obs is the observed pseudo-first order rate constant for hydrolysis at a given pH.

The rate constant may contain contributions from acid-catalyzed hydrolysis, alkaline hydrolysis, and neutral hydrolysis.

Consequently,

where,
k_a, k_b, and k_n are the specific rate constants for acid-catalyzed, alkaline-hydrolysis, and neutral hydrolysis, respectively (17).

When a reaction follows first-order kinetics, the concentration decreases exponentially with time. According to equation 1, a plot of ln[C]_t against time will vary linearly with a slope of -k_obs. This slope and the rate are dependent on the concentration.

The hydrolysis half-life, the time required for 50% of the compound to disappear, will be determined for first-order and pseudo-first order reactions by:

In aquatic environments endosulfan can be expected to hydrolyze rapidly in alkaline conditions, but not in acidic conditions. In addition, each of these reaction routes is sensitive to temperature. Chemical reaction rates generally increase with increasing temperature. The temperature dependence of the rate constant is expressed by the Arrhenius equation.

Arrhenius Equation
This Arrhenius equation can be written as:

where
A is the probability that a given collision involving sufficient energy will be successful,
e is the case of the natural logarithm system,
R is the gas constant,
E_a is the activation energy, which is the energy the molecules must have in order to react,
T is the absolute temperature.

Another form of the Arrhenius equation, which is obtained by taking the logarithms of both sides of equation (4), is

Question 5: Express the relationship of the kinetic rate (k) versus temperature. Is it inversely or directly proportional? Check your answer.

The activation energy, E_a, is generally stated in units of joules or calories per mole (SI unit). Calculating the activation energy of a reaction can be important in predicting the rate of a reaction at any temperature and in identifying individual reaction steps that control overall rates in a complex reaction process. The magnitude of the activation energy for a complex reaction involving several steps or stages is controlled by the slowest or rate-limiting step (18). Hence an experimental evaluation of E_a for a multiple process can indicate the rate-limiting step of the natural reaction by comparing E_a for the overall reaction with Eas for simple steps. In addition, the activation energy is a direct determinant of reaction rate. The larger the value of E_a, the slower the reaction will be (18).