Zero Order Reactions
Zero order reactions are unique in that their rate is independent of the concentration of the reactants. In mathematical terms, the rate can be expressed as:
$$Rate = -\frac{d[R]}{dt} = k$$
Where k is the rate constant.
Key Characteristics
- The rate of reaction remains constant over time, provided that the concentration of the reactant does not drop below a certain threshold.
- A common feature of zero order reactions is their occurrence under saturated conditions, specifically when a catalyst is involved or when surface reactions occur, such as the decomposition of ammonia on hot platinum surfaces.
Integrated Rate Equation
The integrated rate law for a zero order reaction can be derived as:
$$[R] = -kt + [R]_0$$
This indicates that plotting concentration versus time results in a linear graph where:
- The slope of the line equals -k.
- The y-intercept equals the initial concentration [R]_0.
Half-Life of Zero Order Reactions
For zero order reactions, the half-life is expressed as:
$$t_{1/2} = \frac{[R]_0}{2k}$$
This equation shows that half-life is directly proportional to the initial concentration of the reactants, meaning higher concentrations will yield longer half-lives.
Examples
- The decomposition of ammonia on a platinum catalyst at high pressures shows zero-order behavior, where the reaction rate does not change with ammonia concentration.
- Alcohol dehydrogenase in the liver catalyzes the conversion of ethanol, showing zero-order kinetics at high ethanol concentrations, indicating that the enzyme is saturated.
Understanding zero order reactions not only helps in predicting reaction kinetics but is also essential in industries where precise control over reaction rates is required.