Which of the following is a zero order reaction?

1. Decomposition of \(N_2O_5\)

2. Decomposition of \(NH_3\)

3. Decomposition of \(N_2O\)

4. Radioactive decay of unstable nuclei

Decomposition of \(NH_3\)

The correct answer is option 2. Decomposition of \(NH_3\).

A zero-order reaction is a chemical reaction where the rate of the reaction is independent of the concentration of the reactants. This means that increasing or decreasing the concentration of the reactants does not affect the rate at which the reaction proceeds.  

Zero-order reactions typically occur under specific conditions:

Saturation: When a catalyst is present in excess, it can become saturated with reactants. Once saturated, adding more reactants does not increase the rate of reaction because all available active sites on the catalyst are occupied.

Surface Reactions: Reactions occurring on solid surfaces, such as heterogeneous catalysis, can often follow zero-order kinetics. The rate is primarily determined by the number of active sites on the surface, rather than the concentration of reactants in the bulk solution.

Enzyme-Catalyzed Reactions: Under certain conditions, enzyme-catalyzed reactions can exhibit zero-order kinetics. This can happen when the enzyme is saturated with substrate, and increasing the substrate concentration no longer increases the rate.

Rate Law for Zero-Order Reactions:

The rate law for a zero-order reaction is:

\(\text{Rate = k}\)

Where:

\(\text{Rate}\) is the rate of the reaction

\(k\) is the rate constant, a proportionality constant that depends on the reaction and temperature

Characteristics of Zero-Order Reactions:

Constant Rate: The rate of the reaction remains constant over time.

Half-Life: The half-life of a zero-order reaction is directly proportional to the initial concentration of the reactant. This means that it takes longer to consume half of the reactant as the initial concentration increases.  

Units of Rate Constant: The units of the rate constant for a zero-order reaction are \(molL^{-1}s^{-1}\).

Let us noe look at the given options:

2. Decomposition of \(NH_3\)

The decomposition of ammonia (\(NH_3\)) on a platinum catalyst can indeed exhibit zero-order kinetics under certain conditions.

In this scenario, the reaction is:

\(2 \text{NH}_3 (g) \rightarrow 3 \text{H}_2 (g) + \text{N}_2 (g) \)

Under high pressure or high concentration of \(NH_3\), and when the catalyst is saturated with ammonia, the reaction rate can become independent of the concentration of \(NH_3\). Instead, the reaction rate is controlled by the properties of the catalyst and the availability of active sites. This situation leads to zero-order kinetics, where the rate law is:

\(\text{Rate} = k \)

In this case, the rate of decomposition is constant and does not change with variations in the concentration of \(NH_3\). This zero-order behavior occurs because the catalyst is fully utilized, and the reaction rate is limited by factors other than the concentration of the reactant, such as the rate at which the catalyst can convert ammonia to products.

The other options are:

1. Decomposition of \(N_2O_5\):

The decomposition of \(N_2O_5\) is  a first-order reaction. It follows the rate law:

\( \text{Rate} = k [N_2O_5] \)

where the rate of decomposition depends on the concentration of \(N_2O_5\).

3. Decomposition of \(N_2O\):

The decomposition of nitrous oxide (\(N_2O\)) is indeed a first-order reaction. In a first-order reaction, the rate of the reaction is directly proportional to the concentration of one reactant.

For the decomposition of \(N_2O\), the reaction can be represented as:

\( 2 \text{N}_2\text{O} \rightarrow 2 \text{N}_2 + \text{O}_2 \)

The rate law for a first-order reaction is generally expressed as:

\(\text{Rate} = k [\text{N}_2\text{O}] \)

where \(k\) is the rate constant and \([\text{N}_2\text{O}]\) is the concentration of \(N_2O\).

4. Radioactive decay of unstable nuclei :

The radioactive decay of unstable nuclei follows first-order kinetics. In a first-order reaction, the rate of decay is proportional to the amount of the radioactive substance present at any given time.

For radioactive decay, the rate law is:

\(\text{Rate} = -\frac{dN}{dt} = \lambda N \)

where:

\( \frac{dN}{dt} \) is the rate of change of the number of radioactive nuclei (\(N\)) over time (\(t\)),

\( \lambda \) is the decay constant (a measure of the probability of decay per unit time),

\( N \) is the number of radioactive nuclei at time \(t\).

The integrated form of this rate law gives the exponential decay equation:

\( N(t) = N_0 e^{-\lambda t} \)

where \( N_0 \) is the initial number of nuclei at \( t = 0 \), and \( N(t) \) is the number of nuclei remaining at time \(t\).

The half-life (\(t_{1/2}\)) of a radioactive substance, which is the time required for half of the radioactive nuclei to decay, is related to the decay constant by:

\(t_{1/2} = \frac{\ln(2)}{\lambda} \)

This characteristic of first-order kinetics means that the decay rate is constant regardless of the amount of substance present.