Question

Many reactions involving heterogeneous catalysts are zeroth order; that is, rate \(=k\). An example is the decomposition of phosphine \(\left(\mathrm{PH}_{3}\right)\) over tungsten \((\mathrm{W})\) $$ 4 \mathrm{PH}_{3}(g) \longrightarrow \mathrm{P}_{4}(g)+6 \mathrm{H}_{2}(g) $$ It is found that the reaction is independent of \(\left[\mathrm{PH}_{3}\right]\) as long as phosphine's pressure is sufficiently high \((\geq 1\) atm \()\). Explain.

Short answer

The reaction rate is constant and independent of \( [\text{PH}_3] \) as long as the catalyst surface is saturated at high pressure.

Step-by-step solution

Define Zeroth Order Reaction

In a zeroth order reaction, the rate of reaction is constant and does not depend on the concentration of the reactants involved. This means that as long as the reactant is present in sufficient quantity, the reaction rate remains constant, denoted by the rate equation: \( \text{rate} = k \), where \( k \) is the rate constant.

Analyze the Given Reaction

The reaction given is the decomposition of phosphine (\( \text{PH}_3 \)) into \( \text{P}_4 \) and \( \text{H}_2 \). The reaction is found to be zeroth order, meaning the rate of this decomposition reaction is constant and independent of the concentration of \( [\text{PH}_3] \) under the specified conditions.

Understand the Role of Pressure

The reaction rate remains constant as long as the pressure of \( \text{PH}_3 \) is sufficiently high (greater than or equal to 1 atm). At these conditions, the active sites on the tungsten catalyst are saturated with \( \text{PH}_3 \), so the rate of reaction is not limited by the concentration of \( \text{PH}_3 \).

Summarize the Explanation

The pressure's role in maintaining a high concentration ensures that the catalyst's surface remains fully occupied by \( \text{PH}_3 \). Thus, even though the concentration changes might occur, the surface catalysis area is saturated, making the rate depend only on the rate constant \( k \), defining the zeroth order behavior.

Key concepts

Heterogeneous Catalysis

Heterogeneous catalysis is a process where the catalyst is in a different phase than the reactants. In the context of the decomposition of phosphine, the catalyst used is tungsten (W), which is a solid. The phosphine (\( \text{PH}_3 \)), on the other hand, is a gas, making this a classic example of heterogeneous catalysis.

Heterogeneous catalysts work by providing a surface on which the chemical reaction can take place more efficiently. The gaseous phosphine molecules come into contact with the solid tungsten surfaces, allowing the reaction to proceed at an accelerated rate.

This process is characterized by

• multiple phases at play, typically solid and gas as seen here
• the reaction occurring at the interface between the catalyst and the reactants
• an increased rate of reaction compared to what would happen without the catalyst.

Understanding heterogeneous catalysis is key to explaining why the rate can appear independent of the concentration of phosphine under certain conditions.

Reaction Rate

The reaction rate is central to understanding chemical kinetics and specifically describes how quickly a reaction occurs. For zeroth order reactions, like the decomposition of phosphine over tungsten, the reaction rate is constant. It does not depend on the concentration of the reactants.

In mathematical terms, the rate equation for a zeroth order reaction is the simplest, expressed as: \[\text{rate} = k\] where \( k \) is the rate constant.

The essential factors influencing the reaction rate include:

• temperature, since increasing temperature usually increases the reaction rate
• presence and nature of a catalyst, in this case, tungsten speeds up the reaction

This constant rate is ensured as long as the catalyst surface is saturated with reactant molecules. Thus, the reaction will proceed steadily, independent of reactant concentration, maintaining this consistent rate.

Phosphine Decomposition

Phosphine (\( \text{PH}_3 \)) decomposition offers a practical demonstration of zeroth order reactions when catalyzed by tungsten. This decomposition process converts phosphine into phosphorous (\( \text{P}_4 \)) and hydrogen gas (\( \text{H}_2 \)) through the reaction:\[4 \text{PH}_{3}(g) \rightarrow \text{P}_{4}(g) + 6 \text{H}_{2}(g)\]

During this reaction, phosphine molecules interact with the tungsten catalyst surface, breaking down over the catalyst. The zero-order nature arises here because significant saturation of the tungsten surface with phosphine ensures that the breakdown proceeds at a constant rate. Any excess change in concentration of \( [\text{PH}_3] \) does not affect the rate, as the catalyst surface molecules have reached a saturation point where additional phosphine molecules do not influence the reaction speed.

Catalyst Surface Saturation

Catalyst surface saturation is crucial for explaining the constant reaction rate in zeroth order reactions involving heterogeneous catalysis. When phosphine decomposes over tungsten, it ensures that the rate does not depend on the concentration of phosphine.

At high pressures (≥ 1 atm), the tungsten surface becomes fully occupied by phosphine molecules. This means the active sites available for catalysis are fully utilized.

The implications include:

• The reaction continues steadily as long as these active sites on the tungsten remain saturated.
• Further increases in phosphine pressure or concentration do not increase the number of reactions occurring at the surface.
• Surface saturation is a prerequisite for maintaining the zero-order kinetic characteristics.

Thus, catalyst surface saturation explains why, beyond a certain concentration of phosphine, the rate remains constant, illustrating the saturated surface's critical role in driving the zeroth order reaction.