The decomposition of phosphine `[PH_(3)]` on tungsten at low pressure is a first-order reaction. It is because the

Options

A. rate is proportional to the surface coverage
B. rate is inversely proportional to the surface coverage
C. rate is independent of the surface coverage
D. rate of decomposition is very slow

Explanation

**Step-by-Step Solution:**

1. **Understanding the Reaction**: The decomposition of phosphine (PH₃) on tungsten is a first-order reaction. This means that the rate of the reaction depends linearly on the concentration (or pressure) of the reactant, in this case, phosphine.

2. **Identifying the Products**: The decomposition of phosphine results in the formation of phosphorus (P₄) and hydrogen gas (H₂). The balanced chemical equation for this reaction can be represented as:
\[ 4PH_3 \rightarrow P_4 + 6H_2 \]

3. **Role of the Catalyst**: Tungsten acts as a catalyst in this reaction. A catalyst increases the rate of a reaction without being consumed in the process. It provides a surface for the reactants to adsorb and react.

4. **Surface Coverage and Reaction Rate**: The rate of the reaction is proportional to the surface coverage of phosphine on the tungsten surface. As more phosphine molecules attach to the tungsten surface, the rate of reaction increases.

5. **Dependence on Partial Pressure**: The surface coverage of phosphine is directly related to its partial pressure. At low partial pressures, there are many available sites on the tungsten surface for phosphine to adsorb, leading to a higher reaction rate.

6. **First-Order Kinetics**: Since the rate of reaction is linearly dependent on the surface coverage, which in turn depends on the partial pressure of phosphine, the reaction exhibits first-order kinetics at low pressures. This means that as the pressure of phosphine increases, the rate of reaction increases proportionally until all active sites on the tungsten are occupied.

7. **Graphical Representation**: If we were to plot the rate of reaction against the partial pressure of phosphine, we would observe a linear relationship at low pressures. However, as the pressure increases further, the rate would eventually plateau, indicating that all active sites are occupied, leading to zero-order kinetics at high pressures.

8. **Conclusion**: Therefore, the decomposition of phosphine on tungsten at low pressure is a first-order reaction because the rate is proportional to the surface coverage of phosphine, which is dependent on its partial pressure.

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