Problem 63 - Chemistry: The Central Science

Question

Write a balanced equation for each of the following reactions: (a) preparation of white phosphorus from calcium phosphate, (b) hydrolysis of \(\mathrm{PBr}_{3}\), (c) reduction of \(\mathrm{PBr}_{3}\) to \(\mathrm{P}_{4}\) in the gas phase, using \(\mathrm{H}_{2}\).

Step-by-Step Solution

Answer

(a) \(2\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2} + 6\mathrm{SiO}_{2} + 10\mathrm{C} \rightarrow 6\mathrm{CaSiO}_{3} + 10\mathrm{CO} + \mathrm{P}_{4}\) (b) \(\mathrm{PBr}_{3} + 3\mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{H}_{3}\mathrm{PO}_{3} + 3\mathrm{HBr}\) (c) \(6\mathrm{PBr}_{3} + 6\mathrm{H}_{2} \rightarrow \mathrm{P}_{4} + 18\mathrm{HBr}\)

Step 1: (a) Preparation of white phosphorus from calcium phosphate

Calcium phosphate, \(\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2}\), is heated with carbon and silica in an electric furnace to produce white phosphorus, calcium silicate, and carbon monoxide. The reaction is as follows: \[2\mathrm{Ca}_{3}(\mathrm{PO}_{4})_{2} + 6\mathrm{SiO}_{2} + 10\mathrm{C} \rightarrow 6\mathrm{CaSiO}_{3} + 10\mathrm{CO} + \mathrm{P}_{4}\] Ensure that the atoms are balanced on both sides of the equation.

Step 2: (b) Hydrolysis of PBr₃

When phosphorus tribromide, PBr₃, reacts with water, phosphorous acid (H₃PO₃) and hydrogen bromide (HBr) are produced. The balanced equation for this reaction is: \[ \mathrm{PBr}_{3} + 3\mathrm{H}_{2}\mathrm{O} \rightarrow \mathrm{H}_{3}\mathrm{PO}_{3} + 3\mathrm{HBr} \] Verify that the atoms are balanced on both sides of the equation.

Step 3: (c) Reduction of PBr₃ to P₄ using H₂

The reduction of phosphorus tribromide, PBr₃, to white phosphorus, P₄, in the gas phase using hydrogen gas can be represented by the following balanced equation: \[ 6\mathrm{PBr}_{3} + 6\mathrm{H}_{2} \rightarrow \mathrm{P}_{4} + 18\mathrm{HBr} \] Check that the atoms are balanced on both sides of the equation.

Key Concepts

Balanced Chemical Equations

A balanced chemical equation provides quantitative information about a chemical reaction. It ensures that the same number of each atom is present on both sides of the equation. This is crucial because, according to the law of conservation of mass, atoms are neither created nor destroyed in a chemical reaction. This means that all the atoms you start with in the reactants must equal the atoms found in the products.
To balance an equation, follow these steps:

• Write the unbalanced equation using proper chemical formulas for all substances.
• Count the number of each type of atom in both reactants and products.
• Add coefficients before the chemical formulas to equalize the number of atoms of each element on both sides.
• Repeat step two and adjust as necessary until all atoms are balanced.

Balancing equations ensures that the equation reflects what happens in the physical world. For instance, in the preparation of white phosphorus from calcium phosphate, the balanced equation includes all reactants and products, ensuring the equation aligns with empirical data.

Phosphorus Compounds

Phosphorus appears in nature in various compounds, with phosphorus pentoxide (P₄O₁₀) and phosphorus tribromide (PBr₃) being notable examples. Each phosphorus compound has unique properties and uses in different industrial and chemical applications. White phosphorus, for instance, is produced by reducing calcium phosphate as demonstrated in the exercise.
Understanding phosphorus’s reactivity is key to using it effectively in diverse chemical reactions:

• White phosphorus (P₄) is reactive and is often stored underwater to protect it from the air.
• Phosphorus tribromide (PBr₃) is used both as a reagent in organic synthesis and in the formulation of flame retardants.

Grasping these compounds' behavior is essential for their safe handling and for predicting the outcomes of chemical reactions they partake in.

Hydrolysis Reaction

Hydrolysis is a chemical process where a water molecule breaks a compound into two or more parts, often involving the cleavage of chemical bonds. In the hydrolysis of phosphorus tribromide (PBr₃), water molecules react to produce phosphorous acid (H₃PO₃) and hydrogen bromide (HBr).
This type of reaction is significant in both biological and chemical processes:

• Hydrolysis is crucial in digestion, breaking down larger molecules into absorbable units.
• In chemical industries, hydrolysis reactions facilitate the breakdown and transformation of substances.

The balanced equation for this reaction shows that three water molecules are required for every molecule of PBr₃, making sure that every hydrogen and bromine atom is accounted for on both sides of the equation, as outlined in the step-by-step solution.

Reduction Reaction

Reduction reactions are essential transformations in chemistry where a substance gains electrons or reduces its oxidation state. This is often accompanied by the removal of oxygen or the addition of hydrogen. In the reduction of phosphorus tribromide (PBr₃) to white phosphorus (P₄), hydrogen gas ( H₂) acts as a reducing agent.
Here are a few points about reduction reactions:

• The reactant that accepts electrons is reduced, while the one donating electrons is oxidized.
• Reduction is paired with oxidation, making these reactions part of redox (reduction-oxidation) processes.
• The balanced chemical equation for this reaction shows that six molecules of PBr₃ react with six H₂ molecules to form P₄ and hydrogen bromide (HBr).

Understanding reduction helps in grasping the energy transfers and transformations potential in chemical reactions, crucial for industrial applications and theoretical chemistry.