Problem 79 - General Chemistry: Principles and Modern Applications

Question

A method of producing phosphine, \(\mathrm{PH}_{3}\), from elemental phosphorus, \(P_{4}\), involves heating the \(P_{4}\) with \(\mathrm{H}_{2} \mathrm{O} .\) An additional product is phosphoric acid, \(\mathrm{H}_{3} \mathrm{PO}_{4}\) Write a balanced equation for this reaction.

Step-by-Step Solution

Answer

The balanced chemical equation for the reaction is \(P_{4} + 6H_{2}O → 4PH_{3} + 4H_{3}PO_{4}\).

Step 1: Write down the unbalanced chemical equation

First, write down the unbalanced chemical equation from the given information: \(P_{4} + H_{2}O → PH_{3} + H_{3}PO_{4}\)

Step 2: Balance the equation

According to the law of conservation of mass, the amount of atoms that enter a chemical reaction must be equal to the amount of atoms that leave the reaction. Therefore, balance the equation by adjusting the coefficient of each compound so that the number of atoms of each element on the reactant side is equal to the number of atoms of the same element on the product side. The balanced equation is: \(P_{4} + 6H_{2}O → 4PH_{3} + 4H_{3}PO_{4}\).

Key Concepts

Reaction Balancing

Balancing a chemical equation is a crucial skill in chemistry. It ensures that the number of each type of atom is the same on both sides of the equation, adhering to the conservation of mass. Here's how you can balance the reaction for phosphine production.

First, you start with the unbalanced equation: \(P_4 + H_2O \rightarrow PH_3 + H_3PO_4\). Count the number of each type of atom on both sides. On the reactant side: there are 4 phosphorus atoms and 2 hydrogen atoms from water. On the product side, you need to distribute these atoms across both \(PH_3\) and \(H_3PO_4\).

To balance phosphorous, you'll need 4 \(PH_3\) molecules because each contains one phosphorus atom. This adjustment gives you 12 hydrogen atoms. You also balance hydrogen by adding 6 \(H_2O\) molecules to provide the required hydrogen and oxygen atoms. Now the balanced equation looks like: \(P_4 + 6H_2O \rightarrow 4PH_3 + 4H_3PO_4\). This equation represents a balanced reaction adhering to the law of conservation of mass.

Phosphine Production

Phosphine, \(PH_3\), is a compound produced using elemental phosphorus and water. This process involves a chemical reaction where phosphorus is heated with water. Phosphine is a toxic, colorless gas and has a distinctive garlic-like odor.

During the reaction, phosphorus, \(P_4\), interacts with water molecules to produce phosphine gas and phosphoric acid \(H_3PO_4\). The reaction equation is already balanced in previous steps showing that these materials are fully converted without remaining elements in stoichiometrically incorrect proportions.

Understanding this process is important because phosphine has applications in industries such as agriculture, where it is used as a fumigant, and in semiconductor manufacturing. It's essential to follow careful procedures when producing phosphine due to its toxicity and flammability.

Law of Conservation of Mass

The law of conservation of mass is a fundamental concept in chemistry that states that mass is neither created nor destroyed in a chemical reaction. This principle guides the balancing of chemical equations.

For our specific reaction of phosphine production, this law implies that the number of atoms for each element remains constant from reactants to products. In our balanced equation \(P_4 + 6H_2O \rightarrow 4PH_3 + 4H_3PO_4\), notice how the atom count before and after the reaction doesn't change, maintaining equilibrium.

• 4 phosphorus atoms are in both reactants and products.
• The hydrogen atoms are balanced with 18 atoms on each side (12 from phosphine and 6 from phosphoric acid).
• Oxygen is balanced with 24 atoms on each side (all from phosphoric acid and water).

This balance confirms the adherence to the conservation of mass, reassuring that chemical transformations respect the unchanging nature of matter.