Problem 42 - General Chemistry: Principles and Modern Applications

Question

Write a chemical equation to represent (a) the reaction of potassium cyanide solution with silver nitrate solution; (b) the combustion of \(\mathrm{Si}_{3} \mathrm{H}_{8}\) in an excess of oxygen; (c) the reaction of dinitrogen with calcium carbide to give calcium cyanamide (CaNCN).

Step-by-Step Solution

Answer

(a) KCN(aq) + AgNO3(aq) → AgCN(s) + KNO3(aq) \n(b) 3Si3H8(g) + 16O2(g) → 9SiO2(s) + 12H2O(g) \n(c) N2(g) + 3CaC2(s) → 3CaNCN(s) + C(s)

Step 1: (a) Reaction of potassium cyanide with silver nitrate

To write the chemical equation, identify the reactants and products. For this reaction, potassium cyanide (KCN) and silver nitrate (AgNO3) are reactants. When these two react, they undergo a double displacement reaction to form silver cyanide (AgCN) and potassium nitrate (KNO3). Hence the unbalanced chemical equation is:\nKCN(aq) + AgNO3(aq) → AgCN(s) + KNO3(aq).\nThe equation is already balanced.

Step 2: (b) Combustion of Si3H8 in oxygen

The reactants for this reaction are the silicon hydride (Si3H8) and oxygen (O2). In a typical combustion reaction with an excess of oxygen, the products are expected to be silicon dioxide (SiO2) and water (H2O). The unbalanced reaction is: \nSi3H8(g) + O2(g) → SiO2(s) + H2O(g).\nBalancing the equation gives: \n3Si3H8(g) + 16O2(g) → 9SiO2(s) + 12H2O(g).

Step 3: (c) Reaction of dinitrogen with calcium carbide

For this reaction, dinitrogen (N2) reacts with calcium carbide (CaC2) to yield calcium cyanamide (CaNCN). The nitrogen atom in N2 is triple-bonded, highly un-reactive and requires a significant amount of energy to break. It is usually performed in presence of a catalyst under high heat and pressure but for simplicity's sake, we'll ignore these details. The unbalanced reaction is: \nN2(g) + CaC2(s) → CaNCN(s).\nBalancing this equation gives: \nN2(g) + 3CaC2(s) → 3CaNCN(s) + C(s). Note the addition of Carbon (C) as a product to balance the carbons on both sides.

Key Concepts

Double Displacement Reaction

In chemistry, a **double displacement reaction** is one in which two compounds exchange ions to form two new compounds. This type of reaction typically occurs in aqueous solutions where ions are free to move.
In a double displacement reaction, the cations and anions of the reactants switch places. For example, when potassium cyanide (\( \text{KCN} \)) reacts with silver nitrate (\( \text{AgNO}_{3} \)), the respective ions are exchanged to form new products: silver cyanide (\( \text{AgCN} \)) and potassium nitrate (\( \text{KNO}_{3} \)).

Here is the chemical equation of this reaction:

• Reactants: \( \text{KCN (aq)} + \text{AgNO}_{3} \text{(aq)} \)
• Products: \( \text{AgCN (s)} + \text{KNO}_{3} \text{(aq)} \)

Remember, solids are often formed as precipitates, which separates the products from the solution. In this case, \( \text{AgCN} \) is the precipitate.
Although the equation appears straightforward, understanding how these ions rearrange deepens comprehension of chemical processes and stoichiometry.

Combustion Reaction

A **combustion reaction** is a type of chemical reaction where a substance combines with oxygen to produce oxides and releases energy in the form of heat and light. This process is quite common and essential in activities ranging from burning fuels to cellular respiration.
When considering the combustion of the compound \( \text{Si}_{3} \text{H}_{8} \), silicon hydride reacts with oxygen \( \text{O}_2 \), the products formed are silicon dioxide \( \text{SiO}_2 \)and water \( \text{H}_{2} \text{O} \). The need for balancing the equation arises from conservation principles - matter cannot be created or destroyed, so the number of atoms for each element must be equal on both sides of the equation.

The balanced equation for the combustion of \( \text{Si}_{3} \text{H}_{8} \) in excess oxygen is:

• \( 3\text{Si}_{3} \text{H}_{8} \text{(g)} + 16\text{O}_2 \text{(g)} \rightarrow 9\text{SiO}_2 \text{(s)} + 12\text{H}_{2} \text{O} \text{(g)} \)

Balancing involves adjusting coefficients to ensure there are the same number of atoms for each element on both sides. Here, the three-fold increase in reactants and products reflects this conservation.

Balancing Chemical Equations

The concept of **balancing chemical equations** is foundational in chemistry. It ensures that the law of conservation of mass is satisfied, as it mandates that matter cannot be created nor destroyed in a chemical reaction.
When balancing chemical equations, the goal is to have the same number of each type of atom on both sides of the equation. This process is crucial to accurately depict the transformation of reactants into products. Let's consider the balancing of the reaction between dinitrogen \( \text{N}_2 \) and calcium carbide \( \text{CaC}_2 \):

The unbalanced equation for this conversion into calcium cyanamide \( \text{CaNCN} \) is:

• \( \text{N}_2 \text{(g)} + \text{CaC}_2 \text{(s)} \rightarrow \text{CaNCN} \text{(s)} \)

By applying stoichiometric principles, we balance the equation as follows:

• \( \text{N}_2 \text{(g)} + 3\text{CaC}_2 \text{(s)} \rightarrow 3\text{CaNCN} \text{(s)} + \text{C} \text{(s)} \)

Through inspection and adjustment, it is clear that balancing involves altering coefficients to achieve equal atom counts for each element on both sides of the equation. Practice and repetition help in mastering these balancing skills, essential for engaging with complex chemical processes.