Problem 89 - Chemistry and Chemical Reactivity

Question

Silane, \(\mathrm{SiH}_{4},\) reacts with \(\mathrm{O}_{2}\) to give silicon dioxide and water vapor: $$ \mathrm{SiH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{SiO}_{2}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ If you mix \(\mathrm{SiH}_{4}\) with \(\mathrm{O}_{2}\) in the correct stoichiometric ratio, and if the total pressure of the mixture is \(120 \mathrm{mm} \mathrm{Hg}\), what are the partial pressures of \(\mathrm{SiH}_{4}\) and \(\mathrm{O}_{2} ?\) When the reactants have been completely consumed, what is the total pressure in the flask? (Assume T is constant.)

Step-by-Step Solution

Answer

Partial pressures are 40 mmHg for \( \mathrm{SiH}_{4} \) and 80 mmHg for \( \mathrm{O}_{2} \). Total pressure remains 120 mmHg after reaction.

Step 1: Understand the Reaction

The balanced chemical reaction is \( \mathrm{SiH}_{4} + 2 \mathrm{O}_{2} \rightarrow \mathrm{SiO}_{2} + 2 \mathrm{H}_{2} \mathrm{O} \). This tells us that one mole of \( \mathrm{SiH}_{4} \) reacts with two moles of \( \mathrm{O}_{2} \). We must ensure that the initial pressure ratio is the same as the stoichiometric ratio.

Step 2: Initial Stoichiometric Ratio

In the correct stoichiometric ratio, partial pressures of gases must reflect the mole ratio from the balanced equation. For \( 1 \) mole of \( \mathrm{SiH}_{4} \), there are \( 2 \) moles of \( \mathrm{O}_{2} \). Thus, the pressure contributed by \( \mathrm{SiH}_{4} \) is \( \frac{1}{3} \) of the total, while \( \mathrm{O}_{2} \) is \( \frac{2}{3} \).

Step 3: Calculate Partial Pressures Before Reaction

The total pressure is given as \( 120 \mathrm{mmHg} \). Thus, the partial pressure of \( \mathrm{SiH}_{4} \) is \( \frac{1}{3} \times 120 = 40 \mathrm{mmHg} \) and the partial pressure of \( \mathrm{O}_{2} \) is \( \frac{2}{3} \times 120 = 80 \mathrm{mmHg} \).

Step 4: Reaction Completion and Product Formation

Assuming complete reaction, \( \mathrm{SiH}_{4} \) and \( \mathrm{O}_{2} \) are completely consumed. \( \mathrm{SiO}_{2} \) is a solid and does not contribute to the gas pressure. Hence, only \( \mathrm{H}_{2} \mathrm{O} \) (as vapor) contributes to pressure.

Step 5: Calculate Partial Pressure After Reaction

2 moles of \( \mathrm{H}_{2} \mathrm{O} \) form for every initial 1 mole of \( \mathrm{SiH}_{4} \), maintaining the total moles of gas constant as initially \( 1 + 2 = 3 \) moles become 2 moles \( \mathrm{H}_{2} \mathrm{O} \) after reaction, the pressure remains \( 120 \mathrm{mmHg} \).

Step 6: Answer Verification

We verified all calculation steps uphold the conservation of moles and pressure laws at constant temperature. The calculations are consistent with the statement of complete consumption and formation.

Key Concepts

Chemical Reaction

Chemical reactions involve substances, known as reactants, undergoing a process to transform into new substances, called products. In our exercise, the reactants are silane (\( \mathrm{SiH}_4 \)) and oxygen (\( \mathrm{O}_2 \)). These react together to produce silicon dioxide (\( \mathrm{SiO}_2 \)) and water vapor (\( \mathrm{H}_2 \mathrm{O} \)).
The specific reaction given:

• \( \mathrm{SiH}_4 + 2 \mathrm{O}_2 \rightarrow \mathrm{SiO}_2 + 2 \mathrm{H}_2 \mathrm{O} \) is a balanced chemical equation.
• Balancing a chemical equation ensures the number of atoms of each element is equal on both sides, reflecting the conservation of mass.
• This equation tells us that 1 mole of \( \mathrm{SiH}_4 \) reacts with 2 moles of \( \mathrm{O}_2 \) to produce 1 mole of \( \mathrm{SiO}_2 \) (a solid) and 2 moles of \( \mathrm{H}_2 \mathrm{O} \) (as gas).

The balanced nature of this equation is crucial for determining the proportions of substances needed to achieve the reaction without any leftover reactants.

Partial Pressure

Partial pressure is the pressure exerted by an individual gas in a mixture. Dalton's Law of Partial Pressures states that the total pressure of a gas mixture is equal to the sum of the partial pressures of each component gas.
In the exercise:

• The total pressure is 120 mmHg, and the gases \( \mathrm{SiH}_4 \) and \( \mathrm{O}_2 \) are involved initially.
• Given the reaction stoichiometry (1:2 ratio for \( \mathrm{SiH}_4 \) to \( \mathrm{O}_2 \)), partial pressures can be determined.
• \( \mathrm{SiH}_4 \), being 1 part of the total 3 parts (1 mole of \( \mathrm{SiH}_4 \) + 2 moles of \( \mathrm{O}_2 \)), contributes \( \frac{1}{3} \times 120 \mathrm{mmHg} = 40 \mathrm{mmHg} \).
• \( \mathrm{O}_2 \), being 2 parts, contributes \( \frac{2}{3} \times 120 \mathrm{mmHg} = 80 \mathrm{mmHg} \).

This understanding is vital for calculating how much pressure each gas contributes and shows how individual gases in a mixture influence overall pressure.

Gas Laws

The behavior of gases can be predicted using gas laws. In this exercise, we assume constant temperature, which implies certain laws are at play.
Key Points to Note:

• When reactants \( \mathrm{SiH}_4 \) and \( \mathrm{O}_2 \) are completely consumed, the gases form \( \mathrm{H}_2 \mathrm{O} \).
• Boyle's Law, Charles's Law, and Avogadro's Law are inherent within these transformations; yet, the key here is that the reaction selects pressure conservation based on changing compositions.
• Despite the reactive change, the total number of moles of gas remains similar due to conversion of gas to gas (\( 3 \) initial moles become \( 2 \) \( \mathrm{H}_2 \mathrm{O} \) vapor moles each doubling).

This results in maintaining a constant total pressure of 120 mmHg, considering the reaction completion and constant temperature. Understanding these principles simplifies making predictions about gas behavior post-reaction.

Silicon Compounds

Silicon compounds are prevalent in both natural and industrial scenarios. In our reaction, silicon is part of silane (\( \mathrm{SiH}_4 \)) and transforms into silicon dioxide (\( \mathrm{SiO}_2 \)).
Characteristics of Silicon Compounds:

• Silane is a silicon hydride compound and acts as a reducing agent reacting with oxygen.
• Silicon dioxide, the reaction product, is known as silica, a primary component in glass and sand.
• The formation of \( \mathrm{SiO}_2 \) is vital in many chemical processes, acting as a robust and inert material.

This conversion underpins opportunities for various applications, including manufacturing, silica sand applications, and semiconductor industries. The study of reactions involving silicon compounds demonstrates their versatility and importance in different sectors.