Question

Silane, \(\operatorname{SiH}_{4},\) reacts with \(\mathrm{O}_{2}\) to give silicon dioxide and water: $$ \sin _{4}(g)+2 \mathbf{O}_{2}(g) \longrightarrow \operatorname{SiO}_{2}(s)+2 \mathbf{H}_{2} \mathbf{O}(\ell) $$ A \(5.20-\mathrm{L}\) sample of \(\mathrm{SiH}_{4}\) gas at \(356 \mathrm{mm}\) Hg pressure and \(25^{\circ} \mathrm{C}\) is allowed to react with \(\mathrm{O}_{2}\) gas. What volume of \(\mathrm{O}_{2}\) gas, in liters, is required for complete reaction if the oxygen has a pressure of \(425 \mathrm{mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C} ?\)

Short answer

8.77 L of \( \text{O}_2 \) gas is required.

Step-by-step solution

Calculate Moles of SiH4

First, use the ideal gas law to find the moles of \( \text{SiH}_4 \). The ideal gas law is given by:\[ PV = nRT \]Where:- \( P \) is the pressure in atm- \( V \) is the volume in liters- \( n \) is the number of moles- \( R \) is the ideal gas constant \((0.0821 \, \text{L atm K}^{-1}\text{mol}^{-1})\)- \( T \) is the temperature in KelvinConvert the pressure of \( \text{SiH}_4 \) from \( 356 \, \text{mm Hg} \) to atm:\[ 356 \, \text{mm Hg} \times \frac{1 \, \text{atm}}{760 \, \text{mm Hg}} = 0.4684 \, \text{atm} \]Convert the temperature from Celsius to Kelvin:\[ 25^\circ \text{C} + 273.15 = 298.15 \, \text{K} \]Now, plug these values into the ideal gas law:\[ n = \frac{PV}{RT} = \frac{(0.4684 \, \text{atm})(5.20 \, \text{L})}{(0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1})(298.15 \, \text{K})} \approx 0.0999 \, \text{mol} \]

Determine Moles of O2 Required

According to the stoichiometry of the reaction, 1 mole of \( \text{SiH}_4 \) reacts with 2 moles of \( \text{O}_2 \).Thus, the moles of \( \text{O}_2 \) required is twice the moles of \( \text{SiH}_4 \):\[ \text{Moles of } \text{O}_2 = 2 \times 0.0999 = 0.1998 \, \text{mol} \]

Calculate Volume of O2 Required

Use the ideal gas law again to find the volume of \( \text{O}_2 \), given its pressure and temperature. The rearranged ideal gas law for volume is:\[ V = \frac{nRT}{P} \]The pressure of \( \text{O}_2 \) in atm is:\[ 425 \, \text{mm Hg} \times \frac{1 \, \text{atm}}{760 \, \text{mm Hg}} = 0.5592 \, \text{atm} \]Now calculate the volume:\[ V = \frac{(0.1998 \, \text{mol})(0.0821 \, \text{L atm K}^{-1} \text{mol}^{-1})(298.15 \, \text{K})}{0.5592 \, \text{atm}} \approx 8.77 \, \text{L} \]

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves calculating the quantities of reactants and products involved in a chemical reaction. It allows us to understand how substances interact at the molecular level and how much of each substance is necessary to complete a reaction. When analyzing a chemical equation, stoichiometry enables us to determine the proportions in which substances combine.

• The coefficients in a balanced chemical equation, like the one in our exercise, indicate the ratio of moles of each substance involved in the reaction. For instance, a balanced equation of the reaction between Silane (\( \text{SiH}_4 \)) and Oxygen (\( \text{O}_2 \)) shows that 1 mole of Silane reacts with 2 moles of Oxygen.
• This relationship is crucial because it tells us that to fully react with a given amount of Silane, twice that amount of Oxygen (in moles) is required.
• By calculating the moles of Silane, we can easily calculate the moles of Oxygen needed, using the stoichiometric coefficients from the reaction.

Understanding stoichiometry is essential for determining how much of each reactant is needed or how much of a product will be produced, ensuring that reactions can be performed efficiently and economically.

Chemical Reactions

Chemical reactions involve a transformation where reactants convert into products via the breaking and forming of chemical bonds. The reaction given in our exercise is between Silane (\( \text{SiH}_4 \)) and Oxygen (\( \text{O}_2 \)) which yields Silicon Dioxide and Water.

• This reaction requires a sufficient amount of each reactant, according to the stoichiometric ratios discussed earlier, for it to proceed to completion without any reactant leftover.
• The balanced chemical equation helps us to predict the amount of product formed or the amount of each reactant that will be consumed.
• This specific reaction is a combustion reaction where Silane burns in the presence of Oxygen. Such reactions generally release energy in the form of light or heat.

Knowing how to read and balance chemical equations is crucial. It ensures that the amounts of products and reactants are accurate and helps in predicting the behavior of chemical reactions.

Gas Laws

Gas laws describe the behavior of gases, relating their pressure, volume, and temperature. In the exercise provided, the Ideal Gas Law, \( PV = nRT \), is used. It is one of the central gas laws that help to solve many practical problems in chemistry.

• In this equation, \( P \) represents the pressure of the gas, \( V \) stands for the volume, \( n \) denotes the number of moles, \( R \) is the ideal gas constant, and \( T \) indicates the temperature in Kelvin.
• The exercise uses the Ideal Gas Law to convert known amounts of Silane and Oxygen into moles. This is critical as stoichiometric calculations require moles to compare different substances in a reaction.
• Additionally, by rearranging the equation, the volume of Oxygen required for the reaction is found.
  The Ideal Gas Law provides the framework for understanding how gases will react under varying conditions and enables us to predict their behavior in a given situation.

Understanding gas laws like the Ideal Gas Law is essential for solving problems involving gas reactions, predicting how changes in conditions will affect the reaction, and ensuring that reactions involving gases proceed efficiently.