Question

Although they were formerly called the inert gases, at least the heavier elements of Group 8 do form relatively stable compounds. For example, xenon combines directly with elemental fluorine at elevated temperatures in the presence of a nickel catalyst. $$\mathrm{Xe}(g)+2 \mathrm{F}_{2}(g) \rightarrow \mathrm{XeF}_{4}(s)$$ What is the theoretical mass of xenon tetrafluoride that should form when \(130 . \mathrm{g}\) of xenon is reacted with \(100 . \mathrm{g}\) of \(\mathrm{F}_{2}\) ? What is the percent yield if only \(145 \mathrm{g}\) of \(\mathrm{XeF}_{4}\) is actually isolated?

Short answer

The theoretical mass of xenon tetrafluoride (XeF4) formed is 256.68g, and the percent yield is approximately 56.45%.

Step-by-step solution

Determine the limiting reactant

To find the limiting reactant, we'll first need to find the mole ratios of the reactants using the balanced chemical equation: \[Xe(g) + 2F_2(g) \rightarrow XeF_4(s)\] Next, convert the given mass of each reactant to moles using their molar masses: Molar mass of Xe = 131.29g/mol Moles of Xe = \(moles = \frac{mass}{molar\;mass}\) = \(\frac{130g}{131.29g/mol}\) = 0.99 moles Molar mass of \(F_2\) = 38g/mol Moles of \(F_2\) = \(moles = \frac{mass}{molar\;mass}\) = \(\frac{100g}{38g/mol}\) = 2.63 moles Now, divide the moles of each reactant by their respective coefficients in the balanced chemical equation to identify the limiting reactant: Moles of Xe divided by coefficient 1 = 0.99 Moles of \(F_2\) divided by coefficient 2 = 1.315 Since the result for Xe (0.99) is less than the result for \(F_2\) (1.315), Xenon is the limiting reactant.

Calculate the theoretical moles and mass of the product

Using the limiting reactant, let's determine the moles of XeF4 formed. From the balanced equation, 1 mole of Xe forms 1 mole of XeF4, so the moles of XeF4 produced is equal to the moles of Xe (0.99 moles). Now, convert the moles of XeF4 to mass using its molar mass: Molar mass of XeF4 = 131.29g/mol(Xe) + 4 * 19g/mol(F) = 259.29 g/mol Mass of XeF4 = \((0.99 moles)(259.29g/mol)\) = 256.68g So the theoretical mass of XeF4 formed is 256.68g.

Calculate the percent yield

Now that we have the theoretical mass and the actual mass isolated, we can calculate the percent yield: \[%\;yield = \frac{actual\;mass}{theoretical\;mass}\times{100}\] \[%\;yield = \frac{145g}{256.68g}\times{100}\] \[%\;yield = 56.45\%\] Therefore, the percent yield of the reaction is approximately 56.45%.

Key concepts

Inert Gases

The term "inert gases" was once used to describe the elements in Group 8, otherwise known as the noble gases. These gases were thought to be completely non-reactive because of their full valence electron shells. However, further research has shown that the heavier noble gases like xenon can indeed form compounds under certain conditions. This discovery challenged the initial inert designation, leading to the updated name "noble gases."

• They possess a complete set of electrons in their outer shell, which makes them very stable.
• Under specific conditions such as elevated temperatures and the presence of a catalyst, heavier noble gases can form compounds, an example being the reaction of xenon with fluorine to form xenon tetrafluoride ( XeF_4).

This reactivity in xenon is significant because it shows that even what we consider stable can change under the right conditions.

Mole Calculation

Mole calculation is a pivotal concept in chemistry that helps relate mass to the number of particles, providing a bridge between tangible and atomic worlds.The mole is a standard unit of measurement for amount of substance in chemistry. It allows chemists to count particles by weighing them.

• A mole is equivalent to Avogadro's number, 6.022 imes 10^{23}, which is the number of atoms or molecules in one mole.
• To convert mass into moles, you use the formula: \( moles = \frac{mass}{molar\ mass} \). This requires knowing the substance's molar mass, usually found on the periodic table.
• In a reaction, such calculations are essential to identify the limiting reactant, which determines the maximum amount of product that can be formed.

By understanding mole calculation, students can accurately determine the amount of reactants and products involved in chemical reactions.

Percent Yield

Percent yield is a key concept in chemical reactions, revealing the efficiency of a reaction in practical terms.In chemistry, reactions may not always proceed to completion, often due to side reactions or incomplete reactions leading to losses.

• Percent yield is calculated using the formula: \( \% yield = \frac{actual\ mass}{theoretical\ mass} \times 100 \).
• The actual yield is the measured amount of product obtained from the reaction, whereas the theoretical yield is the predicted amount from stoichiometric calculations.
• A high percent yield indicates a highly efficient reaction, while a lower yield could suggest issues in the reaction process.

Understanding percent yield helps chemists optimize reaction conditions to increase efficiency and reduce waste.

Chemical Reactions

Chemical reactions are the key processes that convert reactants into products. Their importance spans from industrial applications to biological systems.

• A chemical reaction involves the rearrangement of atoms, transforming substances and releasing or absorbing energy.
• Key considerations in reactions include the identification of the limiting reactant, determining the amount of product formed, and calculating the percent yield.
• In industrial settings, conditions like pressure, temperature, and catalysts play crucial roles in driving reactions forward efficiently.

From synthesizing new compounds to understanding metabolic processes, chemical reactions are fundamental in explaining how substances interact and change in various environments.