Question

A 20.0-L nickel container was charged with \(0.500\) atm of xenon gas and \(1.50\) atm of fluorine gas at \(400 .{ }^{\circ} \mathrm{C}\). The xenon and fluorine react to form xenon tetrafluoride. What mass of xenon tetrafluoride can be produced assuming \(100 \%\) yield?

Short answer

The balanced chemical equation for the reaction between xenon and fluorine is \(Xe + 2F_2 \rightarrow XeF_4\). Using the ideal gas law equation and the given conditions, we can find that the number of moles of xenon is \(n_{Xe} = \frac{0.5 atm \times 20.0 L}{0.0821 \frac{L \cdot atm}{mol \cdot K} \times 673.15 K}\) and the number of moles of fluorine is \(n_{F_2} = \frac{1.5 atm \times 20.0 L}{0.0821 \frac{L \cdot atm}{mol \cdot K} \times 673.15 K }\). Comparing their moles with their stoichiometric coefficients, we can determine the limiting reactant, and calculate the moles of xenon tetrafluoride produced. Finally, multiply the moles of xenon tetrafluoride by its molar mass (207.29 g/mol) to get the mass of xenon tetrafluoride produced, assuming 100% yield: \(Mass\ XeF_4 = \ moles\ XeF_4 \times Molar\ Mass\ XeF_4\).

Step-by-step solution

Write the balanced chemical equation

The balanced chemical equation for the formation of xenon tetrafluoride from xenon and fluorine is: \(Xe + 2F_2 \rightarrow XeF_4\)

Convert pressure and volume to moles of reactants

To calculate the moles of reactants, we will use the ideal gas law equation: \(P \times V = n \times R \times T\) Where: - \(P\) is pressure (in atm), - \(V\) is volume (in L), - \(n\) is the number of moles, - \(R\) is the universal gas constant (0.0821 \(\frac{L \cdot atm}{mol \cdot K}\)), - \(T\) is the temperature in Kelvin. First, we need to convert the temperature to Kelvin: \(T_{Kelvin} = 400 + 273.15 = 673.15 K\) Now, we can calculate the number of moles for each reactant: For Xenon: \(n_{Xe} = \frac{0.5 atm \times 20.0 L}{0.0821 \frac{L \cdot atm}{mol \cdot K} \times 673.15 K}\) For Fluorine: \(n_{F_2} = \frac{1.5 atm \times 20.0 L}{0.0821 \frac{L \cdot atm}{mol \cdot K} \times 673.15 K }\)

Determine the limiting reactant

From the balanced equation, 1 mole of xenon reacts with 2 moles of fluorine. Now we need to compare the actual mole ratio of the reactants to the stoichiometric mole ratio from the balanced equation: Calculate mole ratio: \(\frac{n_{F_2}}{n_{Xe}}\) Determine the limiting reactant by comparing the actual molar ratio with the stoichiometric molar ratio. If the actual ratio is greater than or equal to the stoichiometric ratio, xenon is the limiting reactant. If the actual ratio is less than the stoichiometric ratio, fluorine is the limiting reactant.

Calculate moles of the product

Based on the limiting reactant, calculate the moles of xenon tetrafluoride, using the stoichiometric coefficients from the balanced equation.

Convert moles of xenon tetrafluoride to mass

To find the mass of xenon tetrafluoride produced, multiply the moles of xenon tetrafluoride by its molar mass (207.29 g/mol): \(Mass\ XeF_4 = \ moles\ XeF_4 \times Molar\ Mass\ XeF_4\) Now you have the mass of xenon tetrafluoride that can be produced, assuming 100% yield.

Key concepts

Ideal Gas Law

The Ideal Gas Law is a crucial tool in chemical stoichiometry, making it easier to relate pressure, volume, and temperature to moles of a gas. The equation is given by:\(PV = nRT\). This can help convert measurements you can easily take, such as pressure and volume, into the amount of substance, which is harder to measure directly.- **Pressure (P)** is measured in atmospheres for this equation.- **Volume (V)** is in liters.- **Temperature (T)** must be in Kelvin. Always remember to convert temperatures from Celsius to Kelvin by adding 273.15.- **Universal gas constant (R)** is 0.0821 \(\frac{L\cdot atm}{mol\cdot K}\).In the exercise, you'll use this law to find out how many moles of xenon and fluorine gases are present, setting the stage for further stoichiometric calculations. Knowing these moles allows us to use the balanced equation to predict amounts of other substances involved.

Balanced Chemical Equation

A balanced chemical equation ensures that mass is conserved during a chemical reaction, showing equal numbers of each type of atom on both sides of the equation.For the reaction of xenon and fluorine here, the balanced equation is:\[Xe + 2F_2 \rightarrow XeF_4\]The equation shows that 1 mole of xenon reacts with 2 moles of fluorine to produce 1 mole of xenon tetrafluoride.- **Why balance?** Balancing is critical because it reflects the Reality of atomic rearrangement in chemical reactions. It ensures every atom going into the reaction comes out in the product.- **How to balance?** Adjust coefficients for each reactant and product. Never change subscripts to balance.This balance allows us to relate moles of any reactant to moles of products or other reactants in the reaction, which is fundamental for determining amounts.

Limiting Reactant

The Limiting Reactant (sometimes called the "limiting reagent") is the substance that gets completely used up when the reaction goes to completion. It limits the amount of product you can make. In our example with xenon and fluorine, after calculating the moles of each using the Ideal Gas Law and comparing them to the stoichiometric coefficients from the balanced chemical equation, you'll find which reactant will run out first. - **Determine Limiting Reactant**: - Calculate moles of each reactant. - Use ratio from the balanced equation to compare actual in your container. - If real ratio is <= calculated stoichiometric ratio, it's limiting. With xenon and fluorine, if xenon's calculated moles are enough for the fluorine moles you have, fluorine limits the reaction. Identifying the limiting reactant is crucial because it dictates maximum product formation.

Molar Mass Calculation

To find the mass of a product like xenon tetrafluoride, you first need its molar mass, given in grams per mole. This involves finding the mass of each constituent atom from the periodic table and adding them together.For xenon tetrafluoride (\(XeF_4\)):1. **Calculate Molar Mass**: - Xenon (Xe): 131.29 g/mol - Fluorine (F): 18.998 g/mol - Total mass = 131.29 + 4*(18.998) = 207.29 g/mol2. **Use Molar Mass**: - Multiply the moles of \(XeF_4\) (found from limiting reactant calculations) by the molar mass to get the product mass.Understanding molar mass is vital for converting between moles and grams, allowing us to predict how much of a product can be formed or how much of a reactant was used.