Question

Xenon and fluorine will react to form binary compounds when a mixture of these two gases is heated to \(400^{\circ} \mathrm{C}\) in a nickel reaction vessel. A \(100.0\) -\(\mathrm{mL}\) nickel container is filled with xenon and fluorine, giving partial pressures of \(1.24\) atm and \(10.10\) atm, respectively, at a temperature of \(25^{\circ} \mathrm{C}\). The reaction vessel is heated to \(400^{\circ} \mathrm{C}\) to cause a reaction to occur and then cooled to a temperature at which \(\mathrm{F}_{2}\) is a gas and the xenon fluoride compound produced is a nonvolatile solid. The remaining \(\mathrm{F}_{2}\) gas is transferred to another A \(100.0\) -\(\mathrm{mL}\) nickel container, where the pressure of \(\mathrm{F}_{2}\) at \(25^{\circ} \mathrm{C}\) is \(7.62\) atm. Assuming all of the xenon has reacted, what is the formula of the product?

Short answer

The formula of the product is found by calculating the initial moles of Xenon (Xe) and Fluorine (F2), the moles of F2 remaining after the reaction, and the moles of F2 that reacted. The ratio of moles Xe : F determines the stoichiometry of the reaction and the formula XeFx.

Step-by-step solution

Calculate initial moles of Xenon (Xe) and Fluorine (F2)

To calculate the moles of both Xe and F2, use the Ideal Gas Law formula, PV = nRT, where P is pressure, V is volume, n is moles, R is the ideal gas constant, and T is the temperature in Kelvin. Rearrange the equation to calculate n: n = PV/RT First, we need to convert the temperature from Celsius to Kelvin: T = 25 + 273.15 = 298.15 K Now, calculate the moles of Xe and F2: n(Xe) = (1.24 atm)(0.100 L) / ((0.0821 L.atm/mol.K)(298.15 K)) n(F2) = (10.10 atm)(0.100 L) / ((0.0821 L.atm/mol.K)(298.15 K))

Calculate the moles of F2 remaining after the reaction.

We are given the pressure of the remaining F2 after the reaction, so we can calculate the moles of F2 remaining using the Ideal Gas Law again: n(F2_remaining) = (7.62 atm)(0.100 L) / ((0.0821 L.atm/mol.K)(298.15 K))

Calculate the moles of F2 that reacted.

To find the moles of F2 that reacted, subtract the moles of F2 remaining from the initial moles of F2: n(F2_reacted) = n(F2) - n(F2_remaining)

Find stoichiometry of the reaction and the formula of the product.

Since all of the Xenon has reacted, we can determine the ratio of Xenon to Fluorine atoms in the product by finding the ratio of moles: Xe : F = n(Xe) : n(F2_reacted) After finding the ratio, we can write the chemical formula of the product as XeFx, where x is the number of Fluorine atoms in the product.

Key concepts

Xenon Fluoride

Xenon fluoride is a fascinating compound derived from a reaction between xenon and fluorine gases. In this scenario, xenon and fluorine form binary compounds like \(_{\text{XeF}_x}\), where xenon typically bonds with fluorine atoms. This reaction happens in a controlled environment, such as a nickel reaction vessel, and requires high temperatures of around 400°C to proceed. Xenon, being a noble gas, is generally unreactive; however, under specific conditions, it can form stable bonds with highly electronegative atoms like fluorine. The process of forming xenon fluoride showcases the intriguing ability of xenon to break its usual stability and engage in chemical bonding.The resulting xenon fluoride compound is usually a nonvolatile solid at room temperature, which means it doesn’t easily vaporize and remains as a solid. This property is pivotal in isolating the compound from other reaction products.

Stoichiometry

Stoichiometry is a key concept in chemistry that involves calculating the quantities of reactants and products in chemical reactions. When working with xenon fluoride, stoichiometry helps determine how much fluorine reacts with a given amount of xenon to form the xenon fluoride compound. To begin, chemists measure the initial moles of xenon and fluorine using the ideal gas law, which relates pressure, volume, and temperature to moles. This foundational equation, represented as \(PV = nRT\), is rearranged to solve for moles as \(n = \frac{PV}{RT}\). Temperatures must be converted to Kelvin for precise calculations.Once the initial moles are determined, stoichiometry aids in figuring out which reactant is completely used, called the limiting reactant, and predicts the amount of products formed. With xenon being fully reacted, the ratio of xenon to fluorine moles reveals the composition of the xenon fluoride product.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products through breaking and forming bonds. In the context of xenon and fluorine forming xenon fluoride, a chemical reaction is initiated by heating the mixture, causing the gases to react and form a solid compound. During this process, initial conditions—like the pressure and temperature of the gases—play a critical role in determining the course of the reaction. With all xenon reacting, the fluorine that bonds undergoes a stoichiometric relationship, indicating how many fluorine atoms attach to a single xenon atom.The transformations in this reaction are described by a balanced equation, showcasing conservation of mass where atoms are neither created nor destroyed, only rearranged to form new substances. Through careful measurement and calculation, the exact formula of the xenon fluoride product, represented as \(\text{XeF}_x\), can be ascertained, showcasing the elegant intricacy of chemical reactions.