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 \(10.10 \mathrm{~atm}\). 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 \(100.0\) -mL nickel container, where the pressure of \(\mathrm{F}_{2}\) at \(25^{\circ} \mathrm{C}\) is \(7.62 \mathrm{~atm}\). Assuming all of the xenon has \(\mathrm{re}\) acted, what is the formula of the product?

Short answer

Initially calculate the moles of Xe and F2 using the ideal gas law equation. Then find the moles of F2 after the reaction and moles of F2 consumed. Determine the ratio of xenon to fluorine atoms in the compound and simplify the ratio if necessary. The formula of the xenon fluoride compound can be written as XeFx, where x represents the simplified ratio (number of fluorine atoms) in the product.

Step-by-step solution

Calculate the initial moles of Xe and F2

Using the ideal gas law equation (PV = nRT), we can find the initial moles of Xe and F2. The equation can be rearranged to solve for moles (n): \(n = \frac{PV}{RT}\) where P = pressure, V = volume, R = ideal gas constant (0.0821 L atm/(mol K)), and T = temperature in Kelvin. First, convert the given temperatures to Kelvin: Initial temperature (T1) = \(25^{\circ} \mathrm{C} + 273.15\) = 298.15 K Now, calculate the moles of Xe: \(n_{Xe} = \frac{P_{Xe}V}{RT_1} = \frac{1.24\, \mathrm{atm} \times 100.0\, \mathrm{mL}}{0.0821\, \mathrm{L\, atm /(mol\, K)} \times 298.15\, \mathrm{K}}\) And moles of F2: \(n_{F2} = \frac{P_{F2}V}{RT_1} = \frac{10.10\, \mathrm{atm} \times 100.0\, \mathrm{mL}}{0.0821\, \mathrm{L\, atm /(mol\, K)} \times 298.15\, \mathrm{K}}\)

Calculate the moles of F2 after reaction

Since the remaining F2 gas is transferred to another container of the same volume, we can find the moles of F2 after the reaction using the same ideal gas law equation with the final pressure (7.62 atm) and the initial temperature (T1) in Kelvin. \(n'_{F2} = \frac{P'_{F2}V}{RT_1} = \frac{7.62\, \mathrm{atm} \times 100.0\, \mathrm{mL}}{0.0821\, \mathrm{L\, atm /(mol\, K)} \times 298.15\, \mathrm{K}}\)

Calculate the moles of Xe and F2 in the product

Now that we have calculated the moles of F2 before and after the reaction, we can then find the number of F2 moles consumed in the reaction. Since all of the xenon has reacted, the moles of Xe in the reaction will be equal to the initial moles of Xe calculated in step 1. Moles of F2 consumed (n_F2_consumed) = moles of F2 before reaction - moles of F2 after reaction

Determine the formula of the xenon fluoride compound

To determine the formula of the xenon fluoride compound, we need to find the ratio of xenon to fluorine atoms in the compound. We can do this by dividing the moles of F2 consumed by the moles of Xe in the reaction. Ratio (F2:Xe) = (n_F2_consumed)/(n_Xe) Since the ratio of moles doesn't necessarily represent the ratio of atoms in the compound, we need to check whether the obtained ratio needs simplification or not. If the ratio does need simplification, divide the numbers in the ratio by their greatest common divisor (GCD). Once the simplest whole number ratio is determined, we can write the formula of the xenon fluoride compound as XeFx, where x is the simplified ratio (number of fluorine atoms) in the product.

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that is used to link together the pressure, volume, temperature, and number of moles of a gas. It is expressed as \( PV = nRT \), where:

• \( P \) is the pressure of the gas
• \( V \) is the volume
• \( n \) represents the number of moles
• \( R \) is the ideal gas constant (0.0821 L atm/(mol K))
• \( T \) is the temperature in Kelvin

This law assumes that gases behave ideally, meaning their particles do not interact and move freely. To use the Ideal Gas Law effectively, always ensure your pressure is in atmospheres, volume in liters, and temperature in Kelvin. For conversion, remember that Celsius can be changed to Kelvin by adding 273.15. In the exercise, the Ideal Gas Law helps to calculate the initial moles of xenon and fluorine gases by rearranging the formula to \( n = \frac{PV}{RT} \). This rearrangement allows us to determine how much of each gas is available to take part in the chemical reaction when heated.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products via chemical changes. In the provided exercise, xenon and fluorine undergo a reaction to form a new compound, xenon fluoride. When heated to \(400^{\circ} \text{C}\), these gases react because of the increased energy that facilitates breaking and forming chemical bonds. This gas reaction involves combining individual xenon atoms with fluorine molecules to create a stable compound.

The conditions for reactions often include temperature and pressure, which, in this case, shift dramatically during the process. The reaction also leads to one of the substances (xenon fluoride) becoming a nonvolatile solid, emphasizing a phase change from gaseous to solid state. Understanding the conditions under which reactions naturally proceed helps predict outcomes and articulate the type of compound formed in such environments. Recognizing these processes, one can infer that only a specific stoichiometric ratio of reactions is needed for the formation of xenon fluoride.

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the elements in a chemical reaction. It helps chemists determine the ideal ratios of reactants needed to produce a desired product. Through stoichiometry, it is possible to identify how much of each compound interacts and the proportions they form in the output.

In this exercise, stoichiometry is essential to establish the exact formula of the xenon fluoride product. By determining the moles of reactants and the remaining unreacted \( \mathrm{F}_2 \), the exercise guides us through calculating the moles of fluorine consumed in the reaction. This consumed amount is contrasted against the initial moles of xenon to provide the ratio of \( \mathrm{F}_2 \) to \( \mathrm{Xe} \), expressed as \( \frac{n_{F2\text{ consumed}}}{n_{Xe}} \).

The stoichiometric calculation ultimately aims to find the simplest whole number ratio, revealing the molecular formula. If needed, this ratio can be simplified by finding the greatest common divisor, turning complex ratios into easily understandable formulas. Hence, stoichiometry not only quantifies aspects of reactions but simplifies understanding of the chemical formula for students.