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 -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 \(100.0-\mathrm{mL}\) 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 reacted, what is the formula of the product?

Short answer

The formula of the xenon fluoride compound produced is XeF₂.

Step-by-step solution

Use the ideal gas law to calculate the initial moles of xenon and fluorine

The ideal gas law formula is \(PV = nRT\), where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant (0.0821 L atm / K mol) and T is the temperature in Kelvin. Using this formula, we can calculate the initial moles of xenon and fluorine: For xenon: \(P=\) 1.24 atm, \(V=\) 100.0 mL = 0.1 L, \(R=\) 0.0821 L atm / K mol, \(T=\) (25 + 273.15) K = 298.15 K \(n_Xe = \frac{PV}{RT}\) \(n_Xe = \frac{(1.24 \,\mathrm{atm})(0.1 \,\mathrm{L})}{(0.0821\, \mathrm{L\, atm / K\, mol})(298.15\, \mathrm{K})}\) \(n_Xe \approx 0.00506 \,\mathrm{moles}\) For fluorine: \(P=\) 10.10 atm, \(V=\) 100.0 mL = 0.1 L, \(R=\) 0.0821 L atm / K mol, \(T=\) (25 + 273.15) K = 298.15 K \(n_F = \frac{PV}{RT}\) \(n_F = \frac{(10.10 \,\mathrm{atm})(0.1 \,\mathrm{L})}{(0.0821\, \mathrm{L\, atm / K\, mol})(298.15\, \mathrm{K})}\) \(n_F \approx 0.04083 \,\mathrm{moles}\)

Calculate the moles of remaining fluorine after the reaction

We'll perform a similar calculation for the moles of remaining fluorine after the reaction: Remaining fluorine: \(P=\) 7.62 atm, \(V=\) 100.0 mL = 0.1 L, \(R=\) 0.0821 L atm / K mol, \(T=\) (25 + 273.15) K = 298.15 K \(n_F' = \frac{PV}{RT}\) \(n_F' = \frac{(7.62 \,\mathrm{atm})(0.1 \,\mathrm{L})}{(0.0821\, \mathrm{L\, atm / K\, mol})(298.15\, \mathrm{K})}\) \(n_F' \approx 0.03110 \,\mathrm{moles}\)

Calculate the moles of fluorine that reacted with xenon

Subtract the moles of fluorine remaining after the reaction from the initial moles of fluorine to obtain the moles of fluorine that reacted with xenon: \(n_{F,reacted} = n_F - n_F'\) \(n_{F,reacted} = 0.04083 \,\mathrm{moles} - 0.03110 \,\mathrm{moles}\) \(n_{F,reacted} \approx 0.00973 \,\mathrm{moles}\)

Calculate the mole ratio between xenon and fluorine in the compound

Divide the moles of reacted fluorine by the moles of xenon to find the mole ratio between them in the compound: Mole ratio = \(\frac{n_{F,reacted}}{n_Xe}\) Mole ratio = \(\frac{0.00973 \,\mathrm{moles}}{0.00506 \,\mathrm{moles}}\) Mole ratio ≈ 1.922 Since the mole ratio must be an integer, we conclude that the mole ratio is 2.

Determine the formula of the product

For every mole of xenon, there are approximately 2 moles of fluorine. So the formula of the product should be: XeF₂ The formula of the xenon fluoride compound produced is XeF₂.

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry that relates the pressure, volume, temperature, and amount of a gas. It is expressed as \(PV = nRT\), where:

• \(P\) is the pressure of the gas
• \(V\) is the volume it occupies
• \(n\) is the number of moles
• \(R\) is the ideal gas constant, and
• \(T\) is the temperature in Kelvin

The formula allows us to solve for one variable if we know the others. This is particularly useful when dealing with reactions involving gases. By rearranging the formula to \(n = \frac{PV}{RT}\), we can determine the number of moles present in a system, as demonstrated with xenon and fluorine gases. Knowing this quantity is essential for understanding how these gases interact in a chemical reaction.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of bonds, resulting in new compounds. In the given example, xenon and fluorine gases react to form a binary compound. This reaction involves heating the gases to a specific temperature, which allows them to combine.
Reactions occur due to the properties of the reactants, their ability to bond, and the conditions under which they are brought together - like temperature and pressure. In our case, these gases at 400°C in a nickel vessel facilitate the formation of xenon fluoride. Understanding reactions requires us to predict how much of each gas is consumed or remains post-reaction, crucially guided by concepts such as the conservation of mass.

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to predict the amounts of substances consumed and produced. Using stoichiometry, chemists determine the balanced equation that describes the reaction – which in this case resulted in the compound Xenon Fluoride, \(\text{XeF}_2\).
By calculating moles of reactants before and after the reaction, we infer the moles that participated in forming the product.
For example, the exercise showed us how to find the moles of fluorine that reacted by subtracting the post-reaction quantity from its initial amount. The mole ratio between the reactants then helps in deducing the smallest whole numbers to write balanced chemical equations, such as 1 mole of xenon reacting with 2 moles of fluorine, leading to \(\text{XeF}_2\). This principle ensures that matter is conserved during chemical transformations.