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?

Step by step solution

01

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))

02

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))

03

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)

04

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.

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