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Chapter 2: Problem 59

A compound of xenon and fluorine is found to be \(53.5 \%\) xenon by mass. What is the empirical formula of the compound?

Short Answer

Expert verified
The empirical formula is \( \text{XeF}_6 \).

Step by step solution

01

Convert Percentage to Mass

Assume you have 100 grams of the compound. This makes it easy to assume you have 53.5 grams of xenon (Xe) since xenon comprises 53.5% of the compound by mass.
02

Calculate Moles of Xenon

Find the moles of xenon by dividing the mass of xenon by its atomic mass. The atomic mass of xenon is 131.29 g/mol.\[ \text{Moles of Xe} = \frac{53.5 \text{ g}}{131.29 \text{ g/mol}} \approx 0.407 \text{ moles} \]
03

Determine Mass of Fluorine

Since the remaining percentage must be fluorine, subtract the xenon percentage from 100% to get fluorine鈥檚 mass percentage: \[ 100 ext{ extpercent} - 53.5 ext{ extpercent} = 46.5 ext{ extpercent} \]This implies you have 46.5 grams of fluorine.
04

Calculate Moles of Fluorine

Find the moles of fluorine by dividing the mass of fluorine by its atomic mass. The atomic mass of fluorine is 19.00 g/mol.\[\text{Moles of F} = \frac{46.5 \text{ g}}{19.00 \text{ g/mol}} \approx 2.447 \text{ moles} \]
05

Find Molar Ratio

Now, find the simplest whole-number ratio between the moles of xenon and fluorine by dividing each by the smallest number of moles calculated:\[\frac{0.407}{0.407} = 1 \ \frac{2.447}{0.407} \approx 6 \]
06

Conclude Empirical Formula

The simplest whole-number ratio is 1:6 for xenon to fluorine. Therefore, the empirical formula of the compound is \( \text{XeF}_6 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Xenon Compounds
Xenon compounds might seem a bit unusual as xenon is a noble gas, traditionally known to be quite unreactive. However, under the right conditions, xenon can form compounds with fluorine and oxygen, among other elements. Fluorine is an exceptionally reactive element, which allows it to bond with xenon, forming stable compounds like xenon hexafluoride (\( \text{XeF}_6 \)). These compounds reveal the unique chemistry of xenon, showing that even noble gases can form bonds under the correct conditions. Understanding and analyzing such compounds can provide insights into molecular structure, bonding, and more.
Mass Percentage
Mass percentage is a way to express the concentration of an element within a compound. It is calculated by dividing the mass of the element by the total mass of the compound, then multiplying by 100 to get a percentage. For example, if a compound contains 53.5% xenon by mass, it means that in every 100 grams of the compound, 53.5 grams are xenon. Understanding mass percentage is crucial in analytical chemistry, where it helps to determine the empirical formulas of compounds. It provides a snapshot of the composition and quantity of elements present.
Molar Ratio
Molar ratio is key in determining the empirical formula. It represents the ratio of the moles of each element in a compound.To find the molar ratio, you first need to convert the mass of each element into moles, using their atomic masses. Then, divide the number of moles of each element by the smallest number of moles calculated.This gives a simple whole-number ratio, indicating the proportion in which atoms combine to form the compound. In our exercise, xenon and fluorine's moles yield a 1:6 ratio, leading to the empirical formula \( \text{XeF}_6 \). This ratio shows how many atoms of each element are present relative to the others.
Chemical Calculations
Chemical calculations are essential for understanding and predicting chemical processes. They involve using formulas and relationships between quantities of reactants and products in chemical reactions.In the case of determining empirical formulas, chemical calculations help convert percentages to masses, masses to moles, and eventually moles to the simplest ratios.Key Steps in Chemical Calculations:
  • Convert given percentages to grams, especially when considering a sample of 100 grams.
  • Calculate the number of moles using the formula: \[ \text{Moles} = \frac{\text{mass in grams}}{\text{atomic mass}} \]
  • Determine the simplest molar ratio by dividing all moles by the smallest number of moles.
These calculations not only reveal the empirical formula but also deepen understanding of the compound's composition and stoichiometry.

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