Question

Molecular chlorine and molecular fluorine combine to form a gaseous product. Under the same conditions of temperature and pressure it is found that one volume of \(\mathrm{Cl}_{2}\) reacts with three volumes of \(\mathrm{F}_{2}\) to yield two volumes of the product. What is the formula of the product?

Short answer

The product formula is \(\text{ClF}_3\).

Step-by-step solution

Understand the Problem

We have a reaction between chlorine (\(\text{Cl}_2\)) and fluorine (\(\text{F}_2\)). The volumes of these gases reacting under the same conditions are given: 1 volume of \(\text{Cl}_2\) reacts with 3 volumes of \(\text{F}_2\) to produce 2 volumes of a new gaseous product. We need to determine the molecular formula for this product.

Use Avogadro's Law

According to Avogadro's Law, equal volumes of gases at the same temperature and pressure contain the same number of molecules. This means that the volume ratios of reacting gases can be used directly to deduce the mole ratios in the balanced chemical equation.

Write the Volume Ratios

Based on the problem statement, the volume ratio is 1:3:2 for \(\text{Cl}_2\), \(\text{F}_2\), and the product, respectively. This suggests the following reaction:1 \(\text{Cl}_2\) volume reacts with 3 \(\text{F}_2\) volumes to produce 2 volumes of the product.

Propose Balanced Equation

Assuming each type of molecule contributes its atoms proportionately, we hypothesize that the reaction can be written as:\[\text{Cl}_2 + 3\text{F}_2 \rightarrow 2\text{Product} \]

Determine Product's Formula

Let's assume that each product molecule contains one chlorine atom from \(\text{Cl}_2\) and, since 2 product molecules result from 3 \(\text{F}_2\), this implies each product molecule includes a portion of the 6 fluorine atoms (because 3 F2 = 6 F atoms). Thus, each molecule of product contains 1 Cl atom and 3 F atoms, making the formula \(\text{ClF}_3\).

Verify Molecular Formula

The proposed balanced equation is:\[ \text{Cl}_2 + 3\text{F}_2 \rightarrow 2\text{ClF}_3 \]. Check that the number of atoms of each element is balanced: there are 2 chlorines and 6 fluorines on both sides, confirming our product formula \(\text{ClF}_3\) is correct.

Key concepts

Avogadro's Law

Avogadro's Law is a fundamental concept in chemistry that helps us understand how gases behave. This law states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules.
Therefore, when we look at gaseous reactions, such as the combination of chlorine (\( \text{Cl}_2 \)) and fluorine (\( \text{F}_2 \)), we can directly use the volume ratios of the reacting gases to determine the mole ratios.
This application of Avogadro's Law makes it easier to deduce the balanced chemical equation for the reaction, as the arithmetic of volumes corresponds to the arithmetic of moles.
In the given exercise, the three gases react in specific ratios, and knowing Avogadro's Law allows us to align these ratios with the respective reactants and products, simplifying the determination of the molecular formula.

Volume Ratios in Gas Reactions

When dealing with gas reactions, the volumes of the gases involved can provide significant insights into the reaction's stoichiometry.
In our example, 1 volume of chlorine gas reacts with 3 volumes of fluorine gas to form 2 volumes of the product.
This directly suggests a mole ratio of 1:3:2 for \( \text{Cl}_2 \), \( \text{F}_2 \), and the product respectively under identical conditions.

• Volume ratios help visualize how many units of one gas combine with another.
• These ratios also inform us about the number of molecules involved.

Understanding volume ratios is essential for writing and balancing the corresponding chemical equations. As gases react, their volumes can contract, remain constant, or expand, depending on the number of gas molecules involved in the reaction.

Chemical Equation Balancing

Balancing chemical equations is key to accurately representing a chemical reaction.
This involves ensuring that the number of atoms for each element is the same on both sides of the equation.
Given the volume ratios in our exercise, we propose a balanced equation:\[ \text{Cl}_2 + 3\text{F}_2 \rightarrow 2\text{ClF}_3 \]

• On the left side: 2 chlorine atoms from \( \text{Cl}_2 \) and 6 fluorine atoms from \( 3 \times \text{F}_2 \).
• On the right side: 2 chlorine and 6 fluorine atoms in \( 2 \times \text{ClF}_3 \).

This verification confirms that mass conservation is adhered to, with no atoms lost or gained, providing assurance that our proposed molecular formula is correct.

Molecule

A molecule is a group of atoms bonded together, representing the smallest unit of a chemical compound that can take part in a chemical reaction.
Molecules can be composed of the same type of atom, like \( \text{O}_2 \) (oxygen gas), or different atoms, like \( \text{H}_2\text{O} \) (water).
For chlorine trifluoride (\( \text{ClF}_3 \)), the molecule consists of one chlorine atom and three fluorine atoms, reflecting the chemical compound formed from its gaseous reactants.
Understanding the composition of molecules helps in predicting their chemical properties and behaviors during reactions.

Gaseous Compounds

Gaseous compounds are substances that exist in the gas phase at room temperature.
These compounds have distinct arrangements of atoms and engage in reactions where volume ratios are easily measurable due to their gaseous nature.
In our exercise, the product formed is \( \text{ClF}_3 \), a gaseous compound useful in various industrial applications.
Understanding the properties and reactions of gaseous compounds is crucial in fields like industrial chemistry and environmental science.
These compounds exhibit properties like compressibility and expansion, highlighting the effects of temperature and pressure on their behavior. Grasping these elements is critical for chemists and students alike in predicting how gaseous reactions proceed under different conditions.