Problem 67 - Chemistry Matter and Change

Question

Assess A classmate tells you that experimental data shows a compound’s molecular formula to be 2.5 times its empirical formula. Is he correct? Explain.

Step-by-Step Solution

Answer

No, the classmate is incorrect. Molecular formulas must consist of whole numbers of atoms, and therefore can only be whole-number multiples of their empirical formula. A molecular formula being 2.5 times the empirical formula would result in fractional numbers of atoms, which is not possible.

Step 1: Understanding Molecular and Empirical Formulas

An empirical formula represents the simplest whole-number ratio of the elements in a compound. A molecular formula represents the actual number of atoms of each element in a molecule of the compound. The molecular formula is always a whole-number multiple of the empirical formula.

Step 2: Empirical Formula Example

For example, consider a compound with the empirical formula CH_2. The simplest whole-number ratio of carbon to hydrogen atoms in this compound is 1:2.

Step 3: Molecular Formula Example

The molecular formula of the same compound could be C_2H_4 or C_3H_6 (or other whole-number multiples of CH_2). In these cases, the molecular formula is a whole-number (2, 3 in the examples) times the empirical formula.

Step 4: Can It Be 2.5 Times?

Now, let's consider the claim that the molecular formula can be 2.5 times the empirical formula. Using the same empirical formula CH_2, we would have a situation where the molecular formula would be (2.5 x CH_2). This would result in the molecular formula being C_2.5H_5.

Step 5: Conclusion

Since molecular formulas must consist of whole numbers of atoms, it is not possible for the molecular formula to be 2.5 times the empirical formula, as this would result in fractional numbers of atoms. Therefore, the classmate's statement is incorrect. Molecular formulas can only be whole-number multiples of their empirical formula.

Key Concepts

Empirical Formula

The empirical formula of a chemical compound is the simplest way to express its composition. It shows the simplest whole-number ratio of the elements in the compound. Unlike the molecular formula, the empirical formula does not reveal the exact number of atoms of each element present in a compound.

For example, let's consider glucose, which has a molecular formula of \( C_6H_{12}O_6 \). The empirical formula of glucose, showing the simplest whole-number ratio, is \( CH_2O \). As you can see, this does not specify the actual number of atoms in each molecule but rather provides the most reduced ratio.

Empirical formulas are critically important in chemistry as they provide essential insights into the basic proportions of elements in compounds. Without knowing the empirical formula, chemists might not be able to derive the molecular formula efficiently.

• Expresses the simplest ratio of elements.
• Does not give the exact number of atoms.
• Helps in determining the molecular formula.

Chemical Compounds

Chemical compounds are substances formed from two or more different elements that are chemically bonded together. The elements in a compound are always present in fixed ratios, which are represented by chemical formulas.

Each compound has a unique set of properties and the combination of elements defines its identity. These combinations can be described by both empirical and molecular formulas. For instance, water, a simple compound, has molecules composed of 2 hydrogen (H) atoms and 1 oxygen (O) atom, represented by the molecular formula \( H_2O \). The empirical formula is also \( H_2O \) in this case.

Understanding chemical compounds requires familiarity with concepts such as:

• Chemical bonds, which hold the atoms together.
• Stoichiometry, which involves calculations based on the ratios in a chemical reaction.

By knowing the empirical and molecular formulas, chemists can predict the behavior and properties of compounds under different conditions.

Whole-number Ratio

The concept of whole-number ratios is fundamental in chemistry, especially when dealing with chemical formulas. A whole-number ratio describes how elements combine in fixed proportions to form compounds.

In the context of empirical and molecular formulas, the whole-number ratio shows the simplest ratio of atoms in a compound, without any fractions or decimals. For molecular formulas, the numbers indicate the actual count of atoms within a single molecule.

A compound's molecular formula is typically a whole-number multiple of its empirical formula. For instance, if the empirical formula of a compound is \( CH_2 \), possible molecular formulas could include \( C_2H_4 \), \( C_3H_6 \), and so forth. Each of these reflects a whole-number multiple (2, 3,...) of the empirical formula.

This characteristic ensures that each atom is counted entirely and results in quantifiable data that support stoichiometric calculations, crucial for predicting yields and behaviors in reactions.

• Ensures that formulas are accurate representations of actual compounds.
• Supports meaningful and practical chemical calculations.