Problem 197 - Chemistry Matter and Change

Question

Which of these molecular formulas are also empirical formulas: ethyl ether \(\left(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}\right),\) aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right),\) butyl dichloride \(\left(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{O}_{2}\right),\) glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right) ?\)

Step-by-Step Solution

Answer

The molecular formulas for ethyl ether \(\left(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{O}\right)\) and aspirin \(\left(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}\right)\) are also empirical formulas, as they cannot be reduced to a simpler whole number ratio.

Step 1: Analyze Ethyl Ether (C4H10O)

Calculate the greatest common divisor (GCD) for the given atoms: GCD(4, 10, 1) = 1 As GCD is 1, no simplification is needed, and the given formula ethyl ether (C4H10O) is already an empirical formula.

Step 2: Analyze Aspirin (C9H8O4)

Calculate the greatest common divisor (GCD) for the given atoms: GCD(9, 8, 4) = 1 As GCD is 1, no simplification is needed, and the given formula for aspirin (C9H8O4) is already an empirical formula.

Step 3: Analyze Butyl Dichloride (C4H8O2)

Calculate the greatest common divisor (GCD) for the given atoms: GCD(4, 8, 2) = 2 Dividing the original formula by the GCD, we get C2H4O. Since the formula provided was divisible by the GCD and can be simplified, the original formula for butyl dichloride (C4H8O2) is not an empirical formula.

Step 4: Analyze Glucose (C6H12O6)

Calculate the greatest common divisor (GCD) for the given atoms: GCD(6, 12, 6) = 6 Dividing the original formula by the GCD, we get CH2O. Since the formula provided was divisible by the GCD and can be simplified, the original formula for glucose (C6H12O6) is not an empirical formula. Based on the results of our analysis, the molecular formulas for ethyl ether (C4H10O) and aspirin (C9H8O4) are also empirical formulas.

Key Concepts

Molecular Formula

A molecular formula represents the actual number and type of atoms in a molecule.
It tells us exactly how many of each element are found in a compound. For instance, ethyl ether has a molecular formula of \(\mathrm{C}_4\mathrm{H}_{10}\mathrm{O}\), which shows four carbon atoms, ten hydrogen atoms, and one oxygen atom.

Unlike empirical formulas, molecular formulas can represent a multiple of the simplest ratio of elements.
Take glucose, for example, which has a molecular formula of \(\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6\). It indicates twice the ratio of the simpler empirical formula \(\mathrm{CH}_2\mathrm{O}\).
In short, molecular formulas provide us with the detailed architecture of a compound, which is crucial for understanding its chemical characteristics.

Chemical Simplification

Chemical simplification is the process of reducing a molecular formula to its simplest form, known as the empirical formula.
This involves dividing the subscripts of the elements by their greatest common divisor (GCD).

For example, the original formula for butyl dichloride \(\mathrm{C}_4\mathrm{H}_8\mathrm{O}_2\) has subscripts (4, 8, 2) with a GCD of 2.
By dividing each subscript by the GCD, we simplify it to \(\mathrm{C}_2\mathrm{H}_4\mathrm{O}\).
Whenever the GCD is 1, no further simplification is possible, and the molecular formula is already an empirical formula.
In essence, this process allows us to see the purest ratio of atoms within a chemical compound, akin to finding the simplest form of a mathematical fraction.

Greatest Common Divisor

The greatest common divisor (GCD) is a mathematical concept used to simplify molecular formulas into empirical formulas.
The GCD of a set of numbers is the largest positive integer that divides each of the numbers without a remainder.
In chemistry, the GCD helps us determine if a chemical formula can be simplified.
For example, when analyzing the formula for aspirin \(\mathrm{C}_9\mathrm{H}_8\mathrm{O}_4\), the subscripts are 9, 8, and 4.
The GCD is 1, indicating that the formula cannot be simplified further.

On the other hand, for glucose \(\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6\), the GCD is 6, which allows the formula to be reduced to \(\mathrm{CH}_2\mathrm{O}\).
Thus, finding the GCD is a key step in determining whether a molecular formula can also serve as its empirical formula.

Chemical Analysis

Chemical analysis involves the process of determining the composition of a chemical compound.
It helps in understanding the proportions of elements in any given chemical formula and detecting their empirical counterparts.
This analysis considers both qualitative and quantitative perspectives.

Qualitatively, it identifies the kinds of elements present in a compound.
Quantitatively, it assesses the actual number of atoms of each element, as depicted in a molecular formula.

• For ethyl ether, the analysis reveals that it is already in its simplest form as there is no possible simplification.
• In contrast, glucose can be reduced to show that its empirical formula is \(\mathrm{CH}_2\mathrm{O}\).

Through chemical analysis, we gain insightful information into the nature of compounds, enabling chemists to compute and predict reactions and properties effectively.