Percent Composition and Empirical Formula in General Chemistry

Percent Composition and Empirical Formula

Introduction

This section covers the concept of percent composition and empirical formulas, which are fundamental topics in General Chemistry. Understanding these concepts allows students to determine the simplest ratio of elements in a compound and relate experimental data to chemical formulas.

Empirical Formula

The empirical formula of a compound represents the simplest whole number ratio of the elements present. It is derived from experimental data and may differ from the molecular formula, which shows the actual number of atoms in a molecule.

• Definition: The simplest whole number ratio of elements in a compound.

• Example:

  • Molecular formula of glucose: $C_6H_{12}O_6$ (true formula, how it appears in nature)

  • Empirical formula of glucose: $CH_2O$

Percent Composition

Percent composition refers to the percentage by mass of each element in a compound. It is used to determine the empirical formula from experimental data.

• Calculation:

  • Assume 100 g of the compound for ease of calculation.

  • Calculate the mass of each element present.

  • Convert mass to moles using the molar mass ($n = \frac{m}{M}$).

  • Divide each mole value by the smallest number of moles to get the simplest ratio.

  • If necessary, multiply to obtain whole numbers.

Example Calculation: Na2S2O3

Given percent composition data for sodium thiosulfate:

• Na: 29.08%

• S: 40.58%

• O: 30.34%

Assume 100 g sample:

• Na: 29.08 g

• S: 40.58 g

• O: 30.34 g

Convert to moles:

• Na: $n = \frac{29.08}{22.99} = 1.266$

• S: $n = \frac{40.58}{32.07} = 1.266$

• O: $n = \frac{30.34}{16.00} = 1.896$

Divide by the smallest value (1.266):

• Na: $\frac{1.266}{1.266} = 1$ (multiplied by 2 for whole number: 2)

• S: $\frac{1.266}{1.266} = 1$ (multiplied by 2 for whole number: 2)

• O: $\frac{1.896}{1.266} = 1.5$ (multiplied by 2 for whole number: 3)

Empirical formula: Na2S2O3

Mass Spectrometer

A mass spectrometer is an instrument used to determine the composition of a compound by measuring the mass-to-charge ratio of its ions. The lightest ions reach the detector first, while the heaviest arrive last.

• Application: Used to determine percent composition and empirical formula.

• Graph: Peaks correspond to different elements (O, Na, S) in the sample.

Worked Table Example

The following table summarizes the calculation steps for determining the empirical formula from percent composition data:

Element	%	Mass (g)	Moles (n)	Divide by Smallest	Whole Number Ratio
Na	29.08	29.08	1.266	1	2
S	40.58	40.58	1.266	1	2
O	30.34	30.34	1.896	1.5	3

Key Equations

• Moles: $n = \frac{m}{M}$

• Percent composition: $\%\,\text{element} = \frac{\text{mass of element in 1 mole}}{\text{molar mass of compound}} \times 100$

Summary

• Empirical formulas provide the simplest ratio of elements in a compound.

• Percent composition data can be used to determine empirical formulas.

• Mass spectrometry is a key technique for analyzing composition.

Additional info: The notes also briefly mention the relationship between moles of H2O and its constituent elements, and the use of mass spectrometry in determining composition.