Determining the Empirical Formula of a Hydrocarbon from Combustion Data

Introduction

In organic chemistry, the empirical formula of a compound represents the simplest whole-number ratio of the elements present in the compound. This guide will walk you through the steps to determine the empirical formula of a hydrocarbon based on its combustion data. By following a systematic approach, you will be able to understand the crucial aspects of a combustion reaction and how to apply the ideal gas law to derive the empirical formula.

Understanding the Combustion Reaction

When a hydrocarbon burns completely in the presence of excess oxygen, it produces carbon dioxide (CO2) and water (H2O). The general chemical equation for a hydrocarbon (C_xH_y) burning in excess oxygen can be written as:

(C_xH_y (x frac{y}{4})O_2 rightarrow xCO_2 frac{y}{2}H_2O)

Analyzing the Volume Data

The problem provides the following volumes:

20 cm3 of hydrocarbon 60 cm3 of CO2 40 cm3 of H2O

Given that equal volumes of gases at the same temperature and pressure represent equal moles, we can infer the molar ratios directly from the volumes.

Step 1: Determine the Mole Ratios 20 cm3 of hydrocarbon → 60 cm3 of CO2 20 cm3 of hydrocarbon → 40 cm3 of H2O

This implies:

20 moles of hydrocarbon 60 moles of CO2 40 moles of H2O

Determining the Moles of Carbon and Hydrogen

Using the information that each mole of CO2 contains 1 mole of carbon, and each mole of H2O contains 2 moles of hydrogen, we can calculate the moles of carbon and hydrogen from the given amounts of CO2 and H2O.

Moles of carbon 60 moles (since each mole of CO2 contains 1 mole of carbon) Moles of hydrogen 80 moles (since each mole of H2O contains 2 moles of hydrogen)

Calculating the Carbon-to-Hydrogen Ratio

The next step is to determine the ratio of carbon to hydrogen:

Ratio of carbon to hydrogen 60 moles / 80 moles 3/4

From this ratio, we can infer the empirical formula of the hydrocarbon as:

CH4/3

However, to express the formula in simplest whole numbers, we multiply both the carbon and hydrogen coefficients by 3:

CH4 → C3H4

Conclusion

In conclusion, the empirical formula of the hydrocarbon, based on the given combustion data, is C3H4. This formula represents the simplest whole-number ratio of carbon to hydrogen in the compound. Understanding this process is crucial for chemists and students of organic chemistry, as it allows for the determination of the composition of a compound based on its combustion products.