Question

What are the empirical formulas of the compounds with the following compositions? (a) \(85.62 \% \mathrm{C}, 14.38 \% \mathrm{H}\) (b) \(63.15 \% \mathrm{C}, 5.30 \% \mathrm{H}, 31.55 \% \mathrm{O}\)

Short answer

The empirical formulas for compounds with the given compositions are: (a) \( CH_4 \) , (b) \( C_5H_{10}O \).

Step-by-step solution

Convert percentages to moles

The percentage composition of each element in a compound can be assumed to be out of 100g. So these percentages can be considered as grams of each element in 100g of the compound. This amount is then converted into moles using the molar mass of each element. For (a), calculate the moles of Carbon (C) and Hydrogen (H), and for (b), calculate the moles of Carbon (C), Hydrogen (H), and Oxygen (O).

Calculate the mole ratio

Divide each mole amount obtained in step 1 by the smallest amount among them to obtain the mole ratio. This mole ratio will form the subscripts in the empirical formula. For compound (a), divide the moles of C and H by the smaller amount. For compound (b), divide the moles of C, H, and O by the smallest amount among them.

Write the empirical formula

The empirical formula of the compound can be written using the mole ratio obtained in step 2. If the subscripts are not whole numbers, they may need to be multiplied by a whole number to convert them to whole numbers. For compound (a), write the empirical formula with C and H, and for compound (b), write the empirical formula with C, H, and O.

Key concepts

Percentage Composition

Understanding the percentage composition of a compound is a fundamental concept in chemistry. It indicates the relative amounts of each element present in the compound, showing how much each element contributes to the total mass. To grasp the idea effectively, imagine you have a 100g sample of a compound. The percentage composition tells you how many grams of each element are in that 100g sample.

For example, if you have a compound with 40% carbon and 60% oxygen by mass, it means that in a 100g sample, there would be 40g of carbon and 60g of oxygen. From this information, we can start to explore the compound's empirical formula, which is the simplest whole number ratio of the elements in the compound.

Molar Mass Calculation

Molar mass calculation is the process of determining the mass of one mole of a substance. The molar mass is expressed in grams per mole (g/mol) and can be found by summing the atomic masses of all the atoms in a molecule. A key tool for this task is the periodic table, where you find the atomic mass of each element.

As an example, the molar mass of water (H₂O) is calculated by adding the molar mass of two hydrogen atoms (2 x 1.008 g/mol) to the molar mass of one oxygen atom (16.00 g/mol), totaling approximately 18.02 g/mol. Knowing the molar mass allows chemists to convert between grams of a substance and the number of moles, which is crucial for finding the empirical formula.

Mole Ratio

After calculating the number of moles of each element in a compound, you'll need to determine the mole ratio to write the empirical formula. The mole ratio is the ratio of the moles of one element to the moles of another in the compound. Mole ratios are usually found by dividing the number of moles of each element by the smallest number of moles in the set.

This division normalizes the ratio and often yields a simple whole number, which is integral for determining the empirical formula. If any of the mole ratios are not whole numbers, they must be multiplied by the smallest common factor to obtain whole numbers before being used as subscripts in the empirical formula.

Chemical Composition Analysis

Chemical composition analysis involves determining the exact percentages and types of elements within a chemical compound. This analytical process begins with sample collection and proceeds through various laboratory techniques to uncover precise data about the compound's makeup. Techniques often used for such analysis include mass spectrometry, infrared spectroscopy, and X-ray fluorescence.

The final goal is to provide a detailed report of each element's quantity and ratio, which can be used to deduce the empirical formula. For student purposes, working with simplified theoretical percentages, as in the example problems, provides an ideal starting point for mastering the steps needed for practical chemical composition analysis in the lab.