Question

One of the compounds in cement has the following composition: \(52.66 \% \mathrm{Ca}, 12.30 \% \mathrm{Si}\), and \(35.04 \% \mathrm{O}\). What is its empirical formula?

Short answer

The empirical formula of the compound is Ca₃SiO₅.

Step-by-step solution

Convert the percentages to moles

In order to find the empirical formula, we must first convert the percentage composition into moles. To do this, we should assume that we have 100g of the compound (since the percentage composition totals to 100%), which means that the percentage of each element can be read as its mass in grams. Let's calculate the amount of moles for each element:- For Ca: \( \frac{{52.66 g}}{{40.08 g/mol}} = 1.31 mol \) - For Si: \( \frac{{12.30 g}}{{28.09 g/mol}} = 0.44 mol \) - For O: \( \frac{{35.04 g}}{{16.00 g/mol}} = 2.19 mol \)

Find the ratio of mole quantities

Next, each of these mole quantities are divided by the smallest mole quantity (in this case 0.44) to get the ratio of moles of each element:- For Ca: \( \frac{{1.31 mol}}{{0.44 mol}} = 3 \)- For Si: \( \frac{{0.44 mol}}{{0.44 mol}} = 1 \)- For O: \( \frac{{2.19 mol}}{{0.44 mol}} = 5 \)

Write the empirical formula

The empirical formula is written by taking the elemental symbols and writing the subscripts using the ratio found in Step 2. Therefore, the empirical formula of our compound is Ca₃SiO₅.

Key concepts

Percentage Composition and Its Role in Chemistry

Understanding percentage composition is fundamental to determining the empirical formula of a compound. This concept involves expressing the relative amount of each element in a compound as a percentage of the total mass. To make this clearer, imagine we have a compound made of several elements. Each element contributes a certain mass to the compound, and percentage composition helps us determine what fraction of the total mass each element represents.

In the example provided, the compound is made up of calcium (Ca), silicon (Si), and oxygen (O), with respective percentage compositions of 52.66%, 12.30%, and 35.04%. This means, for instance, that calcium makes up 52.66% of the compound's mass.

• Assume 100 grams of the compound to make calculations straightforward.
• This assumption allows the percentages to directly translate into grams, such as 52.66g of Ca.

After calculating the mass in grams, you can move forward to the next step: converting these masses into moles, based on the molar mass of each element.

Mole Conversion and Its Importance

Mole conversion is an essential part of chemistry that allows us to move from the macroscopic world of grams to the atomic world of moles. The mole is a central concept that makes it possible to quantify atoms, molecules, and ions in a way that lines up with their enormous numbers and tiny sizes.

To find the empirical formula, we need to convert the mass of each element (expressed from the percentage composition) into moles. This is achieved using the molar mass of each element. For example, calcium has a molar mass of 40.08 g/mol, silicon is 28.09 g/mol, and oxygen is 16.00 g/mol.

• To calculate moles, divide the mass of each element by its molar mass.
• This conversion provides the number of moles for each element: 1.31 mol for Ca, 0.44 mol for Si, and 2.19 mol for O.

This information sets the stage for mole ratio calculations, crucial for deriving the simplest ratio between the different elements in a compound.

Chemical Compounds and the Empire of Empirical Formulas

Chemical compounds are substances composed of two or more elements chemically bonded together. Understanding how to express the composition of these compounds is key in chemistry. One way to do this is through empirical formulas, which provide the simplest whole-number ratio of atoms in a compound.

After converting mass to moles and determining relative mole amounts, the task is to find the simplest ratio of moles of each element in the compound. In our example, this involves comparing each mole quantity to the smallest mole number in the set—here, 0.44 mol for Si.

• Divide the moles of each element by the smallest number of moles from any element.
• This gives a simplified mole ratio: 3 for Ca, 1 for Si, and 5 for O.

These ratios become the subscripts in the empirical formula, providing an empirical representation of the compound: Ca₃SiO₅. This formula reveals not just the composition but also the proportions of each element, making it an invaluable tool in chemistry for identifying and studying substances.