Question

Trichloroethylene (TCE) is a common solvent used to degrease machine parts. Calculate the empirical formula for TCE if the percent composition is \(18.25 \% \mathrm{C}, 0.77 \% \mathrm{H},\) and \(80.99 \% \mathrm{Cl}\)

Short answer

The empirical formula for TCE is \( \text{C}_2\text{HCl}_3 \).

Step-by-step solution

Convert Percentages to Grams

Assume you have a 100 g sample of TCE. This assumption makes the conversion straightforward because the percentage directly equals grams. Therefore, we have 18.25 g of carbon (C), 0.77 g of hydrogen (H), and 80.99 g of chlorine (Cl).

Convert Grams to Moles

Calculate the moles of each element using their respective molar masses: - Carbon (C): Molar mass = 12.01 g/mol. Moles of C: \( \frac{18.25 \text{ g}}{12.01 \text{ g/mol}} = 1.52 \text{ mol} \).- Hydrogen (H): Molar mass = 1.008 g/mol. Moles of H: \( \frac{0.77 \text{ g}}{1.008 \text{ g/mol}} = 0.76 \text{ mol} \).- Chlorine (Cl): Molar mass = 35.45 g/mol. Moles of Cl: \( \frac{80.99 \text{ g}}{35.45 \text{ g/mol}} = 2.29 \text{ mol} \).

Determine the Simplest Ratio

Find the element with the smallest number of moles, which is hydrogen, at 0.76 mol. Divide all moles by this smallest value to find the simplest whole number ratio.- Carbon: \( \frac{1.52}{0.76} = 2 \)- Hydrogen: \( \frac{0.76}{0.76} = 1 \)- Chlorine: \( \frac{2.29}{0.76} = 3.01 \). Since 3.01 is approximately 3, we adopt 3 as the whole number for Cl.

Write the Empirical Formula

With the mole ratios, the empirical formula is obtained by using the whole numbers: C (2), H (1), Cl (3). Therefore, the empirical formula for TCE is \( \text{C}_2\text{HCl}_3 \).

Key concepts

Empirical Formula

The empirical formula is a simple representation of the relative number of atoms of each element in a compound. It provides the smallest whole number ratio of these atoms. This formula is crucial in chemistry because it offers insight into the basic composition and structure of the substance. Whether you're dealing with a simple organic compound like trichloroethylene (TCE) or a more complex molecule, understanding how to determine the empirical formula is an essential skill. To find the empirical formula:

• The first step is to obtain the percent composition of the elements within the compound. This tells you the percentage of the total mass each element contributes.
• Next, convert these percentages to grams assuming you have a sample of 100 grams. This way, the percentage translates directly into grams, simplifying calculations.
• Convert grams to moles using the elements' molar masses. This shifts the focus from mass to the actual number of particles.
• Find the simplest whole number ratio by dividing each element's mole count by the smallest mole value among them.

With this information, you create a formula that represents the ratio of the elements in the compound, giving the basic but crucial information about its composition.

Percent Composition

Percent composition is crucial in understanding what proportion of each element exists within a given compound. It's essentially a percentage by mass that allows chemists to predict the properties and reactions of the compound. Here's how it works:

• Start by determining the mass of each element in the compound. This typically involves assuming you have a total mass that makes calculations simpler, usually 100 grams.
• Next, divide the mass of each element by the total molar mass of the compound, which provides the fraction of the compound mass accounted for by each element.
• Multiply this fraction by 100 to convert it to a percentage. This final value is the percent composition of the element in the compound.

The percent composition then acts as a recipe for constructing the compound and is the first step in calculating molecular or empirical formulas. Knowing the exact percentage can pinpoint how much of each element you have, bringing you one step closer to understanding the nature and behavior of the compound.

Moles Calculation

Moles calculation is a fundamental technique in chemistry, allowing for the quantification of chemical entities. It is rooted in the concept of the mole, which is a standardized number (Avogadro's number) that denotes the quantity of atoms, ions, or molecules. Here's how moles calculation is typically performed:

• To convert a substance's mass to moles, you divide the mass of the substance by its molar mass (mass of one mole of the compound). This step is crucial for stoichiometric calculations in chemical reactions.
• The molar mass can usually be found on the periodic table, where it is listed as the atomic mass of each element.
• For compounds, calculate the total molar mass by summing up the molar masses of its constituent elements, based on their proportions in the formula.

These calculations help in determining chemical properties and reactions, as the number of moles directly correlates to the number of particles. This process is foundational, ensuring precise calculations in any chemical context.