Problem 60 - Chemistry Matter and Change

Question

Propane is a hydrocarbon, a compound composed only of carbon and hydrogen. It is 81.82\(\%\) carbon and 18.18\(\%\) hydrogen. What is the empirical formula?

Step-by-Step Solution

Answer

The empirical formula for propane is \( C_3H_8 \).

Step 1: Convert Percentages to Masses

Assume you have 100 grams of propane. This means you can convert the percentages directly to grams: 81.82 grams of carbon and 18.18 grams of hydrogen.

Step 2: Convert Masses to Moles

Use the molar masses of carbon (12.01 g/mol) and hydrogen (1.008 g/mol): - Moles of carbon = \( \frac{81.82 \, \text{g}}{12.01 \, \text{g/mol}} = 6.81 \, \text{mol}\) - Moles of hydrogen = \( \frac{18.18 \, \text{g}}{1.008 \, \text{g/mol}} = 18.04 \, \text{mol}\).

Step 3: Determine the Simplest Ratio

Divide each mole value by the smallest number of moles calculated in the previous step to get a ratio: - Carbon ratio: \( \frac{6.81}{6.81} = 1\) - Hydrogen ratio: \( \frac{18.04}{6.81} \approx 2.65\).

Step 4: Simplify the Ratio

The ratio should be a simple whole number ratio. Multiply the entire ratio by a factor that makes both values whole numbers. In this case, multiply by 3: - Carbon = 1 \( \times 3 = 3\)- Hydrogen = 2.65 \( \times 3 = 7.95 \approx 8\).So the empirical formula is approximately \( C_3H_8 \).

Key Concepts

Hydrocarbons

Hydrocarbons are fascinating compounds that consist solely of carbon and hydrogen atoms. They are the building blocks of various types of fuels, and are important in chemistry and industry. These substances come in different forms, such as alkanes, alkenes, and alkynes, characterized by different types of chemical bonds between the carbon atoms.
In the exercise, propane is identified as a hydrocarbon. Propane falls under the category of alkanes, which have single bonds between carbon atoms. Understanding the structure of hydrocarbons helps in analyzing and deriving their chemical formulas, which is crucial when learning about compounds in chemistry.

Mole Conversion

Mole conversion is a key skill in chemistry that allows us to relate the mass of a substance to the number of atoms or molecules present. The mole is a unit that is used to count particles at the atomic level. One mole of any substance contains Avogadro's number of entities, which is approximately 6.022 x 10²³.

• To perform mole conversions, we use the molar mass, which expresses how much one mole of a compound weighs. For carbon, it is 12.01 g/mol, and for hydrogen, it is 1.008 g/mol.
• In the exercise, we calculated the moles of carbon and hydrogen by dividing the given mass by their respective molar masses. This step converts grams to moles, allowing us to work with the simpler concept of ratios to analyze the compound's structure.

Percent Composition

Percent composition is a way of expressing how much of each element constitutes a compound in terms of percentage. This is often used to determine the empirical formula of a compound.
To find the empirical formula, we first assume a sample size, often 100 grams, which simplifies converting percentages into grams directly. In its simplest form:

• You take each element's percentage composition and convert it to grams.
• Then, convert these masses to moles using the element's molar mass.

This method provides a clear path from initial data about a compound to understanding its underlying structure.

Simplest Ratio

Finding the simplest ratio of moles of elements in a compound is crucial to determine its empirical formula. The empirical formula represents the smallest whole-number ratio of atoms in a molecule.
Once we have the number of moles of each element, we find the simplest ratio by:

• Dividing each mole value by the smallest number of moles obtained. This helps simplify the ratio of moles of different elements.
• If the resulting ratio isn't whole numbers, multiply each by a factor to achieve integers, as seen in the case of propane in the exercise.

The process of finding this simplest ratio helps in building a clearer picture of the compound's overall formula.

Chemistry Problem Solving

Chemistry problem solving often involves breaking down complex problems into basic steps that apply fundamental principles. For empirical formula determination, the main steps include converting percentage to mass, mass to moles, and then finding the simplest ratio.
Each of these steps are critical and rely on a strong understanding of basic chemical concepts, such as:

• The nature of hydrocarbons and their significance in calculations.
• Mole concept as an essential tool for translating between the macro and micro worlds.
• Utilizing percent composition to link data with chemical compositions accurately.

Mastering these problem-solving techniques equips students with the ability to tackle a wide range of chemistry challenges efficiently.