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?

Short answer

The empirical formula of propane, which is 81.82% carbon and 18.18% hydrogen, is CH₃.

Step-by-step solution

Convert percentages to grams

Assume we have 100 g of the compound. Then, the amount of carbon is 81.82 g, and the amount of hydrogen is 18.18 g.

Calculate the moles of carbon and hydrogen

Next, divide the mass of each element by its atomic mass: - Carbon: \( \frac{81.82 \text{ g}}{12.01 \text{ g/mol}} = 6.818 \text{ mol C} \) - Hydrogen: \( \frac{18.18 \text{ g}}{1.008 \text{ g/mol}} = 18.05 \text{ mol H} \)

Determine the mole ratio

Divide both values by the smallest number of moles: \( \frac{6.818 \text{ mol C}}{6.818} : \frac{18.05 \text{ mol H}}{6.818} \approx 1 : 2.65 \)

Round to the nearest whole number

Round the mole ratio to the nearest whole number: \( 1(\text{C}) : 3(\text{H}) \)

Write the empirical formula

The simplest whole number ratio is C : H = 1:3, so the empirical formula of propane is CH₃.

Key concepts

Hydrocarbon

Hydrocarbons are fascinating and fundamental organic molecules composed entirely of carbon and hydrogen atoms. They form the backbone of organic chemistry and can be found in various forms, such as gases, liquids, or solids. The simplest hydrocarbons are known as alkanes, alkenes, and alkynes, which vary based on their carbon-carbon bonds.
Propane, the subject of our exercise, is an alkane hydrocarbon with the molecular formula C₃H₈, comprising three carbon atoms and eight hydrogen atoms. Hydrocarbons are prevalent in many everyday substances, including fuels like gasoline and natural gas.

• Alkanes contain single carbon-carbon bonds and are saturated hydrocarbons.
• Alkenes contain at least one double carbon-carbon bond.
• Alkynes have at least one triple carbon-carbon bond.

Understanding hydrocarbons is essential for identifying substances like propane and determining formulas based on their elemental composition.

Mole Ratio

The mole ratio is a crucial concept in chemistry, enabling us to understand the proportions of different elements within a compound. By calculating the mole ratio, we determine how many moles of one element correspond to a certain number of moles of another. This forms the basis for deriving empirical formulas.
In the propane exercise, after computing the moles of carbon and hydrogen, we found them in a ratio of 6.818:18.05. To garner a practical ratio, we divided by the smallest number, 6.818, simplifying to approximately 1:2.65.
However, empirical formulas require whole numbers. Rounding our ratio gives 1:3, meaning for every carbon atom there are three hydrogen atoms.
The mole ratio allows us to represent the simplest form of a compound, crucial for understanding its fundamental structure.

Elemental Composition

Elemental composition describes the percentage by mass of each element in a compound. In our propane example, this is represented by 81.82% carbon and 18.18% hydrogen. From an analytical point of view, knowing the elemental composition of a substance helps us determine its empirical formula and understand its basic make-up.
This is achieved by taking these percentages and converting them to grams, assuming a sample size of 100 grams for simplicity.

• For carbon: 81.82% translates to 81.82 grams.
• For hydrogen: 18.18% translates to 18.18 grams.

Recognizing the elemental composition is fundamental as it enables chemists to unravel the detailed structure of a compound and predict its behavior in chemical reactions.

Atomic Mass

Atomic mass, typically expressed in atomic mass units (amu), is a measure of the mass of an atom. It provides a basis for calculating the number of moles from a given mass of an element. Every element in the periodic table has a unique atomic mass reflecting the mass of its atoms relative to the carbon-12 isotope.
In our exercise, the elements of carbon and hydrogen have atomic masses of 12.01 g/mol and 1.008 g/mol, respectively. By dividing the mass of each element by its atomic mass, we calculate the number of moles:

• Carbon: 81.82 g / 12.01 g/mol = 6.818 moles of carbon
• Hydrogen: 18.18 g / 1.008 g/mol = 18.05 moles of hydrogen

Understanding atomic mass is crucial for mapping out the mole ratio and, in turn, determining the empirical formula. It links the subatomic world to measurable quantities, enhancing our comprehension of chemical reactions.