Problem 60 - Chemistry: An Atoms-Focused Approach

Question

Chemistry of Soot A piece of glass held over a candle flame becomes coated with soot, which is the result of the incomplete combustion of candle wax. Elemental analysis of a compound extracted from a sample of soot gave the following results: \(7.74 \%\) H and \(92.26 \%\) C by mass. Calculate the empirical formula of the compound.

Step-by-Step Solution

Answer

Answer: The empirical formula of the compound is CH.

Step 1: Convert mass percentages to mass values

If we assume a 100 g sample of the compound, the mass percentages will directly convert to mass values: - 7.74% H → 7.74 g H - 92.26% C → 92.26 g C

Step 2: Convert mass values to moles

Calculate the number of moles of each element using their atomic masses (gm/mol): - Hydrogen (H) atomic mass: 1 g/mol - Carbon (C) atomic mass: 12 g/mol Number of moles of H: \(\frac{7.74\text{ g}}{1\text{ g/mol}} = 7.74 \text{ mol}\) Number of moles of C: \(\frac{92.26\text{ g}}{12\text{ g/mol}} = 7.688 \text{ mol}\)

Step 3: Calculate the mole ratio

Divide the moles of each element by the smallest value: Mole ratio of H to C: \(\frac{7.74}{7.688} : \frac{7.688}{7.688} = 1.007 : 1\)

Step 4: Round the ratio to whole numbers

Since the mole ratio is approximately 1:1, we can round it to whole numbers: Mole ratio of H to C: \(1:1\)

Step 5: Write the empirical formula

The empirical formula of the compound extracted from a sample of soot is CH.

Key Concepts

Incomplete Combustion

Incomplete combustion often occurs when there is not enough oxygen present to allow a fuel to react completely. Imagine you are burning a candle. When the wax of the candle burns, it ideally should produce carbon dioxide and water in a complete combustion process. However, in the real world, the oxygen supply is not always perfect.

In situations where oxygen is limited, like in the flame of a candle, you often end up with incomplete combustion. This results in the formation of carbon particulates, commonly known as soot, along with other by-products such as carbon monoxide and unburned hydrocarbons.

• Carbon monoxide is a poisonous gas and incomplete combustion of hydrocarbons can release it.
• Soot is a collection of carbon particles that usually appear as a black substance that can stain surfaces.

Incomplete combustion is not as efficient as complete combustion because it does not release as much energy and produces pollutants.
Understanding this concept is vital when studying empirical formulas, as seen in our example involving the soot, where only a portion of carbon is transformed into carbon dioxide.

Elemental Analysis

Elemental analysis is a process used to determine the quantity of individual elements in a chemical compound. It's a powerful tool for chemists especially when they need to determine the composition of an unknown substance.

In the case of the soot sample, elemental analysis revealed that the compound is composed of 7.74% hydrogen and 92.26% carbon by mass. These percentages give us a starting point to find out more about the compound.

• Elemental analysis begins with converting these percentages into actual mass values. Assuming a 100 g total sample makes it simple, as the percentages directly convert to grams.
• This method helps chemists determine what elements are present and in what proportions, crucial information for calculating molecular or empirical formulas.

Knowing the elemental composition allows chemists to deduce potential structures and understand the characteristics of the substance. In this example, the elemental analysis guided the determination of the empirical formula of the compound from the soot.

Mole Ratio Calculation

Mole ratio calculation is a technique used to express the proportions of elements in a compound in the simplest whole number terms. Once you have the number of moles for each element, converting these to mole ratios is a straightforward process.

Here's how you can understand the process:

• First, you'll need to calculate the moles of each element using their atomic masses. For hydrogen and carbon, for instance, you divide the mass of each by their respective atomic masses.
• Next, the smallest number of moles calculated (in this case 7.688 for carbon) acts as a divisor to simplify the ratio for all elements involved.
• This yields the mole ratio, which can be rounded to the closest whole number to define the empirical formula.

For the soot compound, the mole ratio for H to C was approximately 1:1, indicating the empirical formula CH. This simplified formula reflects the simplest integer ratio of the elements within the compound.
Understanding mole ratios is key for chemists when interpreting the empirical formulas that give insight into the simplest composition of compounds.