Question

Mesitylene is a liquid hydrocarbon. Burning \(0.115 \mathrm{g}\) of the compound in oxygen gives \(0.379 \mathrm{g}\) of \(\mathrm{CO}_{2}\) and \(0.1035 \mathrm{g}\) of \(\mathrm{H}_{2} \mathrm{O} .\) What is the empirical formula of mesitylene?

Short answer

The empirical formula of mesitylene is approximately \( \mathrm{C}_3\mathrm{H}_4 \).

Step-by-step solution

Determine Moles of Carbon in CO2

First, we need to find the moles of carbon in the carbon dioxide produced. Carbon dioxide's molecular weight is approximately 44.01 g/mol, and each molecule contains one mole of carbon. So, we calculate: \[ \text{Moles of } \mathrm{C} = \frac{0.379 \text{ g}}{44.01 \text{ g/mol}} = 0.00861 \text{ mol} \].

Determine Moles of Hydrogen in H2O

Next, calculate the moles of hydrogen in the water produced. Water's molecular weight is about 18.02 g/mol, and each molecule contains 2 moles of hydrogen. So, we calculate: \[ \text{Moles of } \mathrm{H} = \frac{0.1035 \text{ g}}{18.02 \text{ g/mol}} \times 2 = 0.0115 \text{ mol} \].

Calculate Moles of Oxygen

The moles of oxygen can be determined from the total reaction. First, find the combined mass of carbon and hydrogen: \[ \text{Mass of C} = 0.00861 \text{ mol} \times 12.01 \text{ g/mol} = 0.1034 \text{ g} \]\[ \text{Mass of H} = 0.0115 \text{ mol} \times 1.008 \text{ g/mol} = 0.0116 \text{ g} \]Thus, the mass of oxygen in mesitylene is:\[ \text{Mass of O} = 0.115 \text{ g} - 0.1034 \text{ g} - 0.0116 \text{ g} = 0 \text{ g} \].This means there is no oxygen in the compound.

Calculate Empirical Formula

Calculate an empirical formula based on the molar ratios. Normalize the number of moles:- Moles of C = 0.00861 mol- Moles of H = 0.0115 molThe ratio of carbon to hydrogen is:\[ \frac{0.00861}{0.00861} : \frac{0.0115}{0.00861} = 1 : 1.335 \approx 3 : 4 \].Therefore, the empirical formula is approximately \( \mathrm{C}_3\mathrm{H}_4 \).

Conclusion

The empirical formula obtained in Step 4 is based on simplified ratios of moles of carbon and hydrogen in mesitylene. The calculation suggests the empirical formula \( \mathrm{C}_3\mathrm{H}_4 \).

Key concepts

Molar Ratios

When you're given the masses of different elements within a compound, it can seem tricky to figure out the simplest proportion, or ratio, of atoms in the compound. That's where the concept of molar ratios becomes incredibly handy. Molar ratios help us translate the mass of elements into a format that shows the simplest whole-number ratio of those atoms.

To find a molar ratio, you first need to determine the number of moles of each element present in the compound. This is done using their respective atomic or molecular weights. Once you have the moles, simplifying these values to the smallest possible whole numbers will yield the molar ratios. In our example with mesitylene, after calculating the moles of carbon and hydrogen, you'll see how their ratios are simplified to reveal the empirical formula.

This process is essential for chemists to communicate the makeup of a compound in the clearest terms possible.

Combustion Analysis

Combustion analysis is a widely used method for determining the empirical formula of organic compounds. When a hydrocarbon like mesitylene burns, it reacts with oxygen, producing carbon dioxide and water. By studying the amounts of these products, we can glean vital information about the original compound's composition.

Here's how it works:

• First, accurately measure the mass of the compound that is burned.
• Then, capture and measure the masses of carbon dioxide and water produced in the combustion.

Using the masses of these combustion products, you can calculate the moles of carbon and hydrogen present in the compound.

Understanding this process allows us to deduce the proportion of the substance's elements, paving the way for calculating its empirical formula. This technique is not only crucial in academic settings but also essential in industrial applications for product analysis.

Moles Calculation

Moles calculation is a key concept in chemistry that allows us to convert a given mass of a substance into moles, which is a count of how many molecules or atoms of that substance are present. This measurement is often crucial when comparing quantities of different substances.

To find the number of moles, divide the mass of the substance by its molar mass (molecular weight). For carbon dioxide (CO2) in the mesitylene example, this is done as follows:

• Determine the molar mass of CO2, which is 44.01 g/mol.
• Calculate the moles using the given mass of CO2: \( \frac{0.379 \text{ g}}{44.01 \text{ g/mol}} \approx 0.00861 \text{ mol} \)

This simple calculation directly links the mass of a substance to its amount in moles, allowing further analysis, such as determining the empirical formula.

This foundational principle also helps convey how substances will react with one another, fundamental to everything from pharmaceuticals to understanding environmental processes.