Question

Vanillin, the dominant flavoring in vanilla, contains C, H, and O. When \(1.05 \mathrm{~g}\) of this substance is completely combusted, \(2.43 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(0.50 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are produced. What is the empirical formula of vanillin?

Short answer

The empirical formula of vanillin is C₂HO.

Step-by-step solution

Determine the moles of carbon, hydrogen, and oxygen in the CO₂ and H₂O produced

Given the masses of CO₂ and H₂O produced, we can calculate the moles of each element present. For Carbon: Mass of CO₂ = 2.43 g Molar mass of CO₂ = 12.01 g/mol (for carbon) + 2 * 16.00 g/mol (for oxygen) = 44.01 g/mol Moles of carbon = mass of CO₂ / molar mass of CO₂ Moles of carbon = \( \frac{2.43}{44.01} \) = 0.0552 moles For Hydrogen: Mass of H₂O = 0.50 g Molar mass of H₂O = 2 * 1.01 g/mol (for hydrogen) + 16.00 g/mol (for oxygen) = 18.02 g/mol Moles of hydrogen = mass of H₂O / molar mass of H₂O Moles of hydrogen = \( \frac{0.50}{18.02} \) = 0.0278 moles

Calculate the moles of oxygen in vanillin

Given the mass of vanillin combusted, we can now subtract the masses of carbon and hydrogen from it to find the mass of oxygen in vanillin. Mass of vanillin combusted = 1.05 g Mass of carbon = moles of carbon * molar mass of carbon = 0.0552 * 12.01 = 0.662 g Mass of hydrogen = moles of hydrogen * molar mass of hydrogen = 0.0278 * 1.01 = 0.028 g Mass of oxygen in vanillin = mass of vanillin - mass of carbon - mass of hydrogen Mass of oxygen = 1.05 - 0.662 - 0.028 = 0.360 g Now we can calculate the moles of oxygen in vanillin: Molar mass of oxygen = 16.00 g/mol Moles of oxygen = mass of oxygen / molar mass of oxygen Moles of oxygen = \( \frac{0.360}{16.00} \) = 0.0225 moles

Determine the empirical formula of vanillin

To find the empirical formula, we must find the mole ratio of each element. We will divide the moles of each element by the smallest number of moles among them to get the whole number ratio. Smallest number of moles = 0.0225 (oxygen) Mole ratio of carbon: \(\frac{0.0552}{0.0225} \approx 2.46\) ≈ 2 Mole ratio of hydrogen: \(\frac{0.0278}{0.0225} \approx 1.24\) ≈ 1 Mole ratio of oxygen: \(\frac{0.0225}{0.0225} \) = 1 Thus, the empirical formula of vanillin is C₂H₁O₁, simplified as C₂HO.

Key concepts

Combustion Analysis

Combustion analysis is a widely used method in chemistry to determine the elemental composition of a substance, particularly those containing elements like carbon, hydrogen, and oxygen.
This technique involves combusting a sample in the presence of oxygen and measuring the masses of the resultant combustion products, usually carbon dioxide (\(\text{CO}_2\)) and water (\(\text{H}_2\text{O}\)). For example, in the combustion of vanillin, measuring the \(\text{CO}_2\) and \(\text{H}_2\text{O}\) allows us to deduce the amounts of carbon and hydrogen.

• The carbon present in the sample converts into \(\text{CO}_2\).
• The hydrogen converts into \(\text{H}_2\text{O}\).

To determine the oxygen content, we use the conservation of mass principle. We know the total mass of the combusted sample and can subtract the masses of carbon and hydrogen to find the mass of oxygen. This process effectively gives the amounts of each element within the original compound, making it easier to deduce its empirical formula.

Mole Ratio

The mole ratio is a crucial concept when determining the empirical formula of a compound. It reflects the ratio of the number of moles of each element within a compound to each other. After combustion analysis calculates the moles of carbon, hydrogen, and oxygen, we utilize these figures to find the ratio.

• Identify the smallest number of moles among the elements.
• Divide all moles by this smallest number to derive a simple whole number ratio for each element.

This process is key in translating elemental mole values into a meaningful empirical formula. For vanillin, let's assume we calculated the following numbers of moles:

• Carbon = 0.0552 moles
• Hydrogen = 0.0278 moles
• Oxygen = 0.0225 moles

In this case, 0.0225 is the smallest. Dividing each value by 0.0225 gives us approximately: - Carbon: 2 - Hydrogen: 1 - Oxygen: 1 These values correspond to the simplest whole-number mole ratio, and thus give us the empirical formula, C₂HO.

Chemical Composition

Chemical composition refers to the combination and proportion of different elements in a compound. Understanding it helps us predict the empirical formula, which indicates the simplest ratio of elements within a compound.
To determine a compound's chemical composition, combustion analysis provides a powerful pathway, while the mole ratio method simplifies these findings into an empirical formula. In our example of vanillin, we've delved into how carbon, hydrogen, and oxygen amounts are assessed following combustion.
The resulting ratios are simplified into an empirical formula. This formula is not just a representation of element types but reflects the relative proportions of each element in a molecule.

• Empirical formulas do not indicate actual numbers of atoms, but only the simplest integer ratio.
• The chemical composition tells us about the identity and nature of a compound's atoms.

By understanding these steps and concepts, chemists can recreate and understand the behavior and properties associated with a compound based on its composition.