Question

Helicenes are extended fused polyaromatic hydrocarbons that have a helical or screw-shaped structure. a. A \(0.1450-\mathrm{g}\) sample of solid helicene is combusted in air to give \(0.5063 \mathrm{~g} \mathrm{CO}_{2}\). What is the empirical formula of this helicene? b. If a \(0.0938-\mathrm{g}\) sample of this helicene is dissolved in \(12.5 \mathrm{~g}\) of solvent to give a \(0.0175 \mathrm{M}\) solution, what is the molecular formula of this helicene? c. What is the balanced reaction for the combustion of this helicene?

Short answer

The empirical formula for the helicene is C2H. The molecular formula is C34H17, and the balanced combustion reaction for this helicene is: C34H17 + 51.5 O2 ⟶ 34 CO2 + 17 H2O

Step-by-step solution

Calculate the moles of carbon in the sample

Given the mass of \(\mathrm{CO_{2}}\) produced by combustion, we can find the moles of \(\mathrm{CO_{2}}\) and thus the moles of carbon in the helicene sample. The molar mass of \(\mathrm{CO_{2}}\) is 44.01 g/mol. Moles of \(\mathrm{CO_{2}}\) = mass of \(\mathrm{CO_{2}}\)/molar mass of \(\mathrm{CO_{2}}\) Moles of \(\mathrm{CO_{2}}\) = \(0.5063 \mathrm{g} \mathrm{CO_{2}}\) / \(44.01 \mathrm{g/mol}\) = 0.01150 mol \(\mathrm{CO_{2}}\) Since there is one carbon atom per \(\mathrm{CO_{2}}\) molecule, the moles of carbon in the helicene sample is also 0.01150 mol.

Calculate the moles of hydrogen in the sample

Once the moles of carbon are known, we can find the moles of hydrogen in the helicene sample. With the mass of the helicene sample, we can find the mass of hydrogen present. The molar mass of hydrogen is 1.01 g/mol. Mass of hydrogen = mass of helicene - mass of carbon Mass of hydrogen = \(0.1450 \mathrm{g}\) - (0.01150 mol carbon × \(12.01\mathrm{g/mol}\)) = 0.00692 g hydrogen Moles of hydrogen = mass of hydrogen / molar mass of hydrogen Moles of hydrogen = 0.00692 g / 1.01 g/mol = 0.00685 mol hydrogen

Determine the empirical formula

To find the empirical formula, we will take the ratio of moles of carbon to moles of hydrogen and simplify the ratio. Ratio of carbon to hydrogen: \(\frac{0.01150 \: \mathrm{mol \: carbon}}{0.00685 \: \mathrm{mol \: hydrogen}}\) = 1.678 Since this ratio is close to 2, we can round it to the closest whole number ratio of 2:1. Therefore, the empirical formula is C2H.

Calculate the molecular formula

Now, we will use the given solution data and molar mass of the empirical formula to find the molecular formula of the helicene. Since the empirical formula is C2H, the molar mass of this formula is 25.03 g/mol (2 × 12.01 g/mol + 1 × 1.01 g/mol). We are given the concentration and mass of a solution of the helicene and solvent. First, we need to find the moles of the helicene in this solution: Moles of helicene in solution = concentration × volume Moles of helicene = \(0.0175\mathrm{M}\) × (12.5 g / 1.00 g/mL) = 0.0002187 mol helicene Now, we can find the molar mass of the molecular formula using the given mass of helicene sample, 0.0938 g: Molar mass of molecular formula = mass of helicene / moles of helicene Molar mass = 0.0938 g / 0.0002187 mol = 429 g/mol To find the molecular formula, we will divide the molar mass of the molecular formula by the molar mass of the empirical formula: \(\frac{429\mathrm{g/mol}}{25.03\mathrm{g/mol}}\) ≈ 17 Since the ratio is close to 17, we multiply the empirical formula (C2H) by 17: Molecular formula = (C2H) × 17 = C34H17

Write the balanced reaction for the combustion

Now that we know the molecular formula, we can write the balanced combustion reaction for the helicene: C34H17 + 51.5 O2 ⟶ 34 CO2 + 17 H2O This is the balanced combustion reaction for this helicene.

Key concepts

Helicenes

Helicenes are a class of organic compounds that captivate chemists with their unique helical shape. These compounds are composed of multiple aromatic rings that are fused together, resulting in a screw-like structure. This peculiar arrangement grants helicenes distinctive optical and electronic properties, making them an intriguing subject of study in fields such as materials science and photonics.

A key characteristic of helicenes is their chirality, which means that they can exist in two non-superimposable mirror-image forms, much like left and right hands. This chirality is responsible for their ability to interact with polarized light, resulting in interesting applications in optical devices.

• Enantiomers - these are the mirror-image forms of a chiral compound, like helicenes.
• Aromaticity - refers to the enhanced stability and reactivity of the conjugated ring systems in helicenes.

When analyzing a helicene's molecular structure, understanding its empirical formula provides insight into the simplest ratio of elements present, while the molecular formula reveals the total number of atoms of each element.

Combustion Reaction

A combustion reaction is a chemical process in which a substance reacts rapidly with oxygen, resulting in the release of energy in the form of heat and light. This type of reaction is crucial in various chemical processes and everyday applications, from powering engines to heating homes. In this context, the combustion of helicenes follows a typical pattern where organic compounds are converted into carbon dioxide (\(\text{CO}_2\)) and water (\(\text{H}_2\text{O}\)).

Such reactions are represented by balanced chemical equations that reflect the conservation of mass. In the case of helicenes, knowing their combustion products helps in calculating the empirical composition of the original compound. For instance, if the amount of \[\text{CO}_2\] produced is measured, this can indicate the amount of carbon present in the original helicene sample.

• Oxidation - the process where a substance loses electrons, typically involving the gain of oxygen during combustion.
• Exothermic Reaction - a reaction that releases heat, as seen in the combustion process.

Understanding and balancing these reactions provide critical insights into the chemical makeup and potential energy output of substances like helicenes.

Molecular Formula

Determining a molecular formula is a fundamental step in understanding the exact chemical identity of a compound. It specifies the precise number and types of atoms within a molecule, as opposed to the empirical formula, which only provides the simplest integer ratio of the elements. In the exercise, the molecular formula of helicenes can be calculated using information from both the empirical formula and additional experimental data regarding the substance's behavior in a solution.

For helicenes, after determining the empirical formula to be \[\text{C}_2\text{H}\], the molecular weight is then calculated based on the observed properties of the compound in solution. This enables the calculation of the actual number of each type of atom present in the molecule.

• Molar Mass - important for determining how much of a solute can be dissolved in a given amount of solvent.
• Solution Concentration - used as a tool to infer the molecular formula through molarity and given sample masses.

Through the relationship between the molar mass of the empirical formula and the target molecular formula, in this case, \[\text{C}_{34}\text{H}_{17}\], researchers can establish a more comprehensive understanding of the chemical nature and properties of helicenes.