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Helicenes are extended fused polyaromatic hydrocarbons that have a helical or screw-shaped structure. a. A \(0.1450-\) 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 -g sample of this helicene is dissolved in 12.5 g of solvent to give a 0.0175 M solution, what is the molecular formula of this helicene? c. What is the balanced reaction for the combustion of this helicene?

Short Answer

Expert verified
The empirical formula of the helicene is C鈧侶. The molecular formula of this helicene is C鈧冣倓H鈧佲倗. The balanced reaction for the combustion of this helicene is 4C鈧冣倓H鈧佲倗 (s) + 153O鈧 (g) 鈫 136CO鈧 (g) + 34H鈧侽 (g).

Step by step solution

01

Part a: Finding the empirical formula of helicene

In order to find the empirical formula of helicene, we need to determine the ratio of carbon to hydrogen in the compound. To do this, we will first find the amount of carbon present in the sample by analyzing the mass of CO鈧 produced. 1. Determine the amount of C in the CO鈧 produced: Given mass of CO鈧 = 0.5063 g molar mass of CO鈧 = 12.01 g/mol (C) + 2 * 16.00 g/mol (O) = 44.01 g/mol moles of CO鈧 = mass of CO鈧 / molar mass of CO鈧 = 0.5063 g / 44.01 g/mol = 0.0115 mol Since one mole of CO鈧 contains one mole of carbon, moles of C in the sample = 0.0115 mol. 2. Calculate the mass of H in the sample: Since the only elements present in helicenes are carbon and hydrogen, the mass of hydrogen can be found by subtracting the mass of carbon present in the sample from the total mass of the helicene. mass of C present = moles of C * molar mass of C = 0.0115 mol * 12.01 g/mol = 0.138 g mass of helicene sample = 0.1450 g mass of H present = mass of helicene sample - mass of C present = 0.1450 g - 0.138 g = 0.0070 g 3. Calculate the moles of H in the sample: molar mass of H = 1.008 g/mol moles of H = mass of H / molar mass of H = 0.0070 g / 1.008 g/mol = 0.00695 mol 4. Determine the empirical formula of the helicene: To find the lowest whole number ratio of C to H, divide the moles of both elements by the smallest number of moles. C: 0.0115 mol / 0.00695 mol = 1.65 鈮 2 H: 0.00695 mol / 0.00695 mol = 1 The empirical formula of the helicene is C鈧侶.
02

Part b: Finding the molecular formula of helicene

We are given a concentration and the mass of helicene dissolved in solvent. We can find the molecular formula by finding the molar mass and dividing it by the molar mass of the empirical formula. 1. Find the moles of helicene in the solution: We are given that the solution is 0.0175 M. To find the moles of helicene in the solution, we can use the formula: moles = Molarity * Volume The volume can be found from the mass of the solvent and the mass of helicene in the solution. mass of solvent = 12.5 g mass of helicene in solution = 0.0938 g We can assume the density of the solution is 1 g/mL. Therefore, the total mass = total volume Total volume = 12.5 g + 0.0938 g = 12.5938 g 鈮 12.59 mL Now, we can find the moles of helicene: moles = 0.0175 mol/L * 0.01259 L = 0.0002204 mol 2. Calculate the molar mass of helicene: molar mass = mass / moles = 0.0938 g / 0.0002204 mol = 425.909 g/mol 3. Find the ratio between the molar mass of helicene and the molar mass of the empirical formula: molar mass of empirical formula (C鈧侶) = (2 * 12.01 g/mol) + 1.008 g/mol = 25.028 g/mol ratio = molar mass of helicene / molar mass of empirical formula = 425.909 g/mol / 25.028 g/mol = 17 4. Determine the molecular formula of helicene: Since the ratio is 17, we can multiply the empirical formula by 17 to obtain the molecular formula of helicene. Molecular formula = (C鈧侶) * 17 = C鈧冣倓H鈧佲倗 The molecular formula of this helicene is C鈧冣倓H鈧佲倗.
03

Part c: Balancing the combustion reaction of helicene

Now we are going to write the balanced reaction for the combustion of this helicene. The general combustion reaction of a hydrocarbon can be represented as: Hydrocarbon + O鈧 (g) 鈫 CO鈧 (g) + H鈧侽 (g) For this helicene, our reaction will be: C鈧冣倓H鈧佲倗 (s) + O鈧 (g) 鈫 CO鈧 (g) + H鈧侽 (g) We can balance the above reaction by making sure that the number of each element is the same on both sides of the equation. 1. Balance the carbon atoms: There are 34 carbon atoms in C鈧冣倓H鈧佲倗, so we'll need 34 moles of CO鈧 on the product side: C鈧冣倓H鈧佲倗 (s) + O鈧 (g) 鈫 34CO鈧 (g) + H鈧侽 (g) 2. Balance the hydrogen atoms: There are 17 hydrogen atoms in C鈧冣倓H鈧佲倗, so we'll need 8.5 moles of H鈧侽 on the product side: C鈧冣倓H鈧佲倗 (s) + O鈧 (g) 鈫 34CO鈧 (g) + 8.5H鈧侽 (g) Since we can't have fractional coefficients in a balanced equation, we can multiply the whole equation by 2 to make it a whole number. So, the equation becomes: 2C鈧冣倓H鈧佲倗 (s) + O鈧 (g) 鈫 68CO鈧 (g) + 17H鈧侽 (g) 3. Balance the oxygen atoms: On the product side, we have 68 * 2 (from CO鈧) + 17 (from H鈧侽) = 153 oxygen atoms. Therefore, we'll need 76.5 moles of O鈧 on the reactant side to balance the oxygen atoms. But again, we can't have fractional coefficients, so multiplying the entire reaction by 2 again: 4C鈧冣倓H鈧佲倗 (s) + 153O鈧 (g) 鈫 136CO鈧 (g) + 34H鈧侽 (g) Now, the combustion reaction of this helicene is balanced. The balanced reaction for the combustion of this helicene is: 4C鈧冣倓H鈧佲倗 (s) + 153O鈧 (g) 鈫 136CO鈧 (g) + 34H鈧侽 (g)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Molecular Formula
When dealing with chemical compounds, it's key to know their molecular formula. This formula specifies the exact number of each type of atom within a molecule. It represents the actual arrangement of atoms, giving insight into the molecule's composition and properties. In our helicene example, we initially found the empirical formula, which gives the simplest ratio of elements. However, the molecular formula is often a multiple of the empirical formula.

In the step-by-step solution, we calculated the molar mass of helicene and compared it to the molar mass of the empirical formula (C鈧侶). By finding the ratio of these masses, we could determine the molecular formula of helicene as C鈧冣倓H鈧佲倗. This tells us that in each helicene molecule, there are 34 carbon atoms and 17 hydrogen atoms.

Understanding the difference between empirical and molecular formulas is crucial as it provides insight into the detailed chemical nature of compounds. Once the molecular mass is known, the formula can be expanded to reflect the true nature and size of the compound.
Combustion Reaction
A combustion reaction occurs when a substance reacts with oxygen, producing heat and light. It is commonly associated with hydrocarbons like helicene burning in oxygen to form carbon dioxide and water. The standard format for such a reaction is:

Hydrocarbon + O鈧 鈫 CO鈧 + H鈧侽

In this process, hydrocarbons are broken down, releasing energy. The detailed reaction for helicene in air shows its complete conversion, along with helium, into carbon dioxide and water.

Understanding combustion is essential for many real-world applications, such as energy production, automotive engines, and even when using a simple candle. These reactions are exothermic, meaning they release energy, primarily in the form of heat, making them a vital component of energy systems. Being familiar with combustion reactions aids in optimizing and controlling these energy-releasing processes.
Balancing Chemical Equations
Balancing chemical equations ensures that all atoms present in the reactants are accounted for in the products, adhering to the Law of Conservation of Mass. Every chemical reaction must be balanced; otherwise, it would imply that matter can be created or destroyed.

In the step-by-step solution, the combustion reaction of the helicene molecule shows the importance of balancing. Initially, we accurately counted the carbon and hydrogen atoms from helicene and balanced them in the products as CO鈧 and H鈧侽. The oxygen was then adjusted to make sure both sides had equal atoms.

The final balanced equation is crucial because it tells us the ratios of all the reactants and products involved. Balancing these equations is not just a mathematical exercise; it reflects real-world chemical reactions where precise reactant amounts yield expected product amounts. This is foundational for both theoretical chemistry and practical applications, like predicting amounts of emissions from fuel burning.
Hydrocarbons
Hydrocarbons are organic compounds composed entirely of hydrogen and carbon atoms. They form the basis of a vast number of organic chemistry compounds and are central to the study of chemical reactions like combustion. Hydrocarbons vary greatly, from simple forms like methane (CH鈧) to complex types such as helicene.

In our exercise, helicene is described as a polyaromatic hydrocarbon with a unique helical structure. Such hydrocarbons have linked aromatic rings, and their extensive use ranges from dyes to materials science.

Hydrocarbons are categorized into various classes based on the type of bonds present:
  • **Alkanes** 鈥 Saturated hydrocarbons with single bonds.
  • **Alkenes** 鈥 Unsaturated hydrocarbons with at least one double bond.
  • **Alkynes** 鈥 Unsaturated hydrocarbons with at least one triple bond.
  • **Aromatic hydrocarbons** 鈥 Contain stable ring structures, often with alternating single and double bonds.
Knowing about these different classes helps predict the properties and reactions of hydrocarbons. They are pivotal in the fields of energy (like gasoline), polymers (such as plastics), and many others in our daily lives.

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