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Chapter 22: Problem 162

Consider a sample of a hydrocarbon at 0.959 atm and 298 K. Upon combusting the entire sample in oxygen, you collect a mixture of gaseous carbon dioxide and water vapor at 1.51 atm and 375 K. This mixture has a density of 1.391 g/L and occupies a volume four times as large as that of the pure hydrocarbon. Determine the molecular formula of the hydrocarbon and name it.

Short Answer

Expert verified
The molecular formula of the hydrocarbon is C₃H₈ and its name is propane.

Step by step solution

01

Determine the partial pressures of CO₂ and H₂O in the mixture.

Since the volume of the CO₂ and H₂O mixture is four times the volume of the hydrocarbon, we can calculate the pressure of the hydrocarbon before combustion by using the ideal gas law. Let's denote the initial volume of the hydrocarbon as V and the final volume of the mixture as 4V. From the ideal gas law, we have: P₁V = P₂(4V), where P₁ is the initial pressure of the hydrocarbon (0.959 atm), and P₂ is the final total pressure of the mixture (1.51 atm). Solving for P₂, we get: P₂ = 4 × 0.959 = 3.836 atm Now, the final pressure of the CO₂ and H₂O mixture (1.51 atm) is the sum of their partial pressures, so: Partial pressure of CO₂ + Partial pressure of H₂O = 1.51 atm
02

Use the ideal gas law to determine the moles of CO₂ and H₂O, and from that, the empirical formula of the hydrocarbon.

We are given the density of the collected gas mixture (1.391 g/L). We can calculate the mass (m) of the gaseous mixture using the density formula and volume of the mixture as: Mass (m) = Density × Volume = 1.391 g/L * 4V Now we can use the mass and the molecular weights of CO₂ and H₂O to determine the moles of CO₂ and H₂O in the mixture: nCO₂ = mCO₂ / MCO₂ nH₂O = mH₂O / MH₂O where nCO₂ and nH₂O are the moles of CO₂ and H₂O, mCO₂ and mH₂O are their respective masses, and MCO₂ and MH₂O are their molecular weights (44.01 g/mol and 18.02 g/mol, respectively). To find the moles of carbon (C) and hydrogen (H) in the hydrocarbon, we can use the ratio of moles of CO₂ and H₂O to moles of C and H: nC = nCO₂ nH = 2 * nH₂O
03

Determine the molecular formula from the empirical formula.

Using the moles of C and H, we can represent the empirical formula of the hydrocarbon as CxHy. Dividing both sides by the smallest value (either x or y), we will find the simplest whole number ratio of x and y to obtain the molecular formula. Now, we can name the hydrocarbon using the IUPAC system, considering its carbon and hydrogen atoms in the molecular formula.

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Most popular questions from this chapter

Alcohols are very useful starting materials for the production of many different compounds. The following conversions, starting with 1-butanol, can be carried out in two or more steps. Show the steps (reactants/catalysts) you would follow to carry out the conversions, drawing the formula for the organic product in each step. For each step, a major product must be produced. (See Exercise \(68 . )\) (Hint: In the presence of \(\mathrm{H}^{+},\) an alcohol is converted into an alkene and water. This is the exact reverse of the reaction of adding water to an alkene to form an alcohol.) $$ \begin{array}{l}{\text { a. } 1 \text { -butanol } \longrightarrow \text { butane }} \\ {\text { b. } 1 \text { -butanol } \longrightarrow 2 \text { -butanone }}\end{array} $$

For each of the following, fill in the blank with the correct response. All of these fill-in-the-blank problems pertain to material covered in the sections on alkanes, alkenes and alkynes, aromatic hydrocarbons, and hydrocarbon derivatives. a. The first “organic” compound to be synthesized in the laboratory, rather than being isolated from nature, was , which was prepared from . b. An organic compound whose carbon–carbon bonds are all single bonds is said to be . c. The general orientation of the four pairs of electrons around the carbon atoms in alkanes is . d. Alkanes in which the carbon atoms form a single unbranched chain are said to be alkanes. e. Structural isomerism occurs when two molecules have the same number of each type of atom but exhibit different arrangements of the between those atoms. f. The systematic names of all saturated hydrocarbons have the ending added to a root name that indicates the number of carbon atoms in the molecule. g. For a branched hydrocarbon, the root name for the hydrocarbon comes from the number of carbon atoms in the continuous chain in the molecule. h. The positions of substituents along the hydrocarbon framework of a molecule are indicated by the of the carbon atom to which the substituents are attached. i. The major use of alkanes has been in reactions, as a source of heat and light. j. With very reactive agents, such as the halogen elements, alkanes undergo reactions, whereby a new atom replaces one or more hydrogen atoms of the alkane. k. Alkenes and alkynes are characterized by their ability to undergo rapid, complete reactions, by which other atoms attach themselves to the carbon atoms of the double or triple bond. l. Unsaturated fats may be converted to saturated fats by the process of . m. Benzene is the parent member of the group of hydrocarbons called hydrocarbons. n. An atom or group of atoms that imparts new and characteristic properties to an organic molecule is called a group. o. A alcohol is one in which there is only one hydrocarbon group attached to the carbon atom holding the hydroxyl group. p. The simplest alcohol, methanol, is prepared industrially by the hydrogenation of . q. Ethanol is commonly prepared by the of certain sugars by yeast. r. Both aldehydes and ketones contain the group, but they differ in where this group occurs along the hydrocarbon chain. s. Aldehydes and ketones can be prepared by of the corresponding alcohol. t. Organic acids, which contain the group, are typically weak acids. u. The typically sweet-smelling compounds called result from the condensation reaction of an organic acid with an .

Give an example of a hydrocarbon that, in theory, exhibits each of the following bond angles: \(60^{\circ}, 90^{\circ}, 109.5^{\circ}, 120^{\circ},\) and \(180^{\circ} .\)

When acrylic polymers are burned, toxic fumes are produced. For example, in many airplane fires, more passenger deaths have been caused by breathing toxic fumes than by the fire itself. Using polyacrylonitrile as an example, what would you expect to be one of the most toxic, gaseous combustion products created in the reaction?

The codons (words) in DNA (that specify which amino acid should be at a particular point in a protein) are three bases long. How many such three- letter words can be made from the four bases adenine, cytosine, guanine, and thymine?
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