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Chapter 3: Problem 90

What is the molecular formula of a hydrocarbon containing \(n\) carbon atoms and only one double bond? Can such a hydrocarbon yield a greater mass of \(\mathrm{H}_{2} \mathrm{O}\) than \(\mathrm{CO}_{2}\) when burned in an excess of oxygen?

Short Answer

Expert verified
The molecular formula of a hydrocarbon with \(n\) carbon atoms and one double bond is \(C_{n}H_{2n}\). It cannot yield a greater mass of \(H_{2}O\) compared to \(CO_{2}\) when burned in excess oxygen.

Step by step solution

01

Determine the Molecular Formula

The structure of a hydrocarbon with only one double bond is known as an alkene. The general formula for alkenes is \(C_{n}H_{2n}\). Therefore, for a hydrocarbon with \(n\) carbon atoms and one double bond, the molecular formula would be \(C_{n}H_{2n}\).
02

Write Down the Balanced Combustion Reaction

The general balanced equation for complete combustion of hydrocarbons with oxygen is \[ C_{n}H_{2n} + \frac{3n}{2} O_{2} \rightarrow nCO_{2} + nH_{2}O \] Every mole of \(C_{n}H_{2n}\) reacts with \(\frac{3n}{2}\) moles of \(O_{2}\) to produce \(n\) moles of \(CO_{2}\) and \(n\) moles of \(H_{2}O\).
03

Mass Comparison of CO2 and H2O

Now, let's apply the law of Conservation of Mass to analyze the reaction. From the balanced equation, it is clear that 1 mole of hydrocarbon yields the same number of moles of \(CO_{2}\) as \(H_{2}O\). However, the molar mass of \(H_{2}O\)(18.015 g/mol) is less than the molar mass of \(CO_{2}\)(44.01 g/mol). Therefore, the mass of \(H_{2}O\) produced is less than the mass of \(CO_{2}\) produced in the combustion reaction.

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Most popular questions from this chapter

An oxoacid with the formula \(\mathrm{H}_{x} \mathrm{E}_{y} \mathrm{O}_{z}\) has a formula mass of 178 u, has 13 atoms in its formula unit, contains \(34.80 \%\) by mass, and \(15.38 \%\) by number of atoms, of the element E. What is the element \(\mathrm{E}\), and what is the formula of this oxoacid?

In your own words, define or explain the following terms or symbols: (a) formula unit; (b) \(\mathrm{P}_{4} ;\) (c) molecular compound; (d) binary compound; (e) hydrate.

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