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Chapter 4: Problem 84

How many grams of \(\mathrm{CO}_{2}\) are produced in the complete combustion of \(406 \mathrm{g}\) of a bottled gas that consists of \(72.7 \%\) propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) and \(27.3 \%\) butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\) by mass?

Short Answer

Expert verified
The total amount of \(\mathrm{CO}_{2}\) produced from the combustion reaction of the bottled gas is 1184.33 g.

Step by step solution

01

Determine the amount of propane and butane

First, calculate the amount of propane (\(\mathrm{C}_{3}\mathrm{H}_{8}\)) and butane (\(\mathrm{C}_{4}\mathrm{H}_{10}\)) in grams in the bottled gas using their given percentages respectively. This will give \(406g \times 0.727\) for propane and \(406g \times 0.273\) for butane.
02

Write down the balanced combustion reaction

The balanced chemical equations for the combustion of propane and butane are \(\mathrm{C}_{3}\mathrm{H}_{8}+5\mathrm{O}_{2} \rightarrow 3\mathrm{CO}_{2}+4\mathrm{H}_{2}\mathrm{O}\) and \(\mathrm{C}_{4}\mathrm{H}_{10}+6.5\mathrm{O}_{2} \rightarrow 4\mathrm{CO}_{2}+5\mathrm{H}_{2}\mathrm{O}\) respectively. Notice that in both equations, number of carbon dioxide molecules produced is equal to the number of carbon atoms in the reactant hydrocarbon molecule.
03

Calculate the amount of CO2 produced

For propane, which has 3 carbon atoms in a molecule, this means we will get 3 moles of \(\mathrm{CO}_{2}\) from 1 mole of \(\mathrm{C}_{3}\mathrm{H}_{8}\), and for butane with 4 carbon atoms in a molecule, we will get 4 moles of \(\mathrm{CO}_{2}\) from 1 mole of \(\mathrm{C}_{4}\mathrm{H}_{10}\). To get moles from grams, use the molecular weights (44.1 g/mol for \(\mathrm{CO}_{2}\), 44.1 g/mol for \(\mathrm{C}_{3}\mathrm{H}_{8}\), and 58.12 g/mol for \(\mathrm{C}_{4}\mathrm{H}_{10}\)). Multiply the moles of each hydrocarbon by the corresponding conversion factor to \(\mathrm{CO}_{2}\) moles. Then, convert back to grams using the molecular weight of \(\mathrm{CO}_{2}\).
04

Add up the two amounts

Finally add the amounts for \(\mathrm{CO}_{2}\) produced from both propane and butane to get the total amount of \(\mathrm{CO}_{2}\) produced.

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Most popular questions from this chapter

A 0.3126 g sample of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) requires 26.21 mL of a particular concentration of \(\mathrm{NaOH}(\mathrm{aq})\) to complete the following reaction. What is the molarity of the \(\mathrm{NaOH}(\mathrm{aq}) ?\) \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{s})+2 \mathrm{NaOH}(\mathrm{aq}) \longrightarrow\) $$ \mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) $$

Titanium tetrachloride, \(\mathrm{TiCl}_{4}\) is prepared by the reaction below. $$\begin{aligned} &3 \mathrm{TiO}_{2}(\mathrm{s})+4 \mathrm{C}(\mathrm{s})+6 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow 3 \mathrm{TiCl}_{4}(\mathrm{g})+2 \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{CO}(\mathrm{g}) \end{aligned}$$ What is the maximum mass of \(\mathrm{TiCl}_{4}\) that can be obtained from \(35 \mathrm{g} \mathrm{TiO}_{2^{\prime}} 45 \mathrm{g} \mathrm{Cl}_{2^{\prime}}\) and \(11 \mathrm{g} \mathrm{C} ?\)

How many grams of commercial acetic acid (97\% \(\mathrm{CH}_{3} \mathrm{COOH}\) by mass) must be allowed to react with an excess of \(\mathrm{PCl}_{3}\) to produce \(75 \mathrm{g}\) of acetyl chloride \(\left(\mathrm{CH}_{3} \mathrm{COCl}\right),\) if the reaction has a \(78.2 \%\) yield? $$\begin{aligned} \mathrm{CH}_{3} \mathrm{COOH}+\mathrm{PCl}_{3} & \longrightarrow \mathrm{CH}_{3} \mathrm{COCl}+ \mathrm{H}_{3} \mathrm{PO}_{3}(\text { not balanced }) \end{aligned}$$

An organic liquid is either methyl alcohol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\) ethyl alcohol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right),\) or a mixture of the two. A 0.220-g sample of the liquid is burned in an excess of \(\mathrm{O}_{2}(\mathrm{g})\) and yields \(0.352 \mathrm{g} \mathrm{CO}_{2}(\mathrm{g}) .\) Is the liquid a pure alcohol or a mixture of the two?

The reaction of calcium hydride and water produces calcium hydroxide and hydrogen as products. How many moles of \(\mathrm{H}_{2}(\mathrm{g})\) will be formed in the reaction between \(0.82 \mathrm{mol} \mathrm{CaH}_{2}(\mathrm{s})\) and \(1.54 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) ?\)
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