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Chapter 3: Problem 91

A hydrocarbon mixture consists of \(60.0 \%\) by mass of \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(40.0 \%\) of \(\mathrm{C}_{x} \mathrm{H}_{y} .\) When \(10.0 \mathrm{g}\) of this mixture is burned, \(29.0 \mathrm{g} \mathrm{CO}_{2}\) and \(18.8 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) are the only products. What is the formula of the unknown hydrocarbon?

Short Answer

Expert verified
The formula of the unknown hydrocarbon is \(C_{2}H_{3}\)

Step by step solution

01

Determining the mass of each compound

From 10.0 g of the mixture, 60.0% is \(C_{3}H_{8}\) and 40.0% is the unknown hydrocarbon. So, the mass of \(C_{3}H_{8}\) = \(10.0 g * 0.6 = 6.0 g\). The mass of the unknown hydrocarbon is \(10.0 g * 0.4 = 4.0 g\).
02

Calculating the mass of carbon in CO2 and hydrogen in H2O

When burned completely, a hydrocarbon will produce CO2 and H2O. The mass of carbon in CO2 is \(44%\) and the mass of hydrogen in H2O is \(11.2%\). So, the mass of carbon from CO2 = \(29.0 g * 0.44 = 12.76 g\) and the mass of hydrogen from H2O = \(18.8 g * 0.112 = 2.1 g\).
03

Figuring out the mass of carbon and hydrogen in \(C_{3}H_{8}\)

In \(C_{3}H_{8}\), carbon accounts for \(81.8%\) and hydrogen accounts for \(18.2%\). Therefore, the mass of carbon in \(C_{3}H_{8}\) = \(6.0 g * 0.818 = 4.9 g\) and the mass of hydrogen in \(C_{3}H_{8}\) = \(6.0 g * 0.182 = 1.1 g\).
04

Identifying the mass of carbon and hydrogen in the unknown hydrocarbon

Subtract the mass of carbon and hydrogen in \(C_{3}H_{8}\) from the total mass of carbon and hydrogen found in Step 2. Hence, the unknown hydrocarbon contains \(12.76 g - 4.9 g = 7.86 g\) of carbon and \(2.1 g - 1.1 g = 1.0 g\) of hydrogen.
05

Calculating the amount in moles

Find the number of moles of carbon and hydrogen in the unknown hydrocarbon by dividing the mass by the atomic weight. This results in \(7.86 g / 12.01 g/mol = 0.654\) mol of carbon and \(1.0 g / 1.01 g/mol = 0.990\) mol of hydrogen.
06

Determining the formula of the unknown hydrocarbon

Find the ratio between the number of moles of carbon and hydrogen, which is approximately 1:1.5. The number of carbon and hydrogen atoms must be simple whole numbers, therefore, multiply both by 2 to get 2:3. So, the formula of the unknown hydrocarbon is \(C_{2}H_{3}\)

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Most popular questions from this chapter

Hydrogen and oxygen usually have oxidation states of +1 and \(-2,\) respectively, in their compounds. The following cases serve to remind us that there are exceptions. What are the oxidation states of the atoms in each of the following compounds? (a) \(\mathrm{MgH}_{2}\) (b) \(\mathrm{CsO}_{3} ;\) (c) HOF; (d) \(\mathrm{NaAlH}_{4}\)

A \(1.562 \mathrm{g}\) sample of the alcohol \(\mathrm{CH}_{3} \mathrm{CHOHCH}_{2} \mathrm{CH}_{3}\) is burned in an excess of oxygen. What masses of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) should be obtained?

To deposit exactly one mole of \(\mathrm{Ag}\) from an aqueous solution containing \(\mathrm{Ag}^{+}\) requires a quantity of electricity known as one faraday (F). The electrodeposition requires that each \(\mathrm{Ag}^{+}\) ion gain one electron to become an Ag atom. Use appropriate physical constants listed on the inside back cover to obtain a precise value of the Avogadro constant, \(N_{A}\).

Name these compounds: (a) \(\operatorname{SrO} ;\) (b) \(\mathrm{ZnS} ;\) (c) \(\mathrm{K}_{2} \mathrm{CrO}_{4}\) (d) \(\mathrm{Cs}_{2} \mathrm{SO}_{4} ;(\mathrm{e}) \mathrm{Cr}_{2} \mathrm{O}_{3} ;(\mathrm{f}) \mathrm{Fe}_{2}\left(\mathrm{SO}_{4}\right)_{3} ;(\mathrm{g}) \mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}\) (h) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4} ; \quad\) (i) \(\quad \mathrm{Ca}\left(\mathrm{HSO}_{3}\right)_{2} ; \quad(\mathrm{j}) \quad \mathrm{Cu}(\mathrm{OH})_{2}\) (k) \(\mathrm{HNO}_{3} ;\) (1) \(\mathrm{KClO}_{4} ;\) (m) \(\mathrm{HBrO}_{3} ;\) (n) \(\mathrm{H}_{3} \mathrm{PO}_{3}\).

Explain which of the following statement(s) is (are) correct concerning glucose (blood sugar), \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (a) The percentages, by mass, of \(\mathrm{C}\) and \(\mathrm{O}\) are the same as in CO. (b) The ratio of \(\mathrm{C}: \mathrm{H}: \mathrm{O}\) atoms is the same as in dihydroxyacetone, \(\left(\mathrm{CH}_{2} \mathrm{OH}\right)_{2} \mathrm{CO}\) (c) The proportions, by mass, of \(C\) and \(O\) are equal. (d) The highest percentage, by mass, is that of H.
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