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Chapter 3: Problem 92

A compound contains only \(\mathrm{C}, \mathrm{H}\), and \(\mathrm{N}\). Combustion of \(35.0 \mathrm{mg}\) of the compound produces \(33.5 \mathrm{mg} \mathrm{CO}_{2}\) and \(41.1 \mathrm{mg}\) \(\mathrm{H}_{2} \mathrm{O}\). What is the empirical formula of the compound?

Short Answer

Expert verified
The empirical formula of the compound containing C, H, and N is \(C_3H_7N\).

Step by step solution

01

Determine moles of carbon and hydrogen

We know that one mole of CO₂ contains one mole of carbon, and one mole of H₂O contains two moles of hydrogen. Given the mass of CO₂ and H₂O, we can find the moles of carbon and hydrogen produced after combustion. Moles of Carbon = \( \frac{mass~of~CO_2}{molar~mass~of~CO_2} \times moles~of~C~in~CO_2 \) Moles of Carbon = \( \frac{33.5~mg}{44.01~g/mol} \times 1 \) (convert mg to g: 33.5mg = 0.0335g) Moles of Hydrogen = \( \frac{mass~of~H_2O}{molar~mass~of~H_2O} \times moles~of~H~in~H_2O \) Moles of Hydrogen = \( \frac{41.1~mg}{18.02~g/mol} \times 2 \) (convert mg to g: 41.1mg = 0.0411g)
02

Determine mass of nitrogen

The compound contains only C, H, and N. We can find the mass of nitrogen by subtracting the masses of carbon and hydrogen from the total mass of the compound. Mass of Nitrogen = Total mass of compound - (Mass of Carbon + Mass of Hydrogen) Initially, find the masses of Carbon and Hydrogen: Mass of Carbon = Moles of Carbon * Molar mass of C Mass of Hydrogen = Moles of Hydrogen * Molar mass of H
03

Calculate moles of nitrogen

Now that we have the mass of nitrogen, we need to find the moles of nitrogen in the compound. Moles of Nitrogen = \( \frac{mass~of~N}{molar~mass~of~N} \)
04

Find the whole number ratio

Divide the moles of each element (C, H, and N) by the smallest value among the three and round them off to the nearest whole number.
05

Write the empirical formula

Write the empirical formula of the compound using the whole numbered ratio of the elements (C, H, and N) obtained in step 4. This will give us the empirical formula of the compound.

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Most popular questions from this chapter

Consider the following unbalanced equation: $$ \mathrm{Ca}_{3}\left(\mathrm{PO}_{4}\right)_{2}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{CaSO}_{4}(s)+\mathrm{H}_{3} \mathrm{PO}_{4}(a q) $$ What masses of calcium sulfate and phosphoric acid can be produced from the reaction of \(1.0 \mathrm{~kg}\) calcium phosphate with \(1.0 \mathrm{~kg}\) concentrated sulfuric acid \(\left(98 \% \mathrm{H}, \mathrm{SO}_{4}\right.\) by mass)?

Vitamin A has a molar mass of \(286.4 \mathrm{~g} / \mathrm{mol}\) and a general molecular formula of \(\mathrm{C}_{x} \mathrm{H}_{2} \mathrm{E}\), where \(\mathrm{E}\) is an unknown element. If vitamin \(\mathrm{A}\) is \(83.86 \% \mathrm{C}\) and \(10.56 \% \mathrm{H}\) by mass, what is the molecular formula of vitamin \(\mathrm{A}\) ?

ABS plastic is a tough, hard plastic used in applications requiring shock resistance. The polymer consists of three monomer units: acrylonitrile \(\left(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N}\right)\), butadiene \(\left(\mathrm{C}_{4} \mathrm{H}_{6}\right)\), and styrene \(\left(\mathrm{C}_{8} \mathrm{H}_{8}\right)\). a. A sample of ABS plastic contains \(8.80 \% \mathrm{~N}\) by mass. It took \(0.605 \mathrm{~g}\) of \(\mathrm{Br}_{2}\) to react completely with a \(1.20-\mathrm{g}\) sample of ABS plastic. Bromine reacts \(1: 1\) (by moles) with the butadiene molecules in the polymer and nothing else. What is the percent by mass of acrylonitrile and butadiene in this polymer? b. What are the relative numbers of each of the monomer units in this polymer?

In 1987 the first substance to act as a superconductor at a temperature above that of liquid nitrogen \((77 \mathrm{~K})\) was discovered. The approximate formula of this substance is \(\mathrm{YBa}_{2} \mathrm{Cu}_{3} \mathrm{O}_{7}\). Calculate the percent composition by mass of this material.

An iron ore sample contains \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) plus other impurities. \(\mathrm{A}\) \(752-\mathrm{g}\) sample of impure iron ore is heated with excess carbon, producing \(453 \mathrm{~g}\) of pure iron by the following reaction: $$ \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{C}(s) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}(g) $$ What is the mass percent of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in the impure iron ore sample? Assume that \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) is the only source of iron and that the reaction is \(100 \%\) efficient.
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