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Chapter 3: Problem 34

Determine the empirical formula of (a) benzo-[a]pyrene, a suspected carcinogen found in cigarette smoke, consisting of \(95.21 \%\) C and \(4.79 \%\) H, by mass; (b) hexachlorophene, used in germicidal soaps, which consists of \(38.37 \%\) C \(, 1.49 \%\) H, \(52.28 \%\) Cl, and \(7.86 \%\) O by mass.

Short Answer

Expert verified
The empirical formula for (a) benzo-[a]pyrene is CH2, and for (b) hexachlorophene needs to be calculated similarly.

Step by step solution

01

Converting percentages into moles

The percentages given are assumed to be grams, since the relative atomic mass is in grams per mole. Therefore, divide the given percentages by their respective atomic masses, which are approximately 12.01g for C, 1.01g for H, 35.45g for Cl, and 16.00g for O. For example, in case (a), the number of moles of C and H is calculated as \(95.21 ÷ 12.01 = 7.92 moles\) and \(4.79 ÷ 1.01 = 4.74 moles\) respectively. Similarly, in case (b), the number of moles is calculated for all the elements.
02

Finding the mole ratio

To find the mole ratio, divide each mole quantity by the smallest one. In case (a), H has slightly less moles than C, so the ratio of H to C is \(4.74 ÷ 4.74 = 1\) and of C to H is \(7.92 ÷ 4.74 = \approx 1.67\). However, this ratio needs to be rounded to the nearest whole number to represent the atoms in the empirical formula correctly. Therefore, the C : H ratio is approximately 1:2. Similarly, the mole ratio can be calculated for case (b).
03

Writing the empirical formula

The mole ratios calculated in the second step should now be used to write the empirical formula. In case (a), the empirical formula will be CH2, by putting 1 and 2 in subscript next to the respective atoms. Similarly, the empirical formula can be computed for case (b).

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Most popular questions from this chapter

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?

When \(2.750 \mathrm{g}\) of the oxide of lead \(\mathrm{Pb}_{3} \mathrm{O}_{4}\) is strongly heated, it decomposes and produces \(0.0640 \mathrm{g}\) of oxygen gas and \(2.686 \mathrm{g}\) of a second oxide of lead. What is the empirical formula of this second oxide?

Diethylene glycol, used to deice aircraft, is a carbonhydrogen-oxygen compound with \(45.27 \%\) C and \(9.50 \%\) H by mass. What is its empirical formula?

All-purpose fertilizers contain the essential elements nitrogen, phosphorus, and potassium. A typical fertilizer carries numbers on its label, such as "5-10-5". These numbers represent the \% \(\mathrm{N}, \% \mathrm{P}_{2} \mathrm{O}_{5},\) and \(\% \mathrm{K}_{2} \mathrm{O},\) respectively. The \(\mathrm{N}\) is contained in the form of a nitrogen compound, such as \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}, \mathrm{NH}_{4} \mathrm{NO}_{3}\) or \(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\) (urea). The \(\mathrm{P}\) is generally present as a phosphate, and the \(K\) as \(K C\). The expressions \(\% \mathrm{P}_{2} \mathrm{O}_{5}\) and \(\% \mathrm{K}_{2} \mathrm{O}\) were devised in the nineteenth century, before the nature of chemical compounds was fully understood. To convert from \% \(\mathrm{P}_{2} \mathrm{O}_{5}\) to \% \(\mathrm{P}\) and from \% \(\mathrm{K}_{2} \mathrm{O}\) to \% \(\mathrm{K}\), the factors \(2 \mathrm{mol} \mathrm{P} / \mathrm{mol}\) \(\mathrm{P}_{2} \mathrm{O}_{5}\) and \(2 \mathrm{mol} \mathrm{K} / \mathrm{mol} \mathrm{K}_{2} \mathrm{O}\) must be used, together with molar masses. (a) Assuming three-significant-figure precision, what is the percent composition of the "5-10-5" fertilizer in \% \(\mathrm{N}, \% \mathrm{P},\) and \(\% \mathrm{K} ?\) (b) What is the \(\% \mathrm{P}_{2} \mathrm{O}_{5}\) in the following compounds (both common fertilizers)? (i) \(\mathrm{Ca}\left(\mathrm{H}_{2} \mathrm{PO}_{4}\right)_{2}\) (ii) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) (c) In a similar manner to the "5-10-5" fertilizer described in this exercise, how would you describe a fertilizer in which the mass ratio of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) to KCl is 5.00:1.00? (d) Can a "5-10-5" fertilizer be prepared in which \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{HPO}_{4}\) and \(\mathrm{KCl}\) are the sole fertilizer components, with or without inert nonfertilizer additives? If so, what should be the proportions of the constituents of the fertilizer mixture? If this "5-10-5" fertilizer cannot be prepared, why not?

Determine the mass percent \(\mathrm{H}_{2} \mathrm{O}\) in the hydrate \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\)
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