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Solved: Cinnamic alcohol is used mainly in perfumery,

Chapter 3, Problem 41P

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QUESTION:

Cinnamic alcohol is used mainly in perfumery, particularly in soaps and cosmetics. Its molecular formula is \(\mathrm{C}_{9} \mathrm{H}_{10} \mathrm{O}\).

(a) Calculate the percent composition by mass of C, H, and O in cinnamic alcohol.

(b) How many molecules of cinnamic alcohol are contained in a sample of mass 0.469 g?

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QUESTION:

Cinnamic alcohol is used mainly in perfumery, particularly in soaps and cosmetics. Its molecular formula is \(\mathrm{C}_{9} \mathrm{H}_{10} \mathrm{O}\).

(a) Calculate the percent composition by mass of C, H, and O in cinnamic alcohol.

(b) How many molecules of cinnamic alcohol are contained in a sample of mass 0.469 g?

ANSWER:

Step 1 of 2

(a) The molar mass of cinnamic alcohol  \(\mathrm{C}_{9} \mathrm{H}_{10} \mathrm{O}=134.17 \mathrm{~g}\)

The compound contains 3 elements, C, H, and O. In order to find the percent composition by mass of each element in 1 mole of the compound, use the formula.

\(\text { Percent composition of element }=\frac{n \times \text { molar mass of element }}{\text { Molar mass }} \times 100 \%\)

Let’s calculate the percentage of each element in the compound;

Percentage of carbon:     

\(\text { percentage of } C=\frac{9 \times 12.01 \mathrm{~g}}{134.17 \mathrm{~g}} \times 100 \%=80.56 \%\)

Hence, percentage of carbon in cinnamic alcohol is 80.56 %

Percentage of Hydrogen:    

\(\text { percentage of } H=\frac{10 \times 1.008 \mathrm{~g}}{134.17 \mathrm{~g}} \times 100 \%=7.513 \%\)

Hence, percentage of Hydrogen in cinnamic alcohol is 7.513 %

Percentage of oxygen:            

\(\text { percentage of } O=\frac{1 \times 16.00 \mathrm{~g}}{134.17 \mathrm{~g}} \times 100 \%=11.92 \%\)

Hence, percentage of oxygen in cinnamic alcohol is 11.92 %

Therefore, the percentage compositions of the three elements in the compound are 80.56, 7.513, and 11.92 respectively.

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