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Chapter 3: Problem 51

Allicin is the compound responsible for the characteristic smell of garlic. An analysis of the compound gives the following percent composition by mass: C: 44.4 percent, \(\mathrm{H}: 6.21\) percent, \(\mathrm{S}: 39.5\) percent, \(\mathrm{O}:\) 9.86 percent. Calculate its empirical formula. What is its molecular formula given that its molar mass is about \(162 \mathrm{~g}\) ?

Short Answer

Expert verified
The empirical formula of Allicin is \(C_6H_{10}S_2O\), and as per the provided molar mass, the molecular formula is the same as the empirical formula.

Step by step solution

01

Convert Percentages to Grams

Assume you have 100 g of the compound. Therefore:- Carbon (C): 44.4 g - Hydrogen (H): 6.21 g - Sulfur (S): 39.5 g - Oxygen (O): 9.86 g
02

Convert Grams to Moles

Now, convert the mass of each element to moles using their atomic masses:- For Carbon (C), \(\frac{44.4g}{12.01g/mol}\) = 3.7 moles - For Hydrogen (H), \(\frac{6.21g}{1.008g/mol}\) = 6.16 moles - For Sulfur (S), \(\frac{39.5g}{32.06g/mol}\) = 1.23 moles - For Oxygen (O), \(\frac{9.86g}{16.00g/mol}\) = 0.616 moles
03

Determine the Empirical Formula

Find the ratio of moles by dividing each by the smallest calculated moles:- For Carbon (C), \(\frac{3.7}{0.616}\) = 6 (rounded) - For Hydrogen (H), \(\frac{6.16}{0.616}\) = 10 (rounded) - For Sulfur (S), \(\frac{1.23}{0.616}\) = 2 (rounded) - For Oxygen (O), \(\frac{0.616}{0.616}\) = 1 (rounded) So, the empirical formula is \(C_6H_{10}S_2O_1\), or \(C_6H_{10}S_2O\)
04

Calculate Molecular Formula

First, calculate the molar mass of the empirical formula: \(6(12.01g) + 10(1.008g) + 2(32.06g) + 16.00g = 162g/mol\)Given the molar mass of Allicin is also about 162 g/mol, the molecular formula is same as the empirical formula, as the ratio is 1:1. Hence, the molecular formula of Allicin is \(C_6H_{10}S_2O\)

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Most popular questions from this chapter

If we know the empirical formula of a compound, what additional information do we need to determine its molecular formula?

Fermentation is a complex chemical process of wine making in which glucose is converted into ethanol and carbon dioxide: $$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+2 \mathrm{CO}_{2}$$ Starting with \(500.4 \mathrm{~g}\) of glucose, what is the maximum amount of ethanol in grams and in liters that can be obtained by this process? (Density of ethanol \(=0.789 \mathrm{~g} / \mathrm{mL} .)\)

Balance the following equations using the method outlined in Section 3.7 . (a) \(\mathrm{N}_{2} \mathrm{O}_{5} \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}+\mathrm{O}_{2}\) (b) \(\mathrm{KNO}_{3} \longrightarrow \mathrm{KNO}_{2}+\mathrm{O}_{2}\) (c) \(\mathrm{NH}_{4} \mathrm{NO}_{3} \longrightarrow \mathrm{N}_{2} \mathrm{O}+\mathrm{H}_{2} \mathrm{O}\) (d) \(\mathrm{NH}_{4} \mathrm{NO}_{2} \longrightarrow \mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}\) (e) \(\mathrm{NaHCO}_{3} \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\) (f) \(\mathrm{P}_{4} \mathrm{O}_{10}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{4}\) (g) \(\mathrm{HCl}+\mathrm{CaCO}_{3} \longrightarrow \mathrm{CaCl}_{2}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2}\) (h) \(\mathrm{Al}+\mathrm{H}_{2} \mathrm{SO}_{4} \longrightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\mathrm{H}_{2}\) (i) \(\mathrm{CO}_{2}+\mathrm{KOH} \longrightarrow \mathrm{K}_{2} \mathrm{CO}_{3}+\mathrm{H}_{2} \mathrm{O}\) (j) \(\mathrm{CH}_{4}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (k) \(\mathrm{Be}_{2} \mathrm{C}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{Be}(\mathrm{OH})_{2}+\mathrm{CH}_{4}\) (l) \(\mathrm{Cu}+\mathrm{HNO}_{3} \longrightarrow \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}+\mathrm{NO}+\mathrm{H}_{2} \mathrm{O}\) \((\mathrm{m}) \mathrm{S}+\mathrm{HNO}_{3} \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}+\mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{O}\) (n) \(\mathrm{NH}_{3}+\mathrm{CuO} \longrightarrow \mathrm{Cu}+\mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}\)

Aspirin or acetyl salicylic acid is synthesized by reacting salicylic acid with aceticanhydride:$$\mathrm{C}_{7}\mathrm{H}_{6}\mathrm{O}_{3}+\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{3} \quad \longrightarrow \mathrm{C}_{9} \mathrm{H}_{8}\mathrm{O}_{4}+\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}$$ (a) How much salicylic acid is required to produce \(0.400 \mathrm{~g}\) of aspirin (about the content in a tablet), assuming acetic anhydride is present in excess? (b) Calculate the amount of salicylic acid needed if only 74.9 percent of salicylic acid is converted to aspirin. (c) In one experiment, \(9.26 \mathrm{~g}\) of salicylic acid is reacted with \(8.54 \mathrm{~g}\) of acetic anhydride. Calculate the theoretical yield of aspirin and the percent yield if only \(10.9 \mathrm{~g}\) of aspirin is produced.

The molar mass of caffeine is \(194.19 \mathrm{~g}\). Is the molecular formula of caffeine \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{2} \mathrm{O}\) or \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} ?\)
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