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Chapter 3: Problem 49

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 \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2} ?\)

Short Answer

Expert verified
The molecular formula for caffeine is \(C_{8}H_{10}N_{4}O_{2}\)

Step by step solution

01

Find the molar mass for each element of the first formula

For the first formula \(C_{4}H_{5}N_{2}O\), we can calculate the molar mass as follow: 4 * mass of Carbon (C) + 5 * mass of Hydrogen (H) + 2 * mass of Nitrogen (N) + 1 * mass of Oxygen (O) = 4 * 12.01g/mol + 5 * 1.01g/mol + 2 * 14.01g/mol + 1 * 16.00g/mol = 48.04g/mol + 5.05g/mol + 28.02g/mol + 16.00g/mol = 97.11 g/mol.
02

Find the molar mass for each element of the second formula

For the second formula \(C_{8}H_{10}N_{4}O_{2}\), we can calculate the molar mass as follow: 8 * mass of Carbon (C) + 10 * mass of Hydrogen (H) + 4 * mass of Nitrogen (N) + 2 * mass of Oxygen (O) = 8 * 12.01g/mol + 10 * 1.01g/mol + 4 * 14.01g/mol + 2 * 16.00g/mol = 96.08g/mol + 10.1g/mol + 56.04g/mol + 32.00g/mol = 194.22 g/mol.
03

Compare to the Given Molar Mass

Comparing the computed molar masses of the given formulas to the given molar mass of caffeine \(194.19 g/mol\), we see that the molar mass of the second formula \(C_{8}H_{10}N_{4}O_{2}\) closely matches the given molar mass.

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Most popular questions from this chapter

Carbon dioxide \(\left(\mathrm{CO}_{2}\right)\) is the gas that is mainly responsible for global warming (the greenhouse effect). The burning of fossil fuels is a major cause of the increased concentration of \(\mathrm{CO}_{2}\) in the atmosphere. Carbon dioxide is also the end product of metabolism (see Example 3.13 ). Using glucose as an example of food, calculate the annual human production of \(\mathrm{CO}_{2}\) in grams, assuming that each person consumes \(5.0 \times 10^{2} \mathrm{~g}\) of glucose per day. The world's population is 7.2 billion, and there are 365 days in a year.

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 \(=0.789 \mathrm{~g} / \mathrm{mL} .)\)

How many moles of \(\mathrm{O}\) are needed to combine with 0.212 mole of \(\mathrm{C}\) to form (a) \(\mathrm{CO}\) and (b) \(\mathrm{CO}_{2}\) ?

Nitric oxide (NO) reacts with oxygen gas to form nitrogen dioxide \(\left(\mathrm{NO}_{2}\right)\), a dark-brown gas: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$ In one experiment 0.886 mole of NO is mixed with 0.503 mole of \(\mathrm{O}_{2}\). Calculate which of the two reactants is the limiting reactant. Calculate also the number of moles of \(\mathrm{NO}_{2}\) produced.

When baking soda (sodium bicarbonate or sodium hydrogen carbonate, \(\mathrm{NaHCO}_{3}\) ) is heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, donuts, and bread. (a) Write a balanced equation for the decomposition of the compound (one of the products is \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) ). (b) Calculate the mass of \(\mathrm{NaHCO}_{3}\) required to produce \(20.5 \mathrm{~g}\) of \(\mathrm{CO}_{2}\)
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