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Chapter 3: Problem 53

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 C8H10N4O2.

Step by step solution

01

Calculate the Molar Masses of the Formulas Given

First, calculate the molar mass of each of the suggested formulas by adding up the molar mass of each element in the formula, multiplied by the number of times it appears. Use the atomic masses for carbon (C), hydrogen (H), nitrogen (N), and oxygen (O) from the periodic table: \n\nFor C4H5N2O: Molar mass = 4*(12.01 g) + 5*(1.01 g) + 2*(14.01 g) + 1*(16.00 g) = 97.09 g \n\nFor C8H10N4O2 : Molar mass = 8*(12.01 g) + 10*(1.01 g) + 4*(14.01 g) + 2*(16.00 g) = 194.18 g
02

Compare with Given Molar Mass

Now, compare the calculated molar masses for both suggested formulas with the given molar mass for caffeine. Observe that the calculated molar mass for the formula C8H10N4O2 is nearly identical to the given molar mass, suggesting that is the correct formula.
03

Verify the integrity

Since only integer multiples are valid, and the resulting factor for C4H5N2O (2.00) is integer, we confirm that C8H10N4O2 is indeed the molecular formula of Caffeine.

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Most popular questions from this chapter

When \(0.273 \mathrm{~g}\) of \(\mathrm{Mg}\) is heated strongly in a nitrogen \(\left(\mathrm{N}_{2}\right)\) atmosphere, a chemical reaction occurs. The product of the reaction weighs 0.378 g. Calculate the empirical formula of the compound containing Mg and \(\mathrm{N}\). Name the compound.

A certain metal oxide has the formula MO, where \(\mathrm{M}\) denotes the metal. A 39.46-g sample of the compound is strongly heated in an atmosphere of hydrogen to remove oxygen as water molecules. At the end, \(31.70 \mathrm{~g}\) of the metal is left over. If \(\mathrm{O}\) has an atomic mass of 16.00 amu, calculate the atomic mass of \(\mathrm{M}\) and identify the element.

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What are the empirical formulas of the compounds with the following compositions? (a) 2.1 percent \(\mathrm{H}\), 65.3 percent \(\mathrm{O}, 32.6\) percent \(\mathrm{S}\) (b) 20.2 percent \(\mathrm{Al}\), 79.8 percent \(\mathrm{Cl}\)

Consider the combustion of carbon monoxide (CO) in oxygen gas $$ 2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g) $$ Starting with 3.60 moles of \(\mathrm{CO},\) calculate the number of moles of \(\mathrm{CO}_{2}\) produced if there is enough oxygen gas to react with all of the CO.
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