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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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