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Chapter 3: Problem 147

Vitamin A has a molar mass of \(286.4 \mathrm{~g} / \mathrm{mol}\) and a general molecular formula of \(\mathrm{C}_{x} \mathrm{H}_{\mathrm{y}} \mathrm{E}\), where \(\mathrm{E}\) is an unknown element. If vitamin \(\mathrm{A}\) is \(83.86 \% \mathrm{C}\) and \(10.56 \% \mathrm{H}\) by mass, what is the molecular formula of vitamin \(\mathrm{A}\) ?

Short Answer

Expert verified
The short answer for the molecular formula of Vitamin A, given its molar mass and percentages of Carbon and Hydrogen, is \(\mathrm{C}_{20} \mathrm{H}_{30} \mathrm{O}\).

Step by step solution

01

Determine the grams of Carbon and Hydrogen

First, we will find the grams of Carbon and Hydrogen in one mole of Vitamin A. Using the given percentages, we can calculate the grams as follows: - Grams of Carbon: \(286.4 g/mol * 83.86\% = 240.12 g/mol\) - Grams of Hydrogen: \(286.4 g/mol * 10.56\% = 30.24 g/mol\)
02

Calculate the molar amount of Carbon and Hydrogen

Now, we will find the molar amounts of Carbon and Hydrogen by dividing the grams by their respective atomic masses: - Molar amount of Carbon: \(240.12 g/mol \div 12.01 g/mol = 20 mol\) - Molar amount of Hydrogen: \(30.24 g/mol \div 1.01 g/mol = 30 mol\)
03

Find the molar ratios of Carbon, Hydrogen to the unknown element (E)

As given, the molecular formula of Vitamin A is \(\mathrm{C}_{x} \mathrm{H}_{\mathrm{y}} \mathrm{E}\). We can write the following equations using the information we have gathered: - Grams of Carbon : \(12.01x\) - Grams of Hydrogen : \(1.01y\) - Grams of unknown element (E) : \(286.4 - (12.01x + 1.01y)\) We can now insert the molar amounts of Carbon and Hydrogen: - \(12.01 * 20 + 1.01 * 30 + M_E = 286.4\) Here, M_E is the molar mass of the unknown element (E) in g/mol.
04

Determine the molecular formula of Vitamin A

Solve the equation for M_E: \(M_E = 286.4 - (12.01 * 20 + 1.01 * 30) = 286.4 - (240.2 + 30.3) = 16 g/mol\) The molar mass of the unknown element (E) is 16 g/mol. This corresponds to the molar mass of Oxygen (O). Therefore, the molecular formula of Vitamin A is \(\mathrm{C}_{20} \mathrm{H}_{30} \mathrm{O}\).

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Most popular questions from this chapter

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