The male sex hormone testosterone contains only C, H, and O and has a mass of 288.2089 amu as de

The male sex hormone testosterone contains only C, H, and O...

The male sex hormone testosterone contains only $\mathrm{C}, \mathrm{H},$ and $\mathrm{O}$ and has a mass of 288.2089 amu as determined by high-resolution mass spectrometry. What is the likely molecular formula of testosterone?

Key Concepts

Elemental Composition Analysis

This concept entails analyzing which elements make up a molecule and in what proportions. When restricted to elements like carbon, hydrogen, and oxygen, it narrows down the possibilities for the molecular formula, especially when combined with accurate mass measurements.

High Resolution Mass Spectrometry

This analytical technique measures molecular masses with great accuracy, allowing chemists to distinguish between formulas that have nearly identical masses. The precise mass obtained is critical for determining the molecular formula of a compound.

Molecular Formula Determination

This process involves using the exact mass and the known atomic masses of elements to deduce the number of each type of atom in a molecule. It often includes setting up equations based on the total mass and the elements present, and iterating candidate formulas until one matches the experimental data.

Transcript

00:01 In this problem, we're going to have to use the given mass in atomic mass units.

00:07 Our given mass was 288 .2089 .m.

00:15 U.

00:15 To determine the molecular formula for testosterone with the chemical formula that's going to involve carbon, hydrogen, oxygen atoms.

00:28 Since this was the only information that was given to us, we're going to have to do sort of a trial and error kind of thing and use some of the knowledge from the book in order to figure this out.

00:38 So from the textbook, we know carbon is going to have an isotopic atomic mass of 12 amu.

00:49 Hydrogen is 1 .0078 amu and oxygen is 15 .9949 .949.

01:04 Amu.

01:06 Since this is an organic compound, it's mostly going to be comprised over carbon atoms.

01:11 So what we can do is we can sit here and we can try to determine the maximum amount of carbon atoms that we're going to have in this molecule.

01:19 So we can take our total mass of 288 and divided by the mass of carbon to see how many total carbon atoms that we could possibly have.

01:33 So 288 .209 divided by 12 is going to give us roughly about 24 carbon atoms to fit in this entire molecule.

01:51 Now this would be if we were strictly only having a molecule of only carbon atoms, but we also have to account for the hydrogen and oxygen atoms.

02:00 And there's most likely going to be hydrogen atoms connected to your carbon atoms.

02:04 So that alone for, i guess, 24 different carbon atoms, you're going to have at least 12 atomic mass units worth of hydrogen atoms.

02:16 So we can kind of guesstimate that we know we're not going to have all carbon atoms.

02:23 And we're going to also have to account for the oxygen, which weighs more than our carbon atoms.

02:28 With this information, we can kind of knock off some of these carbon atoms.

02:31 So accounting for our hydrogen atoms, we can not...

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