Question

Estradiol is a female sexual hormone that is responsible for the maturation and maintenance of the female reproductive system. Elemental analysis of estradiol gives the following mass percent composition: \(\mathrm{C} 79.37 \%, \mathrm{H} 8.88 \%, \mathrm{O} 11.75 \% .\) The molar mass of estradiol is \(272.37 \mathrm{~g} / \mathrm{mol}\). Find the molecular formula of estradiol.

Short answer

Using elemental mass percent and molar mass, we calculate moles per element, derive the empirical formula, and scale to the molecular formula, resulting in C18H24O2 as the molecular formula for estradiol.

Step-by-step solution

Calculate the mass of each element per mole of substance

Use the mass percent composition to calculate the mass of each element in one mole of the substance. For example, if estradiol has a molar mass of 272.37 g/mol, then for carbon (C) the mass per mole is 79.37% of 272.37 g/mol which equals 216.29 g of carbon per mole of estradiol.

Determine moles of each element in one mole of the compound

Calculate the moles of each element by dividing the mass of each element per mole of estradiol by the atomic mass of the element. For carbon (C), which has an atomic mass of approximately 12.01 g/mol, this would be 216.29 g / 12.01 g/mol which equals 18.01 moles of carbon. Repeat the calculation for hydrogen (H) and oxygen (O).

Find the simplest whole number ratio

Divide the number of moles of each element by the smallest number of moles calculated in step 2 to get the simplest whole number ratio. If any of the ratios are not whole numbers, they should be multiplied by a suitable factor to convert all ratios to whole numbers.

Write the empirical formula

Using the simplest whole number ratio obtained in step 3, write the empirical formula by assigning these ratios as subscripts to the respective elements.

Determine the molecular formula from the empirical formula

Determine the molar mass of the empirical formula and compare it with the given molar mass of estradiol (272.37 g/mol). If necessary, multiply the empirical formula by an integer to match the molar mass of estradiol and obtain the molecular formula.

Key concepts

Empirical Formula Calculation

Understanding how to calculate the empirical formula of a compound is essential in chemistry. It represents the simplest ratio of elements within a molecule. To obtain the empirical formula of estradiol, a pivotal step involves using the mass percent composition to find out how much of each element is present in one mole of the substance. This involves simple arithmetic calculations, starting with finding the mass of each element in a mole of estradiol based on the given percentages. For estradiol, with a molar mass of 272.37 g/mol, the calculation shows that for Carbon (C) with 79.37%, the mass per mole is 216.29 g.

Next, the number of moles of each element is determined by dividing this mass by the atomic mass of the respective element. Once moles are determined, these are converted into the simplest whole number ratio. This process may require multiplying these ratios by an integer to ensure that all are whole numbers. The result is the empirical formula, which for estradiol provides the foundation to find the molecular formula, giving deeper insights into the structure of the hormone.

Mass Percent Composition

The mass percent composition is a key concept that tells us how much mass of each element is present in a compound, as a percentage of the total mass. It is crucial for determining the empirical and molecular formulas as it sets the stage for all subsequent calculations. In the example of estradiol, the mass percent composition is given for carbon, hydrogen, and oxygen. To make these percentages actionable, they are applied to the molar mass of the compound, providing the mass of each element per mole. For instance, with estradiol’s molar mass at 272.37 g/mol, calculating these percentages gives us the exact mass of C, H, and O in a mole.

This is not only a foundational step in calculating the empirical formula but also extremely useful in various analytical methods in chemistry where understanding composition is vital.

Moles and Molar Mass

The mole is a fundamental unit in chemistry that signifies a specific number of particles, and molar mass is the mass of one mole of a substance. These concepts are intertwined in determining the composition of compounds. In the estradiol calculation, once the mass of each element in a mole is established, these values are divided by the atomic masses to find the number of moles of each element.

For example, the atomic mass of carbon is about 12.01 g/mol; dividing the mass of carbon in a mole of estradiol by this gives the moles of carbon present. It is a crucial step because moles provide a way to compare different elements in their pure ratio, which in turn is the foundation for deducing the empirical formula of the compound.

Elemental Analysis in Chemistry

Elemental analysis in chemistry involves identifying and quantifying the elemental make-up of a substance. In the context of estradiol, this step was crucial to ascertain the mass percent composition. Modern techniques such as combustion analysis, mass spectrometry, or X-ray fluorescence could be used to perform such an analysis with high accuracy. Once the percentages are acquired, they are converted into a more usable form - the numbers of moles of each element in the compound.

This information allows for the determination of the empirical formula, reflecting the proportion of elements in the compound. For educational pursuits, such analysis teaches students the importance of precision and the interconnectedness of different chemical concepts, leading to a comprehensive understanding of the substance in question.