Question

What is the molecular weight of cholesterol if \(0.5731 \mathrm{~mol}\) weighs \(221.6 \mathrm{~g}\) ?

Short answer

The molecular weight of cholesterol is approximately 386.55 g/mol.

Step-by-step solution

Understand the Relationship

To solve this problem, we need to calculate the molecular weight of cholesterol, which is given by the formula: \(M = \frac{m}{n}\) where \(M\) is the molecular weight, \(m\) is the mass of the sample in grams, and \(n\) is the number of moles of the sample.

Identify the Known Variables

From the problem, we are given \(m = 221.6 \text{ g}\) and \(n = 0.5731 \text{ mol}\). We need to substitute these values into our formula to find the molecular weight.

Substitute and Solve

Using the formula \(M = \frac{m}{n}\), substitute \(m = 221.6\) and \(n = 0.5731\): \[M = \frac{221.6}{0.5731}\] Calculate the value to find the molecular weight.

Perform Calculation

Perform the division: \[M = \frac{221.6}{0.5731} \approx 386.55\] Therefore, the molecular weight of cholesterol is approximately \(386.55 \text{ g/mol}\).

Key concepts

Understanding Cholesterol

Cholesterol is a vital molecule in the body. It’s a type of lipid, which means it belongs to the fat family. This particular molecule is essential for building cell membranes and making hormones. - Cholesterol performs many vital tasks in the body: - Helps in the production of vitamin D. - Assists in forming certain hormones like estrogen and testosterone. - Aids in the digestion process via bile production. Despite its vital roles, too much cholesterol can lead to health problems such as heart disease. Therefore, understanding its structure and molecular weight can help in therapeutic designs and interventions. In the context of chemistry, molecular weight is a crucial factor in understanding how cholesterol behaves in biological systems.

The Concept of Moles

When chemists talk about moles, they are referring to a unit that measures quantity at an atomic scale. The concept of moles is central to chemistry, as it helps to connect the macro world with the micro world. Simply put, a mole allows us to count atoms or molecules. It is a number, just like a dozen, but instead of 12, it’s approximately 6.022 x 10^{23}, known as Avogadro's number. This handy tool lets chemists "macroscopically" quantify substances because working with individual molecules is impractical. In the original exercise, you used moles to connect the mass of cholesterol to its molecular formula. By knowing the amount of substance in moles, we can relate it directly to grams and calculate properties such as molecular weight.

Calculating Mass in Grams

Mass in grams is a straightforward concept in chemistry. It is the weight of a substance expressed in grams. In the exercise example, 221.6 grams is the mass of cholesterol equivalent to 0.5731 moles.- To calculate molecular weight using mass: - You take the mass of your sample in grams. - Use the formula: \( M = \frac{m}{n} \) where: - \( M \) is the molecular weight. - \( m \) is the mass of the sample. - \( n \) is the number of moles.By doing this, you can find the molecular weight, which helps us understand how heavy a molecule is in comparison to another.In chemical calculations, accurately measuring the mass in grams is important to ensure the formula yields precise results for tasks involving chemical reactions and formulations. The example exercise demonstrated this well by dividing the mass by moles to find cholesterol's molecular weight.