Question

The meat from one hazelnut has a mass of \(0.985 \mathrm{~g}\). (a) What is the mass of a millionth of a mole \(\left(10^{-6}\right)\) of hazelnut meats? (A millionth of a mole is also called a micromole.) (b) How many moles are in a pound of hazelnut meats?

Short answer

(b) How many moles of hazelnut meats are in a pound of hazelnuts? Answer: (a) To find the mass of a micromole of hazelnut meats, first calculate the mass of one mole by multiplying the mass of one hazelnut (0.985g) by the number of entities in a mole (6.022 x 10^23). Then, divide the mass of one mole by 10^6 to find the mass of one micromole. (b) To find the number of moles in a pound of hazelnut meats, first convert the mass of one pound to grams using the conversion factor (1 lb = 453.592g). Then, divide the mass of hazelnut meats in grams by the mass of one mole calculated in part (a) to find the number of moles.

Step-by-step solution

Calculate the mass of one mole of hazelnut meats

First, we need to find the mass of one mole of hazelnut meats. We know that one hazelnut has a mass of \(0.985 \mathrm{~g}\). Since there are \(6.022 \times 10^{23}\) entities (in this case, hazelnuts) in one mole, we can calculate the mass of one mole by multiplying the mass of one hazelnut by the number of entities in a mole: Mass of one mole = Mass of one hazelnut × Number of entities in a mole

Calculate the mass of a micromole of hazelnut meats

Since a micromole is a millionth of a mole, we need to divide the mass of one mole calculated in Step 1 by one million to find the mass of a micromole: Mass of one micromole = Mass of one mole / \(10^{6}\)

Convert the mass of a pound of hazelnut meats to grams

In part (b), we are given the mass of a pound of hazelnut meats and asked to find the number of moles in it. To do this, we first need to convert the mass from pounds to grams. We know that \(1 \mathrm{~lb} = 453.592 \mathrm{~g}\), so we can convert the mass of one pound of hazelnut meats to grams using the following equation: Mass in grams = Mass in pounds × Conversion factor

Calculate the number of moles in a pound of hazelnut meats

Now that we have the mass of a pound of hazelnut meats in grams, we can calculate the number of moles by dividing this mass by the mass of one mole of hazelnut meats calculated in Step 1: Number of moles = Mass of hazelnut meats in grams / Mass of one mole

Key concepts

Molar Mass

Understanding the concept of molar mass is fundamental in the world of chemistry. It refers to the mass of one mole of a given substance and is typically expressed in grams per mole (g/mol). The molar mass serves as a bridge between the microscopic world of atoms and molecules and the macroscopic world of grams and kilograms that we can measure.

To calculate the molar mass, you need to know the atomic or molecular mass of the substance and then simply scale it up using Avogadro's number. For instance, if the atomic mass of carbon is approximately 12 u (unified atomic mass units), then the molar mass of carbon would be approximately 12 g/mol, because one mole of carbon atoms contains Avogadro's number of atoms, which collectively weigh 12 grams.

Having a firm grasp on how molar mass is determined allows students to tackle problems like the textbook example, requiring the mass of one mole of hazelnut meats to be inferred. The solution begins with identifying the mass of a single hazelnut and then using molar mass as a multiplier to find the total mass of a mole of hazelnuts.

Avogadro's Number

Another pillar in stoichiometry calculations is Avogadro's number (\(6.022 \times 10^{23}\)), which is the number of constituent particles, usually atoms or molecules, that are contained in one mole of a substance. This constant provides a direct link between the atomic scale and the macro scale. It allows chemists and students alike to work with moles, providing a convenient way to talk about very large numbers of tiny entities.

For example, in the hazelnut problem, Avogadro's number is implicitly used when we talk about converting the mass of one hazelnut into the mass of a mole of hazelnuts. The exercise's step-by-step solution employs Avogadro’s number to scale up the mass of a single hazelnut to determine the mass of one mole, demonstrating the practical application of this fundamental constant.

Unit Conversion

Unit conversion is a basic skill in not just chemistry, but in all scientific disciplines. It is the process of converting one unit of measurement to another to facilitate better understanding or calculation. This is critical because measurements can be expressed in numerous units, and it is often necessary to convert these measurements to perform calculations effectively.

In the context of the hazelnut problem, unit conversion is essential in part (b) of the exercise, where the mass given in pounds needed to be converted to grams. Understanding the conversion factor (\(1 \text{ lb} = 453.592 \text{ g}\)) is key here. After converting to grams, students can then use the concept of molar mass to find how many moles of hazelnut meats are present in a pound.

This kind of problem not only tests students' understanding of the concepts but also their ability to apply multiple steps and concepts to reach a solution. Always remember to use precise conversion factors and to keep track of units throughout the calculation to avoid errors.