Problem 5 - Chemistry A Guided Inquiry

Question

a) What number of legs is found in one mole of elephants? b) How many moles of legs are found in one mole of elephants?

Step-by-Step Solution

Answer

a) There are approximately \(2.408 \times 10^{24}\) legs in one mole of elephants. b) There are 4 moles of legs in one mole of elephants.

Step 1: Understanding the concept of a mole and Avogadro's number

Know that a mole is simply a unit of measurement, much like saying a dozen eggs. When you say a dozen, you mean 12. Similarly, when you say a mole, it means you have \(6.02 \times 10^{23}\) of something, according to Avogadro's number.

Step 2: Determining the number of legs in one elephant

Remember that an elephant has 4 legs.

Step 3: Calculate the number of legs in one mole of elephants (part a)

Multiply the number of legs per elephant by Avogadro's number. For one elephant: \(4 \,legs/elephant \times 1 mole/elephant \times 6.02 \times 10^{23} elephants/mole = 2.408 \times 10^{24} legs\).

Step 4: Calculate the number of moles of legs in one mole of elephants (part b)

Knowing that each mole corresponds to Avogadro's number of items, and one mole of elephants, which is \(6.02 \times 10^{23}\) elephants, has 4 legs each, we have 4 moles of legs in one mole of elephants.

Key Concepts

Avogadro's Number

When delving into the realm of chemistry, you'll often encounter the term Avogadro's number. This fundamental constant, named after the scientist Amedeo Avogadro, is crucial for understanding matter at the molecular level.

Avogadro's number, designated as \(6.02 \times 10^{23}\), represents the quantity of entities (atoms, molecules, ions, or other particles) in one mole of a substance. Just as a dozen refers to 12 of anything, a mole signifies this incredibly large number of particles, establishing a bridge between the microscopic world of atoms and the macroscopic world we interact with every day.

Whether dealing with giant creatures like elephants or tiny atoms, Avogadro's number provides a basis for quantification. Understanding this concept allows us to perform calculations related to the amount of substance present in a sample, whether we are counting elephant legs or hydrogen atoms.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It serves as the mathematical backbone of chemistry, enabling chemists to predict the outcomes of reactions, measure reactant proportions, and calculate product yields.

In the context of molar calculations, stoichiometry plays a pivotal role. It ensures that chemical equations are balanced, meaning the number of atoms for each element is the same on both sides of the reaction. The coefficients in a balanced equation indicate the ratio of moles that react and are produced, conforming to the law of conservation of mass.

Basic Principles of Stoichiometry

Understanding stoichiometry involves familiarity with concepts like molar ratios, limiting reactants, and theoretical yield. These principles guide us in converting from moles to grams, liters to moles for gases at standard conditions, and atoms to moles using Avogadro's number.

Molar Calculations

Molar calculations are an essential tool in the chemist's toolkit, allowing for the conversion between mass, volume, and number of particles. They rely heavily on the mole concept and Avogadro's number, as well as the molar mass (the mass of one mole) of substances.

For instance, to find out the amount of a substance needed or produced, a chemist would use molar mass to convert grams to moles, measure the volume of a gas at standard conditions to determine moles, or utilize Avogadro's number to relate moles to discrete particles.

Applying Molar Calculations

When you consider a mole of elephants in practice, as our exercise suggests, we're not counting actual elephants but rather using the concept to carry out molar calculations. In our whimsical example, counting legs becomes a straightforward procedure: number of legs per elephant multiplied by Avogadro's number (for one mole), connecting the concept of moles directly to measurable quantities.