Problem 88 - Chemistry: Principles and Reactions

Question

Perhaps the simplest way to calculate Avogadro's number is to compare the charge on the electron, first determined by Robert Millikan in 1909, with the charge on a mole of electrons, determined electrochemically (Chapter 18). These charges, in coulombs (C), are given in Appendix 1 . Use them to calculate Avogadro's number to five significant figures.

Step-by-Step Solution

Answer

Answer: Avogadro's number is approximately 6.0221 x 10^23.

Step 1: Find the charge on an electron

According to the question, the charge on an electron (e) has been determined by Robert Millikan in 1909. Check Appendix 1 to find the value of the charge on an electron, which is approximately -1.602 \times 10^{-19} C.

Step 2: Find the charge on a mole of electrons

The question also states that the charge on a mole of electrons has been determined electrochemically. Check Appendix 1 to find the value of the charge on a mole of electrons, which is approximately 96485 C.

Step 3: Calculate Avogadro's number

Now that we have the charge on an electron (e) and the charge on a mole of electrons (Q), we can calculate Avogadro's number (N_A) using the formula: N_A = \frac{Q}{e} Substitute the values of Q and e into the equation: N_A = \frac{96485\:C}{-1.602 \times 10^{-19}\:C} Note that we do not need to consider the negative sign as both charges are negative and the result should be a posititve value. Calculating the result gives: N_A \approx 6.022 \times 10^{23} To five significant figures, the value of Avogadro's number is 6.0221 \times 10^{23}. So, the final result is:

Step 4: Write down the final result

Avogadro's number, to five significant figures, is approximately 6.0221 \times 10^{23}.

Key Concepts

Millikan's Experiment

Imagine being able to measure the tiniest of charges—the charge of a single electron! That's exactly what Robert Millikan accomplished back in 1909 with his famous oil drop experiment. This experiment was groundbreaking because it provided the first accurate measurement of the electron charge, laying the cornerstone for modern physics and chemistry.

• In this experiment, Millikan observed tiny oil droplets between two electrically charged plates.
• By adjusting the voltage across the plates, he could balance the gravitational force and the electric force on the droplets, thereby calculating the electron charge.
• The value he determined was approximately \(-1.602 \times 10^{-19}\) coulombs.

This experiment not only offered a precise value for the electron charge but also supported the idea that electric charge is quantized, meaning it exists in discrete "packets." Understanding Millikan’s work helps us delve into the fundamental properties of particles, highlighting the significance of precise measurements in scientific progress.

Electron Charge

The electron charge is one of the fundamental constants of physics. It's a very small but crucial value, determining how individual electrons interact with their environment.

• The established charge of an electron today is \(-1.602 \times 10^{-19}\) coulombs.
• This negative charge signifies that electrons are attracted to positively charged particles and repelled by other negatively charged ones.

This property of electrons is foundational for electromagnetism, one of the four fundamental forces in nature. Electrons move freely in conductors such as metals, which allows the flow of electric charge, or electricity, to happen. When we talk about electron charge in terms of real-world applications, we refer to the movement of these tiny particles as electric current, crucial for powering everything from small gadgets to large industrial machines.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and the macroscopic world we observe daily. A mole is a unit that measures the amount of substance. One mole consists of exactly \(6.0221 \times 10^{23}\) entities of a substance, be they atoms, molecules, or ions. This number is known as Avogadro's number.

• The mole allows chemists to count particles by weighing them, connecting chemistry with mass measurements directly.
• It helps convert a measured mass of an element or compound into the number of atoms, ions, or molecules it contains.

Understanding the mole concept is essential for balancing chemical equations and predicting the yields of reactions. It simplifies calculations by providing a universal standard, enabling scientists to communicate findings and calculations globally without confusion.

Electrochemistry

Electrochemistry is the study of the interaction between electricity and chemical reactions. This fascinating field explores how chemical energy is converted into electrical energy and vice versa.

• It includes processes like electrolysis, where electrical energy drives chemical reactions.
• Another critical aspect is the study of galvanic cells, where chemical reactions produce electrical energy.
• This is foundational for technologies like batteries, fuel cells, and electroplating.

In electrochemical reactions, electrons are transferred between substances. The charge transfer often involves whole moles of electrons, which is why understanding the charge of a mole of electrons in experiments like calculating Avogadro's number is vital. For example, 1 mole of electrons carries a charge of \(96485\) coulombs, a concept derived from principles of electrochemistry, highlighting its importance in both theoretical and practical applications.