(a) Calculate the number of electrons in a small,...

(a) Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 10.0 g. Silver has 47 electrons per atom, and its molar mass is $107.87 \mathrm{g} / \mathrm{mol}.$ (b) Imagine adding electrons to the pin until the negative charge has the very large value $1.00 \mathrm{mC}$. How many electrons are added for every $10^{9}$ electrons already present?

(a) Calculate the number of electrons in a small, electrically neutral silver pin that has a mass of 10.0 g. Silver has 47 electrons per atom, and its molar mass is $107.87 \mathrm{g} / \mathrm{mol}.$
(b) Imagine adding electrons to the pin until the negative charge has the very large value $1.00 \mathrm{mC}$. How many electrons are added for every $10^{9}$ electrons already present?

Key Concepts

Mole Concept

The mole is a fundamental unit in chemistry that relates a given mass of a substance to a specific number of constituent particles, typically atoms or molecules. It allows one to convert between macroscopic amounts of material and the microscopic scale, making it essential for calculations involving chemical reactions, stoichiometry, and properties of matter.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, represents the number of atoms or molecules contained in one mole of a substance. This constant is key to bridging the gap between the atomic scale and bulk quantities, enabling the conversion of mass or moles into individual particles.

Elementary Charge

The elementary charge is the magnitude of the electric charge carried by a single proton or, with opposite sign, by a single electron. This constant is used to convert between the number of electrons or protons and the total electric charge, making it crucial for problems involving charge quantization and electrostatic calculations.

Dimensional Analysis

Dimensional analysis is a systematic method used to convert units and ensure that mathematical expressions in physics and chemistry are dimensionally consistent. By considering the units throughout calculations, one can accurately relate mass, moles, particles, and charge, ensuring that the final computed quantities are meaningful.

Proportional Reasoning in Charge Calculations

Proportional reasoning in charge calculations involves understanding the relationship between added electrons and the existing number of electrons in a system, often expressed as a ratio. This reasoning is used to scale quantities appropriately, such as determining the relative impact of a given charge addition in comparison to a baseline amount of charge.

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