Question

The Boltzmann constant is the gas constant (R) divided by _____

Short answer

Avogadro's number.

Step-by-step solution

Identify the Question

The exercise asks to identify what the gas constant (R) is divided by to obtain the Boltzmann constant.

Recall Definition

Recall that the Boltzmann constant, denoted by \( k \), is defined as the gas constant \( R \) divided by Avogadro's number \( N_A \). Mathematically, this is expressed as: \( k = \frac{R}{N_A} \).

State Avogadro's Number

Avogadro's number, denoted \( N_A \), is approximately \( 6.022 \times 10^{23} \text{ mol}^{-1} \). This is the number of atoms or molecules in one mole of a substance.

Fill in the Blank

Therefore, the Boltzmann constant is the gas constant \( R \) divided by Avogadro's number \( N_A \).

Key concepts

Gas Constant

The gas constant, often represented as \( R \), is a fundamental constant in chemistry that relates energy scales in various physical and chemical processes. It is vital for understanding the behavior of gases and is used in the ideal gas law. The ideal gas law is expressed as \( PV = nRT \), where:

• \( P \) represents the pressure of the gas,
• \( V \) is the volume of the gas,
• \( n \) is the amount of substance in moles,
• \( R \) is the gas constant,
• \( T \) is the temperature in Kelvin.

The value of \( R \) is approximately 8.314 J/mol·K. This constant can be used to convert between units of energy when dealing with quantities of gas. It is crucial for linking macroscopic measurements to the microscopic molecular scale, bridging the gap between different scales of measurement.

Avogadro's Number

Avogadro's number, denoted as \( N_A \), is a central concept in chemistry that is key to the mole concept. Named after the scientist Amedeo Avogadro, this number tells us how many atoms or molecules are present in one mole of a substance. Specifically, \( N_A \) is equal to approximately \( 6.022 \times 10^{23} \text{ mol}^{-1} \). This huge number helps chemists to count particles which are way too numerous and tiny to handle individually. Consider a mole of carbon, for instance, which amounts to \( 6.022 \times 10^{23} \) carbon atoms. By understanding Avogadro's number, we can relate the macroscopic amount we work with in the laboratory to the microscopic world of atoms and molecules. This concept allows chemists to standardize measurements and calculations at the particle level, making it an indispensable tool in molecular chemistry and physics.

Mole Concept

The mole concept is fundamental in chemistry, permeating almost every calculation and standalone chemical process. A mole is a standard method to convey amounts of a chemical substance, offering a bridge from the microscale to the macroscale. When we use the mole concept, we deal with Avogadro's number, \( N_A \), reflecting the number of discrete entities (atoms, molecules, ions) contained in one mole of a substance. For instance:

• 1 mole of water contains \( 6.022 \times 10^{23} \) molecules of \( H_2O \).
• 1 mole of sodium chloride contains \( 6.022 \times 10^{23} \) formula units of \( NaCl \).

The mole concept makes it possible to convert between atoms and molecules and grams easily, aiding in empirical calculations. When combined with the gas constant in the context of the ideal gas law, it further helps in deriving the amount of gas reacting or produced, quality control in manufacturing, and much more. Understanding the mole concept is essential for conducting precise chemical measurements and reactions.