Mole Calculator

What is a Mole?

A mole is a fundamental unit in chemistry that represents a specific number of particles, typically atoms or molecules. One mole contains exactly 6.02214076 × 10²³ particles, known as Avogadro's number. The mole provides a bridge between the microscopic world of atoms and molecules and the macroscopic world of measurable quantities.

How to Calculate Moles

Calculating moles involves relating the amount of a substance to its mass, volume, or number of particles. The most common calculations involve converting between moles and mass or between moles and volume for gases.

Formulas

The key formulas for mole calculations are:

1. Moles from mass: \[ n = \frac{m}{M} \]
2. Moles from volume of gas (at STP): \[ n = \frac{V}{22.4} \]
3. Moles from number of particles: \[ n = \frac{N}{N_A} \]

Where:

• \(n\) is the number of moles
• \(m\) is the mass in grams
• \(M\) is the molar mass in g/mol
• \(V\) is the volume in liters
• \(N\) is the number of particles
• \(N_A\) is Avogadro's number (6.02214076 × 10²³)

Calculation Steps

Let's calculate the number of moles in 50 grams of NaCl (table salt):

1. Determine the molar mass of NaCl: \[ M_{NaCl} = 22.99 \text{ g/mol (Na)} + 35.45 \text{ g/mol (Cl)} = 58.44 \text{ g/mol} \]
2. Apply the formula for moles from mass: \[ n = \frac{m}{M} = \frac{50 \text{ g}}{58.44 \text{ g/mol}} = 0.856 \text{ mol} \]

Example and Visual Representation

Let's visualize the relationship between moles, mass, and particles for our NaCl example:

This diagram illustrates that:

• 0.856 moles of NaCl has a mass of 50 grams
• 0.856 moles contains 0.856 × 6.02214076 × 10²³ = 5.15 × 10²³ particles (atoms or molecules) of NaCl

Understanding the mole concept allows chemists to bridge the gap between the microscopic and macroscopic worlds, enabling precise calculations in chemical reactions and analysis.