Certainly! Let's explore the concept step by step:
### Understanding the Concept of a Mole and Avogadro's Number
1. Mole (mol): In chemistry, a mole is a fundamental unit used to measure the amount of a substance. It is one of the seven base units in the International System of Units (SI).
2. Avogadro's Number: This is a constant that defines the number of particles (such as atoms, molecules, or ions) in one mole of a substance. It is named after the Italian scientist Amedeo Avogadro. Avogadro's number is [tex]\( 6.0221 \times 10^{23} \)[/tex].
### Step-by-Step Solution
1. Understanding the Problem:
- We are given that one mole of any element contains [tex]\( 6.0221 \times 10^{23} \)[/tex] particles (atoms, molecules, ions, etc.).
2. Given Information:
- Avogadro's number, [tex]\( N_A \)[/tex], is [tex]\( 6.0221 \times 10^{23} \)[/tex].
3. Interpretation:
- When we talk about one mole, we are referring to a quantity that contains exactly [tex]\( 6.0221 \times 10^{23} \)[/tex] particles. This number is extremely large and is useful in converting between atomic scale measurements and macroscopic quantities.
4. Representation:
- The scientific notation [tex]\( 6.0221 \times 10^{23} \)[/tex] means the number 6.0221 multiplied by [tex]\( 10 \)[/tex] raised to the power of 23.
### Expressing the Result
- The numerical result of [tex]\( 6.0221 \times 10^{23} \)[/tex] is [tex]\( 6.022099999999999 \times 10^{23} \)[/tex] when calculated with precision. This value is often rounded to significant figures depending on the context.
To summarize:
- One mole of any element contains [tex]\( 6.0221 \times 10^{23} \)[/tex] particles.
This is a critical concept in chemistry that helps bridge the atomic scale and the macroscopic world, allowing for the calculation of quantities in a manageable way. This precise value enables scientists to make accurate predictions and measurements in chemical reactions and phenomena.
